Download Wydown Middle School Summer Math Student Work Packet

Wydown Middle School
Summer Math Student Work Packet
For students entering 8th grade Mathematics
In order to prepare our middle school students for success with higher
standards, it is important that we provide support. This summer work packet
is being supplied to all students currently finishing the 7th grade
mathematics curriculum to ease the transition to 8th grade. The packet
includes practice problems and answer keys.
Students should write everything directly in the packet. If there isn’t enough
room provided for the math, please use additional paper and attach it. We
suggest the pace of two to three sheets per week. The use of calculators
should be discouraged.
If you misplace the packet, you can download another copy on the
Wydown website.
http://www.clayton.k12.mo.us/site/Default.aspx?PageID=3457
Students should bring the completed packet to school on the 1st day of
classes, Wednesday, August 15th, 2012 and turn it into his/her new
math teacher.
Student’s Name: _________________________
Current math teacher: _____________________
Date Completed: _________________________
Parent signature: _________________________
Highly Suggested Problems Sets for
Students Going Into Eighth Grade
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___ 27.
Rounding Numbers (#1-12)
Fractions and Decimals (#1-24 odds)
Fractions, Decimals, and Percents (#1-33 odd)
Adding/Subtracting Integers (#21-30)
Adding/Subtracting Decimals (#21-30)
Adding/Subtracting Fractions and Mixed Numbers
(#12-20)
Dividing Integers (#1-24)
Multiplying Integers (#1-24)
Multiplying Decimals (#5-10)
Multiplying/Dividing Fractions and Mixed Numbers
(#2-20 evens)
Order of Operations (#13-24)
Evaluating Variable Expressions (#13-20)
Proportions (#1-12)
Similar Figures (#2-22 even)
Multistep Equations (#1-12)
One-Step Equation Word Problems (#1-14)
Naming Decimal Places (#1-24)
Divisibility and Factors (#1-25 odd)
Factors and Factorization (#1-16)
Greatest Common Factor (#1-3, 7-9)
Least Common Multiple (#1-10)
Simplifying Variable Expressions (#2-22 even)
The Distributive Property (#2-16 even)
Angle Sum of Triangles and Quadrilaterals (#1-19 odd)
Area of Triangles (#1-13 odd)
Areas of Squares, Rectangles, and Parallelograms
(#2-14 even)
Circles (#2-20 even)
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Rounding Numbers
Date________________ Period____
Round each to the place indicated.
1) 8,632,051
2) 25,952,938
3) 803,119
4) 73,693
5) 2,461,612,242
6) 789,132,377
7) 9,885,659,260; billions
8) 2,628,259; thousands
9) 347,168; ten thousands
10) 9,727,322,054; billions
11) 1,399,179; thousands
12) 271,156,694; millions
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-1-
Worksheet by Kuta Software LLC
13) 44.5443495
14) 5.3373959
15) 8.7495980
16) 74.91
17) 0.72091
18) 23.0368
19) 9.3113; thousandths
20) 6.9788; tenths
21) 6.3761; tenths
22) 1.7354948; hundred-thousandths
23) 1.495485; thousandths
24) 8.121; hundredths
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Rounding Numbers
Date________________ Period____
Round each to the place indicated.
1) 8,632,051
2) 25,952,938
9,000,000
3) 803,119
26,000,000
4) 73,693
803,100
70,000
5) 2,461,612,242
6) 789,132,377
2,000,000,000
7) 9,885,659,260; billions
800,000,000
8) 2,628,259; thousands
10,000,000,000
9) 347,168; ten thousands
2,628,000
10) 9,727,322,054; billions
350,000
11) 1,399,179; thousands
10,000,000,000
12) 271,156,694; millions
1,399,000
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271,000,000
-1-
Worksheet by Kuta Software LLC
13) 44.5443495
14) 5.3373959
44.54435
15) 8.7495980
5.33740
16) 74.91
8.74960
74.9
17) 0.72091
18) 23.0368
0.7209
23.037
19) 9.3113; thousandths
20) 6.9788; tenths
9.311
21) 6.3761; tenths
7.0
22) 1.7354948; hundred-thousandths
6.4
23) 1.495485; thousandths
1.73549
24) 8.121; hundredths
1.495
8.12
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Fractions and Decimals
Date________________ Period____
Write each as a decimal. Use repeating decimals when necessary.
1)
1
4
2) 2
3)
5
8
4)
3
5
5)
7
200
6)
8
33
7)
6
11
8)
7
50
9) 4
27
125
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10)
-1-
3
5
7
20
Worksheet by Kuta Software LLC
11)
1
111
12)
1
125
Write each as a fraction.
13) 2.2
14) 1.6
15) 0.08
16) 0.27
17) 1.76
18) 0.15
19) 0.3
20) 0.09
21) 0.7
22) 0.46
23) 0.005
24) 0.4
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Fractions and Decimals
Date________________ Period____
Write each as a decimal. Use repeating decimals when necessary.
1)
1
4
2) 2
0.25
3)
5
8
2.6
4)
0.625
5)
7
200
6
11
6)
27
125
8)
7
50
0.14
10)
4.216
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8
33
0.24
0.54
9) 4
3
5
0.6
0.035
7)
3
5
7
20
0.35
-1-
Worksheet by Kuta Software LLC
11)
1
111
12)
0.009
1
125
0.008
Write each as a fraction.
13) 2.2
2
14) 1.6
1
5
15) 0.08
1
16) 0.27
2
25
17) 1.76
1
27
100
18) 0.15
5
33
19
25
19) 0.3
20) 0.09
1
3
21) 0.7
1
11
22) 0.46
7
9
23) 0.005
3
5
46
99
24) 0.4
1
200
2
5
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Fractions, Decimals, and Percents
Date________________ Period____
Write each as a decimal. Round to the thousandths place.
1) 90%
2) 30%
3) 115.9%
4) 9%
5) 7%
6) 65%
7) 0.3%
8) 445%
Write each as a percent. Round to the nearest tenth of a percent.
9) 0.452
10) 0.006
11) 0.002
12) 0.05
13) 4.78
14) 0.1
15) 3.63
16) 0.03
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-1-
Worksheet by Kuta Software LLC
Write each as a fraction.
17) 25%
18) 70%
19) 93%
20) 58%
21) 50%
22) 66.6%
23) 20%
24) 80%
25) 71%
26) 30%
Write each as a percent. Use repeating decimals when necessary.
27)
1
2
28)
1
8
29)
2
3
30)
1
100
32)
3
8
34)
87
100
31) 2
33)
1
10
1
10
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Fractions, Decimals, and Percents
Date________________ Period____
Write each as a decimal. Round to the thousandths place.
1) 90%
2) 30%
0.9
0.3
3) 115.9%
4) 9%
1.159
5) 7%
0.09
6) 65%
0.07
7) 0.3%
0.65
8) 445%
0.003
4.45
Write each as a percent. Round to the nearest tenth of a percent.
9) 0.452
10) 0.006
45.2%
0.6%
11) 0.002
12) 0.05
0.2%
5%
13) 4.78
14) 0.1
478%
15) 3.63
10%
16) 0.03
363%
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3%
-1-
Worksheet by Kuta Software LLC
Write each as a fraction.
17) 25%
18) 70%
1
4
19) 93%
7
10
20) 58%
93
100
21) 50%
29
50
22) 66.6%
1
2
23) 20%
2
3
24) 80%
1
5
25) 71%
4
5
26) 30%
71
100
3
10
Write each as a percent. Use repeating decimals when necessary.
27)
1
2
28)
50%
29)
2
3
12.5%
30)
66.6%
31) 2
1
10
1
10
1
100
1%
32)
210%
33)
1
8
3
8
37.5%
34)
10%
87
100
87%
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Adding/Subtracting Integers
Date________________ Period____
Find each sum.
1) (−12) + 7
2) (−10) + (−7)
3) (−6) + 12
4) 8 + 7
5) 3 + 4
6) (−45) + 9
7) (−1) + (−46)
8) (−30) + 10
9) (−34) + 50
10) 38 + (−5)
Find each difference.
11) 2 − (−2)
12) (−1) − 10
13) 8 − 7
14) (−8) − (−6)
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-1-
Worksheet by Kuta Software LLC
15) 11 − 4
16) 48 − (−31)
17) 18 − 41
18) (−38) − 30
19) (−1) − (−3)
20) (−1) − (−40)
Evaluate each expression.
21) (−10) − 47
22) (−29) − 29
23) 13 + (−29)
24) 38 + 22
25) (−32) − 44
26) (−12) + (−11)
27) 2 + 15 + 4
28) 16 + (−13) + 5
29) 2 − (−9) − 8
30) 10 + 3 − (−8)
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Adding/Subtracting Integers
Date________________ Period____
Find each sum.
1) (−12) + 7
2) (−10) + (−7)
−5
−17
3) (−6) + 12
4) 8 + 7
6
5) 3 + 4
15
6) (−45) + 9
7
−36
7) (−1) + (−46)
8) (−30) + 10
−47
−20
9) (−34) + 50
10) 38 + (−5)
16
33
Find each difference.
11) 2 − (−2)
12) (−1) − 10
4
−11
13) 8 − 7
14) (−8) − (−6)
1
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−2
-1-
Worksheet by Kuta Software LLC
15) 11 − 4
16) 48 − (−31)
7
17) 18 − 41
79
18) (−38) − 30
−23
19) (−1) − (−3)
−68
20) (−1) − (−40)
2
39
Evaluate each expression.
21) (−10) − 47
22) (−29) − 29
−57
−58
23) 13 + (−29)
24) 38 + 22
−16
60
25) (−32) − 44
26) (−12) + (−11)
−76
27) 2 + 15 + 4
−23
28) 16 + (−13) + 5
21
29) 2 − (−9) − 8
8
30) 10 + 3 − (−8)
3
21
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Adding/Subtracting Decimals
Date________________ Period____
Find each sum.
1) 5.4 + (−9.7)
2) 10.8 + (−4.73)
3) (−0.5) + 0.3
4) (−4.79) + (−0.4)
5) 3.305 + 1.7
6) (−3.6) + 0.43
7) (−4.3) + 14.5
8) (−7.1) + 3.63
9) 13.7 + 3.2
10) (−10.9) + 6.1
Find each difference.
11) 2.2 − 7.3
12) (−8.1) − (−8.9)
13) 2.9 − 9.4
14) (−3.9) − 8.9
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-1-
Worksheet by Kuta Software LLC
15) 9.8 − 7.1
16) (−18.278) − (−6.8)
17) 17.9 − (−19.4)
18) 15.5 − 15.5
19) 1.58 − (−13.6)
20) 1.81 − 17.17
Evaluate each expression.
21) 19.4 + 24.2
22) (−14.8) − (−9.7)
23) (−9.1) + 3.5
24) 0.96 − 8.5
25) 9.5 − (−19.3)
26) 3.4 − (−12.1)
27) 8.7 + 3.8 + 12.3
28) (−13.6) + 12 − (−15.5)
29) 3.4 − 5 − 10.4
30) (−5.6) − (−12.6) + (−6.6)
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Adding/Subtracting Decimals
Date________________ Period____
Find each sum.
1) 5.4 + (−9.7)
2) 10.8 + (−4.73)
−4.3
3) (−0.5) + 0.3
6.07
4) (−4.79) + (−0.4)
−0.2
−5.19
5) 3.305 + 1.7
6) (−3.6) + 0.43
5.005
−3.17
7) (−4.3) + 14.5
8) (−7.1) + 3.63
10.2
9) 13.7 + 3.2
−3.47
10) (−10.9) + 6.1
16.9
−4.8
Find each difference.
11) 2.2 − 7.3
12) (−8.1) − (−8.9)
−5.1
0.8
13) 2.9 − 9.4
14) (−3.9) − 8.9
−6.5
−12.8
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-1-
Worksheet by Kuta Software LLC
15) 9.8 − 7.1
16) (−18.278) − (−6.8)
2.7
17) 17.9 − (−19.4)
−11.478
18) 15.5 − 15.5
37.3
19) 1.58 − (−13.6)
0
20) 1.81 − 17.17
15.18
−15.36
Evaluate each expression.
21) 19.4 + 24.2
22) (−14.8) − (−9.7)
43.6
23) (−9.1) + 3.5
−5.1
24) 0.96 − 8.5
−5.6
25) 9.5 − (−19.3)
−7.54
26) 3.4 − (−12.1)
28.8
27) 8.7 + 3.8 + 12.3
15.5
28) (−13.6) + 12 − (−15.5)
24.8
29) 3.4 − 5 − 10.4
13.9
30) (−5.6) − (−12.6) + (−6.6)
−12
0.4
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Add/Subtracting Fractions and Mixed Numbers
Date________________ Period____
Evaluate each expression.
1)
5
3
−
4
4
2)
3
1
−
2
2
3)
2
4
+
5
5
4)
1
1
−
3
3
6)
1
1
−
2
2
1
1
+
5
5
8)
7
5
−
6
6
( )
10)
5) 6 −
7)
9) −
1
6
7
4
−
8
5
( )
11) −
13)
1
3
+
3
8
( )
9
4
+ −
5
3
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( )
1
5
− −
3
3
( )
12) −
10
1
+
7
6
14) 2 −
-1-
13
8
Worksheet by Kuta Software LLC
15)
( ) ( )
9
5
−
5
8
16) −
( )
17) (−1) + −2
2
5
4
3
− −
3
2
( )
18) −3
( )
20) 1
( )
22) −1
19) 3
6
1
+ −1
7
7
21) 2
1
2
+ −1
3
3
( )
2
4
+ −3
7
7
( )( )
( )( )
24) −2
( )( )
26) −3
23) −1
25) −2
27) 1
7
1
+ −3
8
2
5
1
− −1
6
4
( )
2
3
− −3
5
4
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3
2
−4
5
5
3
3
+ −3
4
4
( )( )
7
1
+ −1
8
2
( )
28) 2
-2-
5
2
−4
8
5
4 5
−
5 8
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Add/Subtracting Fractions and Mixed Numbers
Date________________ Period____
Evaluate each expression.
5
3
−
4
4
1)
2)
1
1
2
2
4
+
5
5
3)
4)
1
6
5) 6 −
6)
1
1
+
5
5
8)
2
5
7
4
−
8
5
10)
1
3
+
3
8
( )
12) −
1
24
13)
( )
1
5
− −
3
3
2
67
40
( )
11) −
7
5
−
6
6
1
3
( )
−
1
1
−
2
2
0
35
6
9) −
1
1
−
3
3
0
6
5
7)
3
1
−
2
2
−
( )
9
4
+ −
5
3
53
42
14) 2 −
7
15
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10
1
+
7
6
13
8
3
8
-1-
Worksheet by Kuta Software LLC
15)
( ) ( )
9
5
−
5
8
16) −
47
40
1
6
( )
17) (−1) + −2
−3
19) 3
21) 2
2
5
( )
18) −3
( )
20) 1
5
7
( )
−5
( )( )
−5
7
1
+ −3
8
2
−4
−1
5
1
− −1
6
4
( )
5
1
2
7
1
+ −1
8
2
3
8
( )
26) −3
7
12
2
3
− −3
5
4
3
3
+ −3
4
4
( )( )
24) −2
3
8
( )( )
25) −2
2
7
( )( )
22) −1
2
3
27) 1
( )
2
4
+ −3
7
7
−2
1
2
+ −1
3
3
23) −1
3
2
−4
5
5
−8
2
5
6
1
+ −1
7
7
2
4
3
− −
3
2
−8
28) 2
3
20
5
2
−4
8
5
1
40
4 5
−
5 8
2
7
40
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Dividing Integers
Date________________ Period____
Find each quotient.
1) 35 ÷ −5
2) −8 ÷ 4
3) −24 ÷ 4
4) −8 ÷ −2
5) 8 ÷ 4
6) −24 ÷ 8
7) −21 ÷ 7
8) 6 ÷ −6
9) −132 ÷ −11
10) −60 ÷ −15
11) −52 ÷ −4
12) 60 ÷ 12
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-1-
Worksheet by Kuta Software LLC
13) 6 ÷ −1
14) 75 ÷ 15
15) 65 ÷ −13
16) 12 ÷ 4
17) −168 ÷ −12
18) −8 ÷ 2
19)
−105
7
20)
−4
−1
21)
−10
−2
22)
−144
12
23)
24
−12
24)
60
−15
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Dividing Integers
Date________________ Period____
Find each quotient.
1) 35 ÷ −5
2) −8 ÷ 4
−7
3) −24 ÷ 4
−2
4) −8 ÷ −2
−6
5) 8 ÷ 4
4
6) −24 ÷ 8
2
7) −21 ÷ 7
−3
8) 6 ÷ −6
−3
9) −132 ÷ −11
−1
10) −60 ÷ −15
12
4
11) −52 ÷ −4
12) 60 ÷ 12
13
5
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-1-
Worksheet by Kuta Software LLC
13) 6 ÷ −1
14) 75 ÷ 15
−6
5
15) 65 ÷ −13
16) 12 ÷ 4
−5
3
17) −168 ÷ −12
18) −8 ÷ 2
14
19)
−105
7
−4
20)
−15
21)
−10
−2
4
22)
5
23)
24
−12
−4
−1
−144
12
−12
24)
−2
60
−15
−4
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multiplying Integers
Date________________ Period____
Find each product.
1) 6 × −4
2) 4 × 2
3) 3 × −4
4) −6 × 4
5) 5 × −4
6) −3 × 4
7) −5 × 6
8) −2 × −1
9) −8 × −2
10) 11 × 12
11) −7 × 5
12) 9 × −6
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-1-
Worksheet by Kuta Software LLC
13) 10 × 5
14) 9 × 2
15) −12 × 7
16) 8 × −12
17) 9 × 10 × 6
18) −6 × −10 × −8
19) 7 × 9 × 7
20) 6 × 6 × −2
21) −5 × −4 × −10
22) 9 × 9 × −5
23) 8 × 3 × 8
24) 7 × 5 × −5
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multiplying Integers
Date________________ Period____
Find each product.
1) 6 × −4
2) 4 × 2
−24
3) 3 × −4
8
4) −6 × 4
−12
5) 5 × −4
−24
6) −3 × 4
−20
7) −5 × 6
−12
8) −2 × −1
−30
9) −8 × −2
2
10) 11 × 12
16
11) −7 × 5
132
12) 9 × −6
−35
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−54
-1-
Worksheet by Kuta Software LLC
13) 10 × 5
14) 9 × 2
50
18
15) −12 × 7
16) 8 × −12
−84
17) 9 × 10 × 6
−96
18) −6 × −10 × −8
540
−480
19) 7 × 9 × 7
20) 6 × 6 × −2
441
−72
21) −5 × −4 × −10
22) 9 × 9 × −5
−200
−405
23) 8 × 3 × 8
24) 7 × 5 × −5
192
−175
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multiplying Decimals
Date________________ Period____
Find each product.
1) −5.5 × −4.87
2) 1.7 × −2.1
3) 0.2 × −1.6
4) 1.7 × −3.1
5) −4.6 × −7.2
6) −5.928 × −11.6
7) −1.5 × −7.1
8) 7.8 × 5.1
9) −7.5 × 9 × −8.3
10) −4.04 × −9 × 3
11) 3.2 × 8.7 × −1.1
12) 8.1 × 8.6 × −5.2
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multiplying Decimals
Date________________ Period____
Find each product.
1) −5.5 × −4.87
26.785
3) 0.2 × −1.6
−0.32
2) 1.7 × −2.1
−3.57
4) 1.7 × −3.1
−5.27
5) −4.6 × −7.2
6) −5.928 × −11.6
33.12
68.7648
7) −1.5 × −7.1
10.65
9) −7.5 × 9 × −8.3
560.25
11) 3.2 × 8.7 × −1.1
−30.624
8) 7.8 × 5.1
39.78
10) −4.04 × −9 × 3
109.08
12) 8.1 × 8.6 × −5.2
−362.232
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multiplying/Dividing Fractions and Mixed Numbers
Date________________ Period____
Find each product.
1) −
3)
5 1
⋅
4 3
4 7
⋅
9 4
5) −2 ⋅
3
7
2)
8 7
⋅
7 10
4) −
2 5
⋅
3 4
6) −2
2
1
⋅4
3
10
1
⋅9
4
7) −2
1
3
⋅ −1
5
4
8) −1
9) −1
5
1
⋅ −2
7
2
10) −2
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-1-
3
1
⋅2
8
2
Worksheet by Kuta Software LLC
Find each quotient.
11)
−1 7
÷
5
4
12)
−1 5
÷
2
4
13)
−3 −10
÷
2
7
14)
1 8
÷
2 7
15)
−9
÷2
5
16) −3
17) −2 ÷ −3
19) 1
4
5
6
3
÷5
7
4
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18)
1
1
÷ −1
3
9
20) −3
-2-
5
÷3
9
7
1
÷2
10
4
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multiplying/Dividing Fractions and Mixed Numbers
Date________________ Period____
Find each product.
1) −
5 1
⋅
4 3
−
3)
2)
5
12
4 7
⋅
9 4
4
5
4) −
7
9
7) −2
3
9) −1
4
2 5
⋅
3 4
−
5) −2 ⋅
−
8 7
⋅
7 10
3
7
6) −2
6
7
1
3
⋅ −1
5
4
8) −1
10) −2
1
4
3
1
⋅2
8
2
−5
-1-
14
15
1
⋅9
4
−11
2
7
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2
1
⋅4
3
10
−10
17
20
5
1
⋅ −2
7
2
5
6
15
16
Worksheet by Kuta Software LLC
Find each quotient.
11)
−1 7
÷
5
4
−
13)
12)
4
35
−
−3 −10
÷
2
7
14)
21
20
15)
5
÷3
9
−1
4
5
18)
10
19
19) 1
1 8
÷
2 7
16) −3
9
10
17) −2 ÷ −3
2
5
7
16
−9
÷2
5
−
−1 5
÷
2
4
6
3
÷5
7
4
1
1
÷ −1
3
9
−
1
12
20) −3
52
161
5
27
7
1
÷2
10
4
−1
29
45
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Order of Operations
Date________________ Period____
Evaluate each expression.
1) (30 − 3) ÷ 3
3) 1 + 7
2
2) (21 − 5) ÷ 8
4) 5 × 4 − 8
5) 8 + 6 × 9
6) 3 + 17 × 5
7) 7 + 12 × 11
8) 15 + 40 ÷ 20
9) 20 + 16 − 15
10) 19 − 15 − 3
11) 9 × (3 + 3) ÷ 6
12) (9 + 18 − 3) ÷ 8
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-1-
Worksheet by Kuta Software LLC
13) 9 + 6 ÷ (8 − 2)
14) 4(4 ÷ 2 + 4)
15) 6 + (5 + 8) × 4
16) 6 × 6 − (7 + 5)
17) (9 × 2) ÷ (2 + 1)
18) 2 − (4 + 3 − 6)
19) 7 × 7 − (8 − 2)
20) 9 − 7 − 6 ÷ 6
21) (4 − 1 + 8 ÷ 8) × 5
22) (10 × 2) ÷ (1 + 1)
23) 7 × 9 − 7 − 3 × 5
24) 8 − 1 − (18 − 2) ÷ 8
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Order of Operations
Date________________ Period____
Evaluate each expression.
1) (30 − 3) ÷ 3
2) (21 − 5) ÷ 8
9
3) 1 + 7
2
2
4) 5 × 4 − 8
50
12
5) 8 + 6 × 9
6) 3 + 17 × 5
62
88
7) 7 + 12 × 11
8) 15 + 40 ÷ 20
139
9) 20 + 16 − 15
17
10) 19 − 15 − 3
21
11) 9 × (3 + 3) ÷ 6
1
12) (9 + 18 − 3) ÷ 8
9
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3
-1-
Worksheet by Kuta Software LLC
13) 9 + 6 ÷ (8 − 2)
14) 4(4 ÷ 2 + 4)
10
15) 6 + (5 + 8) × 4
24
16) 6 × 6 − (7 + 5)
58
17) (9 × 2) ÷ (2 + 1)
24
18) 2 − (4 + 3 − 6)
6
19) 7 × 7 − (8 − 2)
1
20) 9 − 7 − 6 ÷ 6
43
21) (4 − 1 + 8 ÷ 8) × 5
1
22) (10 × 2) ÷ (1 + 1)
20
23) 7 × 9 − 7 − 3 × 5
10
24) 8 − 1 − (18 − 2) ÷ 8
41
5
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Evaluating Variable Expressions
Date________________ Period____
Evaluate each using the values given.
1) n 2 − m; use m = 7, and n = 8
2) 8( x − y); use x = 5, and y = 2
3) yx ÷ 2; use x = 7, and y = 2
4) m − n ÷ 4; use m = 5, and n = 8
5) x − y + 6; use x = 6, and y = 1
6) z + x ; use x = 1, and z = 19
7) y + yx; use x = 15, and y = 8
8) q ÷ 6 + p; use p = 10, and q = 12
9) x + 8 − y; use x = 20, and y = 17
10) 15 − (m + p); use m = 3, and p = 10
11) 10 − x + y ÷ 2; use x = 5, and y = 2
12) p − 2 + qp; use p = 7, and q = 4
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3
-1-
Worksheet by Kuta Software LLC
13) zy + 4 y; use y = 5, and z = 2
14) b(a + b) + a; use a = 9, and b = 4
15) p 2 ÷ 4 − m; use m = 3, and p = 4
16) x( y ÷ 3) ; use x = 4, and y = 9
17) 4 + m + n − m; use m = 4, and n = 9
18) qp + q − p; use p = 7, and q = 3
19) mn ÷ 6 + 10; use m = 7, and n = 6
20) h + j ( j − h); use h = 2, and j = 6
2
21) (b − 1) + a 2 ; use a = 6, and b = 1
22) y( x − (9 − 4 y)); use x = 4, and y = 2
23) x − ( x − ( x − y 3 )); use x = 9, and y = 1
24) j (h − 9) 3 + 2; use h = 9, and j = 8
2
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Evaluating Variable Expressions
Date________________ Period____
Evaluate each using the values given.
1) n 2 − m; use m = 7, and n = 8
2) 8( x − y); use x = 5, and y = 2
57
3) yx ÷ 2; use x = 7, and y = 2
24
4) m − n ÷ 4; use m = 5, and n = 8
7
5) x − y + 6; use x = 6, and y = 1
3
3
6) z + x ; use x = 1, and z = 19
11
7) y + yx; use x = 15, and y = 8
20
8) q ÷ 6 + p; use p = 10, and q = 12
128
9) x + 8 − y; use x = 20, and y = 17
12
10) 15 − (m + p); use m = 3, and p = 10
11
11) 10 − x + y ÷ 2; use x = 5, and y = 2
2
12) p − 2 + qp; use p = 7, and q = 4
6
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33
-1-
Worksheet by Kuta Software LLC
13) zy + 4 y; use y = 5, and z = 2
14) b(a + b) + a; use a = 9, and b = 4
30
61
2
15) p ÷ 4 − m; use m = 3, and p = 4
2
16) x( y ÷ 3) ; use x = 4, and y = 9
1
36
17) 4 + m + n − m; use m = 4, and n = 9
18) qp + q − p; use p = 7, and q = 3
13
17
19) mn ÷ 6 + 10; use m = 7, and n = 6
20) h + j ( j − h); use h = 2, and j = 6
17
26
2
21) (b − 1) + a 2 ; use a = 6, and b = 1
22) y( x − (9 − 4 y)); use x = 4, and y = 2
6
36
23) x − ( x − ( x − y 3 )); use x = 9, and y = 1
24) j (h − 9) 3 + 2; use h = 9, and j = 8
8
2
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Proportions
Date________________ Period____
State if each pair of ratios forms a proportion.
1)
4
20
and
2
6
2)
3
18
and
2
8
3)
4
16
and
3
12
4)
4
8
and
3
6
5)
12
3
and
24
4
6)
6
2
and
9
3
Solve each proportion.
7)
10 8
=
k
4
8)
m 10
=
10
3
9)
2 7
=
x 9
10)
3
7
=
x 10
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-1-
Worksheet by Kuta Software LLC
11)
4 2
=
9 x
12)
6 3
=
a 8
13)
8n 8
=
8
3
14)
7 a
=
9 5
15)
p 13
=
8
2
16)
3
v
=
13 3
17)
10 2
=
12 n
18)
11
r
=
10 11
19)
x
7
=
9 14
20)
a
11
=
10 14
21)
v
10
=
12
2
22)
6
5
=
14 n
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Proportions
Date________________ Period____
State if each pair of ratios forms a proportion.
1)
4
20
and
2
6
2)
No
3)
4
16
and
3
12
No
4)
Yes
5)
12
3
and
24
4
3
18
and
2
8
4
8
and
3
6
Yes
6)
No
6
2
and
9
3
Yes
Solve each proportion.
7)
10 8
=
k
4
8)
{5 }
9)
2 7
=
x 9
{33.33}
10)
{2.57}
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m 10
=
10
3
3
7
=
x 10
{4.28}
-1-
Worksheet by Kuta Software LLC
11)
4 2
=
9 x
12)
{4.5}
13)
8n 8
=
8
3
{16}
14)
{2.66}
15)
p 13
=
8
2
10 2
=
12 n
16)
x
7
=
9 14
18)
v
10
=
12
2
11
r
=
10 11
{12.1}
20)
{4.5}
21)
3
v
=
13 3
{0.69}
{2.4}
19)
7 a
=
9 5
{3.88}
{52}
17)
6 3
=
a 8
a
11
=
10 14
{7.85}
22)
{60}
6
5
=
14 n
{11.66}
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Similar Figures
Date________________ Period____
Each pair of figures is similar. Find the missing side.
1)
2)
x
3
9
1
3
12
x
20
3)
4)
4
x
16
8
5
x
4
8
5)
6)
2
6
24
14
1
9
x
x
7)
8)
10
10
99
x
100
9
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10
x
-1-
Worksheet by Kuta Software LLC
9)
10)
5
11
x
x
6
22
16
48
11)
12)
3
2
x
x
20
12
13)
14)
90
14
10
10
56
x
40
36
3
14
60
60
7
4
14
126
x
56
15)
16)
9
12
84
x
54
30
11
x
10
60
12
84
17)
9
18)
90
x
8
3
2
3
12
13
13
130
130
x
90
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-2-
Worksheet by Kuta Software LLC
19)
20)
x
39
13
3
3
13
1
1
x
39
11
44
52
4
21)
22)
91
7
14
1
8
1
x
91
11
7
112
x
112
4
52
23)
14
8
196
12
12
14
168
168
x
24)
21
12
4
3
x
84
91
28
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-3-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Similar Figures
Date________________ Period____
Each pair of figures is similar. Find the missing side.
1)
2)
x
3
9
1
3
12
x
3
20
5
3)
4)
4
x
16
8
5
x
2
4
8
10
5)
6)
2
6
24
14
1
9
x
x
7
36
7)
8)
10
10
99
x
100
9
10
x
110
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100
-1-
Worksheet by Kuta Software LLC
9)
10)
5
11
x
x
6
22
16
48
40
8
11)
12)
3
2
x
x
20
12
60
60
30
12
13)
14)
90
14
10
10
56
x
40
36
3
14
7
4
14
126
x
56
63
12
15)
16)
9
12
84
x
54
30
11
x
10
60
12
5
84
77
17)
9
18)
90
x
8
3
2
3
12
13
13
12
130
130
x
90
9
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-2-
Worksheet by Kuta Software LLC
19)
20)
x
39
13
3
3
13
1
1
x
39
11
44
13
52
4
16
21)
22)
91
7
14
1
8
1
x
91
11
7
112
x
112
4
52
8
143
23)
14
14
196
12
12
14
168
168
x
196
24)
21
12
4
3
x
84
91
28
13
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-3-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multi-Step Equations
Date________________ Period____
Solve each equation.
1) 6a + 5a = −11
2) −6n − 2n = 16
3) 4 x + 6 + 3 = 17
4) 0 = −5n − 2n
5) 6r − 1 + 6r = 11
6) r + 11 + 8r = 29
7) −10 = −14v + 14v
8) −10 p + 9 p = 12
9) 42 = 8m + 13m
10) a − 2 + 3 = −2
11) 18 = 3(3 x − 6)
12) 30 = −5(6n + 6)
©O C2W0l1c1O zKZuGtVaY CSUo6fgtewkaGrPen 5LbLZCU.3 Y NAElolp Pr2iMgahUtwsj 7rXeQsueYrHvjeddM.0 0 OM8afdHeT lwoi1tIhA TIwnRfviYnsi8tReD uPnrReY-7AhlegNeEb0rcab.Q
-1-
Worksheet by Kuta Software LLC
13) 37 = −3 + 5( x + 6)
14) −13 = 5(1 + 4m) − 2m
15) 4(− x + 4) = 12
16) −2 = −(n − 8)
17) −6(1 − 5v) = 54
18) 8 = 8v − 4(v + 8)
19) 10(1 + 3b) = −20
20) −5n − 8(1 + 7n) = −8
21) 8(4k − 4) = −5k − 32
22) −8(−8 x − 6) = −6 x − 22
23) 8(1 + 5 x) + 5 = 13 + 5 x
24) −11 − 5a = 6(5a + 4)
25) −5(4 x − 2) = −2(3 + 6 x)
26) 5(2 x + 6) = −4(−5 − 2 x) + 3 x
©U n210b1G1I 6KNuft7ai 1SSo0fbtowVa8rMeP mLUL9Cd.x q BABlXl4 TrCi5g1hqtmss urOecsMedr7vUeVd8.r v 5MRa4dyeN Ewmidt6hD yIDnmf7iZnViMtyeC ePQrje1-WATlSgvehbCrFat.h
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Multi-Step Equations
Date________________ Period____
Solve each equation.
1) 6a + 5a = −11
2) −6n − 2n = 16
{−1}
3) 4 x + 6 + 3 = 17
{−2}
4) 0 = −5n − 2n
{2 }
5) 6r − 1 + 6r = 11
{0 }
6) r + 11 + 8r = 29
{1 }
7) −10 = −14v + 14v
{2 }
8) −10 p + 9 p = 12
{−12}
No solution.
9) 42 = 8m + 13m
10) a − 2 + 3 = −2
{2 }
11) 18 = 3(3 x − 6)
{−3}
12) 30 = −5(6n + 6)
{4 }
©W 82G0E1U16 IKpuctMa2 DS7oHf3t2weairQeJ CLwLsCr.v T 9AllblZ MrjifgWhpt1s3 Sr5ejsZe5rYvteOde.u V AMkaldMeb Zw8iLtrhs cI7n2f4iBnXiyt3et 4PbrCe6-6AulAgjeqbFrbas.j
{−2}
-1-
Worksheet by Kuta Software LLC
13) 37 = −3 + 5( x + 6)
14) −13 = 5(1 + 4m) − 2m
{2 }
15) 4(− x + 4) = 12
{−1}
16) −2 = −(n − 8)
{1 }
17) −6(1 − 5v) = 54
{10}
18) 8 = 8v − 4(v + 8)
{2 }
19) 10(1 + 3b) = −20
{10}
20) −5n − 8(1 + 7n) = −8
{−1}
21) 8(4k − 4) = −5k − 32
{0 }
22) −8(−8 x − 6) = −6 x − 22
{0 }
23) 8(1 + 5 x) + 5 = 13 + 5 x
{−1}
24) −11 − 5a = 6(5a + 4)
{0 }
25) −5(4 x − 2) = −2(3 + 6 x)
{−1}
26) 5(2 x + 6) = −4(−5 − 2 x) + 3 x
{2 }
{10}
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
One-Step Equation Word Problems
Date________________ Period____
1) Lisa is cooking muffins. The recipe calls for
7 cups of sugar. She has already put in 2
cups. How many more cups does she need
to put in?
2) At a restaurant, Mike and his three friends
decided to divide the bill evenly. If each
person paid $13 then what was the total bill?
3) How many packages of diapers can you buy
with $40 if one package costs $8?
4) Last Friday Trevon had $29. Over the
weekend he received some money for
cleaning the attic. He now has $41. How
much money did he receive?
5) Last week Julia ran 30 miles more than
Pranav. Julia ran 47 miles. How many
miles did Pranav run?
6) How many boxes of envelopes can you buy
with $12 if one box costs $3?
7) Amanda and her best friend found some
money buried in a field. They split the
money evenly, each getting $24.28. How
much money did they find?
8) Jenny wants to buy an MP3 player that costs
$30.98. How much change does she receive
if she gives the cashier $40?
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-1-
Worksheet by Kuta Software LLC
9) Last Friday Adam had $22.33. Over the
weekend he received some money for
cleaning the attic. He now has $32. How
much money did he receive?
10) After paying $5.12 for a salad, Norachai has
$27.10. How much money did he have
before buying the salad?
12) Your mother gave you $13.32 with which to
3
buy a present. This covered of the cost.
5
How much did the present cost?
1
cups of
4
1
sugar. Amy has already put in 3 cups.
9
How many more cups does she need to put
in?
11) A recipe for cookies calls for 3
13) If the weight of a package is multiplied by
the result is 40.5 pounds. Find the weight
of the package.
©w o2V0J1y1e TKXu0tGac ASSo7fEtKwyaIrqes ULYLJC2.o s fA8lelj crHiogzh0tZsq Xrdeys8e3rsvleCdt.d r bMBaWdaeQ 8wiiYtLhS OIZnAfNiZnniEtveN MPXrFej-5AylpgZewbQrIaE.W
5
7
14) A stray dog ate 12 of your muffins. That
3
was
of all of them! With how many did
10
you start?
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
One-Step Equation Word Problems
1) Lisa is cooking muffins. The recipe calls for
7 cups of sugar. She has already put in 2
cups. How many more cups does she need
to put in?
Date________________ Period____
2) At a restaurant, Mike and his three friends
decided to divide the bill evenly. If each
person paid $13 then what was the total bill?
$52
5
3) How many packages of diapers can you buy
with $40 if one package costs $8?
5
4) Last Friday Trevon had $29. Over the
weekend he received some money for
cleaning the attic. He now has $41. How
much money did he receive?
$12
5) Last week Julia ran 30 miles more than
Pranav. Julia ran 47 miles. How many
miles did Pranav run?
6) How many boxes of envelopes can you buy
with $12 if one box costs $3?
4
17
7) Amanda and her best friend found some
money buried in a field. They split the
money evenly, each getting $24.28. How
much money did they find?
8) Jenny wants to buy an MP3 player that costs
$30.98. How much change does she receive
if she gives the cashier $40?
$9.02
$48.56
©1 x2Q0F1A11 pKSuYthaL iSMoUfvt7wgaKrgeh GLpLbCI.T Q eAulylW er7iwggh6tFsf YrGepsqe9rKvde8di.R d IM9aodCeJ Nw6iMtehd AIAnpfoiWnyiytMeH gPBrVe5-BAnlOgWefb6rIaX.A
-1-
Worksheet by Kuta Software LLC
9) Last Friday Adam had $22.33. Over the
weekend he received some money for
cleaning the attic. He now has $32. How
much money did he receive?
10) After paying $5.12 for a salad, Norachai has
$27.10. How much money did he have
before buying the salad?
$32.22
$9.67
12) Your mother gave you $13.32 with which to
3
buy a present. This covered of the cost.
5
How much did the present cost?
1
cups of
4
1
sugar. Amy has already put in 3 cups.
9
How many more cups does she need to put
in?
11) A recipe for cookies calls for 3
$22.20
5
36
13) If the weight of a package is multiplied by
the result is 40.5 pounds. Find the weight
of the package.
5
7
14) A stray dog ate 12 of your muffins. That
3
was
of all of them! With how many did
10
you start?
56.7
40
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Naming Decimal Places
Date________________ Period____
Write the name of each decimal place indicated.
1) 725
2) 7,823
3) 199
4) 11,717,555
5) 9,053,496
6) 709,758,968
7) 105,016
8) 43,105
9) 8.68354
10) 9.6456
11) 1.87605
12) 5.642141
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-1-
Worksheet by Kuta Software LLC
13) 6.49890
14) 7.111
15) 2.74939
16) 5.2432
17) 32.658297
18) 6,721.86
19) 69,042,020
20) 9.69
21) 537,225.88
22) 469,523.77
23) 3,376,483,008
24) 639,606,650
©q v2t0q1y1Z fKEu6t4ab sShoaf2tjwtaeroeo LLvLSCW.W i 5Akllly Ur6iIgvhXtTsH GrYeHsKe6rlvLe7d7.B 2 aMjaOd5eD lwIi4tKhn DIQnVfyiwnFiytkey KP4rIeV-tAxlDgWeEb2rQay.e
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Naming Decimal Places
Date________________ Period____
Write the name of each decimal place indicated.
1) 725
2) 7,823
ones
3) 199
ones
4) 11,717,555
ones
5) 9,053,496
ten thousands
6) 709,758,968
hundreds
7) 105,016
ten thousands
8) 43,105
thousands
9) 8.68354
tens
10) 9.6456
ten-thousandths
11) 1.87605
thousandths
12) 5.642141
hundredths
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ten-thousandths
-1-
Worksheet by Kuta Software LLC
13) 6.49890
14) 7.111
ten-thousandths
15) 2.74939
tenths
16) 5.2432
hundredths
17) 32.658297
tenths
18) 6,721.86
hundred-thousandths
19) 69,042,020
ones
20) 9.69
hundred thousands
21) 537,225.88
tenths
22) 469,523.77
hundreds
23) 3,376,483,008
hundreds
24) 639,606,650
hundred millions
hundred millions
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Divisibility and Factors
Date________________ Period____
State if the first number is divisible by the second number.
1) 60 by 2
2) 49 by 6
3) 92 by 10
4) 72 by 6
5) 66 by 3
6) 72 by 3
7) 684 by 9
8) 555 by 3
9) 608 by 2
10) 767 by 9
11) 708 by 6
12) 780 by 10
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-1-
Worksheet by Kuta Software LLC
Each number is divisible by which of the following: 2, 3, 5, 6, 9, 10?
13) 319
14) 411
15) 455
16) 414
17) 382
18) 256
19) 492
20) 410
21) 297
22) 425
23) 9942
24) 8938
25) 7613
26) 7849
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Divisibility and Factors
Date________________ Period____
State if the first number is divisible by the second number.
1) 60 by 2
2) 49 by 6
Yes
3) 92 by 10
No
4) 72 by 6
No
5) 66 by 3
Yes
6) 72 by 3
Yes
7) 684 by 9
Yes
8) 555 by 3
Yes
9) 608 by 2
Yes
10) 767 by 9
Yes
No
11) 708 by 6
12) 780 by 10
Yes
Yes
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-1-
Worksheet by Kuta Software LLC
Each number is divisible by which of the following: 2, 3, 5, 6, 9, 10?
13) 319
14) 411
None
15) 455
3
16) 414
5
17) 382
2, 3, 6, 9
18) 256
2
19) 492
2
20) 410
2, 3, 6
21) 297
2, 5, 10
22) 425
3, 9
23) 9942
5
24) 8938
2, 3, 6
25) 7613
2
26) 7849
None
None
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Factors and Factorization
Date________________ Period____
List all positive factors of each.
1) 30
2) 22
3) 28
4) 16
5) 60
6) 87
7) 68
8) 99
9) 85
10) 72
11) 96
12) 74
13) 86
14) 75
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-1-
Worksheet by Kuta Software LLC
Write the prime-power factorization of each.
15) 48
16) 35
17) 46
18) 40
19) 100
20) 66
21) 75
22) 72
23) 65
24) 81
25) 80
26) 54
27) 972
28) 660
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Factors and Factorization
Date________________ Period____
List all positive factors of each.
1) 30
2) 22
1, 2, 3, 5, 6, 10, 15, 30
3) 28
1, 2, 11, 22
4) 16
1, 2, 4, 7, 14, 28
5) 60
1, 2, 4, 8, 16
6) 87
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
7) 68
1, 3, 29, 87
8) 99
1, 2, 4, 17, 34, 68
9) 85
1, 3, 9, 11, 33, 99
10) 72
1, 5, 17, 85
11) 96
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
12) 74
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
13) 86
1, 2, 37, 74
14) 75
1, 2, 43, 86
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1, 3, 5, 15, 25, 75
-1-
Worksheet by Kuta Software LLC
Write the prime-power factorization of each.
15) 48
16) 35
4
5⋅7
2 ⋅3
17) 46
18) 40
3
2 ⋅ 23
19) 100
2 ⋅5
20) 66
22 ⋅ 52
21) 75
3⋅5
2 ⋅ 3 ⋅ 11
22) 72
2
23) 65
3
2 ⋅3
24) 81
5 ⋅ 13
25) 80
3
4
26) 54
4
2 ⋅5
27) 972
2
2⋅3
3
28) 660
22 ⋅ 35
2 2 ⋅ 3 ⋅ 5 ⋅ 11
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Greatest Common Factor
Date________________ Period____
Find the GCF of each.
1) 39, 6
2) 24, 28
3) 40, 10
4) 39v, 30uv
5) 35n 2 m, 21m 2 n
6) 30 y 3 , 20 y 2
7) 54, 45
8) 25, 55
9) 68, 34
10) 54, 27
11) 55, 75
12) 66 yx, 30 x 2 y
13) 60 y, 56 x 2
14) 36 xy 3 , 24 y 2
15) 18 y 2 , 54 y 2
16) 80 x 3 , 30 yx 2
17) 105 x, 30 yx, 75 x
18) 140n, 140m 2 , 80m 2
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Greatest Common Factor
Date________________ Period____
Find the GCF of each.
1) 39, 6
3
3) 40, 10
10
5) 35n 2 m, 21m 2 n
2) 24, 28
4
4) 39v, 30uv
3v
6) 30 y 3 , 20 y 2
7nm
10 y 2
7) 54, 45
8) 25, 55
9
9) 68, 34
34
11) 55, 75
5
13) 60 y, 56 x 2
4
15) 18 y 2 , 54 y 2
18 y 2
17) 105 x, 30 yx, 75 x
15 x
5
10) 54, 27
27
12) 66 yx, 30 x 2 y
6 yx
14) 36 xy 3 , 24 y 2
12 y 2
16) 80 x 3 , 30 yx 2
10 x 2
18) 140n, 140m 2 , 80m 2
20
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Least Common Multiple
Date________________ Period____
Find the LCM of each.
1) 10, 3
2) 14, 6
3) 15, 6
4) 15, 20
5) 27, 18
6) 4, 30
7) 24, 32
8) 20, 30
9) 24, 36
10) 35, 25
11) 18 xy 2 , 15 y 3
12) 20 x 3 , 16 x 4
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-1-
Worksheet by Kuta Software LLC
13) 18, 6v
14) 3 x 2 , 10
15) 20 y, 14 y 2
16) 25 x 2 , 25 y
17) 32u 2 , 14v 2
18) 18m 2 , 24nm
19) 16 x 2 y, 32 x
20) 30ab 3 , 20ab 3
21) 30, 25, 10
22) 28, 14, 21
23) 10, 4, 18
24) 10ba, 20ba, 28ba
25) 8 y 2 , 16 xy, 16 y
26) 28b 2 , 20ab 3 , 16b 4
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Least Common Multiple
Date________________ Period____
Find the LCM of each.
1) 10, 3
2) 14, 6
30
42
3) 15, 6
4) 15, 20
30
5) 27, 18
60
6) 4, 30
54
7) 24, 32
60
8) 20, 30
96
9) 24, 36
60
10) 35, 25
72
175
11) 18 xy 2 , 15 y 3
12) 20 x 3 , 16 x 4
90 xy 3
80 x 4
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-1-
Worksheet by Kuta Software LLC
13) 18, 6v
14) 3 x 2 , 10
18v
30 x 2
15) 20 y, 14 y 2
16) 25 x 2 , 25 y
140 y 2
25 x 2 y
17) 32u 2 , 14v 2
18) 18m 2 , 24nm
224u 2 v 2
19) 16 x 2 y, 32 x
72m 2 n
20) 30ab 3 , 20ab 3
32 x 2 y
21) 30, 25, 10
60ab 3
22) 28, 14, 21
150
23) 10, 4, 18
84
24) 10ba, 20ba, 28ba
180
25) 8 y 2 , 16 xy, 16 y
140ba
26) 28b 2 , 20ab 3 , 16b 4
16 y 2 x
560b 4 a
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Simplifying Variable Expressions
Date________________ Period____
Simplify each expression.
1) −3 p + 6 p
2) b − 3 + 6 − 2b
3) 7 x − x
4) 7 p − 10 p
5) −10v + 6v
6) −9r + 10r
7) 9 + 5r − 9r
8) 1 − 3v + 10
9) 5n + 9n
10) 4b + 6 − 4
11) 35n − 1 + 46
12) −33v − 49v
13) 30n + 8n
14) 7 x + 31 x
15) 10 x + 36 − 38 x − 47
16) −2(7 − n) + 4
17) −8(−5b + 7) + 5b
18) −4 p − (1 − 6 p)
19) 4 − 5(−4n + 3)
20) −7(k − 8) + 2k
21) 1 + 7(1 − 3b)
22) 3 − 8(7 − 5n)
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Simplifying Variable Expressions
Date________________ Period____
Simplify each expression.
1) −3 p + 6 p
2) b − 3 + 6 − 2b
3p
−b + 3
3) 7 x − x
4) 7 p − 10 p
6x
−3 p
5) −10v + 6v
6) −9r + 10r
−4v
7) 9 + 5r − 9r
9 − 4r
9) 5n + 9n
14n
11) 35n − 1 + 46
35n + 45
r
8) 1 − 3v + 10
11 − 3v
10) 4b + 6 − 4
4b + 2
12) −33v − 49v
−82v
13) 30n + 8n
14) 7 x + 31 x
38n
38 x
15) 10 x + 36 − 38 x − 47
16) −2(7 − n) + 4
−28 x − 11
−10 + 2n
17) −8(−5b + 7) + 5b
18) −4 p − (1 − 6 p)
45b − 56
2p − 1
19) 4 − 5(−4n + 3)
20) −7(k − 8) + 2k
−11 + 20n
−5k + 56
21) 1 + 7(1 − 3b)
8 − 21b
22) 3 − 8(7 − 5n)
−53 + 40n
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
The Distributive Property
Date________________ Period____
Simplify each expression.
1) 6(1 − 5m)
2) −2(1 − 5v)
3) 3(4 + 3r)
4) 3(6r + 8)
5) 4(8n + 2)
6) −(−2 − n)
7) −6(7k + 11)
8) −3(7n + 1)
9) −6(1 + 11b)
10) −10(a − 5)
11) −3(1 + 2v)
12) −4(3 x + 2)
13) (3 − 7k) ⋅ −2
14) −20(8 x + 20)
15) (7 + 19b) ⋅ −15
16) ( x + 1) ⋅ 14
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
The Distributive Property
Date________________ Period____
Simplify each expression.
1) 6(1 − 5m)
2) −2(1 − 5v)
6 − 30m
−2 + 10v
3) 3(4 + 3r)
12 + 9r
5) 4(8n + 2)
32n + 8
4) 3(6r + 8)
18r + 24
6) −(−2 − n)
2+n
7) −6(7k + 11)
8) −3(7n + 1)
−42k − 66
−21n − 3
9) −6(1 + 11b)
−6 − 66b
11) −3(1 + 2v)
−3 − 6v
13) (3 − 7k) ⋅ −2
−6 + 14k
15) (7 + 19b) ⋅ −15
−105 − 285b
10) −10(a − 5)
−10a + 50
12) −4(3 x + 2)
−12 x − 8
14) −20(8 x + 20)
−160 x − 400
16) ( x + 1) ⋅ 14
14 x + 14
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Angle Sum of Triangles and Quadrilaterals
Date________________ Period____
Find the measure of angle b.
1)
2)
31°
29°
115°
b
33°
b
3)
4)
123°
b
39°
b
34°
119°
5)
6)
45°
75°
75°
b
26°
b
7)
8)
108°
b
103°
97°
81°
72°
b
77°
9)
10)
105°75°
b
86°
109°
71°
b
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-1-
Worksheet by Kuta Software LLC
11)
12)
94°
95°
86°
b
121°
b
59°
72°
Find the value of x.
13)
14)
(4x + 18)°
45°
77°
(7x - 3)°
50°
15)
45°
16)
89°
39°
(5x - 6)°
31°
57°
(11x + 11)°
17)
18)
(2x + 3)°
(5x + 16)°
119°
102°
90°
92°
90°
100°
19)
20)
85°
(5x - 18)°
(x + 37)°
98°
(6x + 22)°
69°
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80°
-2-
100°
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Angle Sum of Triangles and Quadrilaterals
Date________________ Period____
Find the measure of angle b.
1)
2)
31°
29°
115°
b
33°
b
34°
118°
3)
4)
123°
b
39°
b
34°
119°
18°
27°
5)
6)
45°
75°
75°
b
26°
b
109°
30°
7)
8)
108°
b
103°
97°
81°
72°
b
77°
99°
9)
83°
10)
105°75°
b
86°
109°
71°
b
94°
90°
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-1-
Worksheet by Kuta Software LLC
11)
12)
94°
95°
86°
b
121°
b
59°
72°
108°
85°
Find the value of x.
13)
14)
(4x + 18)°
45°
77°
(7x - 3)°
50°
45°
8
18
15)
16)
89°
39°
(5x - 6)°
31°
57°
(11x + 11)°
8
9
17)
18)
(2x + 3)°
(5x + 16)°
119°
102°
90°
92°
90°
100°
29
10
19)
20)
85°
(5x - 18)°
(x + 37)°
98°
(6x + 22)°
69°
21
80°
100°
20
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Area of Triangles
Date________________ Period____
Find the area of each.
1)
2)
1.9 km
4.5 mi
5 km
8 mi
3)
4)
2.8 m
1.5 in
3m
4 in
5)
6)
2.9 m
6.6 yd
5m
7 yd
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Worksheet by Kuta Software LLC
7)
8)
18 cm
14 km
11 km
5 cm
7.4 km
20 km
15.4 cm
9)
10)
14 m
19 km
8m
7m
7.7 km
16 m
11 km
11)
12)
14 m
14 m
18 m
12.1 m
14 m
9.3 m
14 m
12 m
13)
14)
8 ft
16 yd
5.1 ft
6 yd
11 ft
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11 yd
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Area of Triangles
Date________________ Period____
Find the area of each.
1)
2)
1.9 km
4.5 mi
5 km
4.75 km²
8 mi
18 mi²
3)
4)
2.8 m
1.5 in
3m
4 in
3 in²
4.2 m²
5)
6)
2.9 m
6.6 yd
5m
7.25 m²
7 yd
23.1 yd²
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-1-
Worksheet by Kuta Software LLC
7)
8)
18 cm
14 km
11 km
5 cm
7.4 km
20 km
15.4 cm
74 km²
38.5 cm²
9)
10)
14 m
19 km
8m
7m
7.7 km
16 m
11 km
56 m²
42.35 km²
11)
12)
14 m
14 m
18 m
12.1 m
14 m
9.3 m
14 m
12 m
84.7 m²
83.7 m²
13)
14)
8 ft
16 yd
5.1 ft
6 yd
11 ft
11 yd
28.05 ft²
48 yd²
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Area of Squares, Rectangles, and Parallelograms
Date________________ Period____
Find the area of each.
1)
2)
2m
7.7 m
1 in
1 in
3)
4)
6.9 in
6 in
2.4 in
8 in
5)
6)
1.5 yd
4 in
4 yd
5.9 in
7)
8)
6 yd
6m
5.8 m
5m
18.7 yd
5.8 m
18.7 yd
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6m
-1-
Worksheet by Kuta Software LLC
9)
10)
14.9 ft
15.1 ft
7 ft
3m
6.6 m
15.1 ft
14.9 ft
11)
12)
14.2 cm
10.2 cm
20 m
10.2 cm
15.2 m
18.8 m
13)
14)
19 in
18 mi
18 in
18 mi
18 in
18 mi
19 in
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Area of Squares, Rectangles, and Parallelograms
Date________________ Period____
Find the area of each.
1)
2)
2m
7.7 m
1 in
15.4 m²
1 in
1 in²
3)
4)
6.9 in
6 in
2.4 in
8 in
16.56 in²
48 in²
5)
6)
1.5 yd
4 in
4 yd
5.9 in
6 yd²
23.6 in²
7)
8)
6 yd
6m
5.8 m
5m
18.7 yd
5.8 m
18.7 yd
6m
30 m²
112.2 yd²
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-1-
Worksheet by Kuta Software LLC
9)
10)
14.9 ft
15.1 ft
7 ft
3m
6.6 m
15.1 ft
14.9 ft
19.8 m²
11)
105.7 ft²
12)
14.2 cm
10.2 cm
20 m
10.2 cm
15.2 m
144.84 cm²
18.8 m
304 m²
13)
14)
19 in
18 mi
18 in
18 mi
18 in
18 mi
19 in
324 mi²
342 in²
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Circles
Date________________ Period____
Find the circumference of each circle. Round to the nearest tenth.
1)
2)
4.5 m
5 cm
3)
4)
30.2 cm
14 in
5)
6)
26 cm
16.8 cm
7) radius = 12 yd
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8) radius = 5.5 mi
-1-
Worksheet by Kuta Software LLC
Find the area of each. Round to the nearest tenth.
9)
10)
10 cm
12 ft
11)
12)
8m
4m
13)
14)
20 yd
34 ft
15) radius = 8 ft
16) radius = 5 cm
Find the diameter of each circle.
17) area = 4π in²
18) area = 49π yd²
19) circumference = 162π yd
20) circumference = 30π yd
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-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Pre-Algebra
Name___________________________________
Circles
Date________________ Period____
Find the circumference of each circle. Round to the nearest tenth.
1)
2)
4.5 m
5 cm
31.4 cm
28.3 m
3)
4)
30.2 cm
14 in
88 in
94.9 cm
5)
6)
26 cm
16.8 cm
81.7 cm
52.8 cm
7) radius = 12 yd
8) radius = 5.5 mi
75.4 yd
34.6 mi
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-1-
Worksheet by Kuta Software LLC
Find the area of each. Round to the nearest tenth.
9)
10)
10 cm
12 ft
314.2 cm²
452.4 ft²
11)
12)
8m
4m
12.6 m²
201.1 m²
13)
14)
20 yd
34 ft
314.2 yd²
907.9 ft²
15) radius = 8 ft
16) radius = 5 cm
201.1 ft²
78.5 cm²
Find the diameter of each circle.
17) area = 4π in²
18) area = 49π yd²
4 in
19) circumference = 162π yd
14 yd
20) circumference = 30π yd
162 yd
30 yd
Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com
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-2-
Worksheet by Kuta Software LLC