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Summer Practice: p. 1
Name:
Date:
Summer Math (Students Expecting to Enter Pre-Algebra): Show ALL work on separate sheets of paper
to receive credit. This will count as a test grade and must be submitted on the first day of school.
Place Value:
1) How many decimal places are there in the number 603.392?
2) In the number 576,143,020,090 which digit is in the ten millions place?
3) In the number 603.392, which digit is in the hundred-thousandths’ place?
4) Write the number 82,009.07 using words. Include hyphens were appropriate.
5) Write the number three million, fifteen and five ten-thousandths using digits.
6) Write the number 2,176.5 using expanded notation with and without exponents.
Reduce the following to Lowest Terms. Your answer may be in improper fraction form when
appropriate.
9
48
15
18
7) 10)
13)
16)
18
60
27
40
8) 20
25
11)
125
150
14)
57
21
17)
16
64
9) 36
18
12)
6
15
15)
64
56
18)
35
25
Fractions & Mixed Numbers:
Solve. All answers should be in lowest terms and in mixed number form when appropriate.
11 3
1 5
7
1
3
19) 22)
25) 4 − 1
28)
+
−
×8
6 6
8
8
4
15 8
20) 5 11
÷
6 3
21) 2 3
2 +
5 5
23)
3 5
−
4 12
8
1
24) 3 ÷ 2
9
3
4
3
26) 1 × 2
7
4
27) 10 −
1
5
29)
12 ÷
30) 7 ×
5
9
3
4
Summer Practice: p. 2
Decimals:
Solve. For the division problems, write the quotients in 3 ways (as a mixed number, decimal, and
remainder notation) and tell whether the quotient is terminating or repeating.
31) 60 – 51.78
35) 29.01 + 51.2
39) 62.1(0.9)
43) 100.2 ÷ 0.09
32) 19 + 115.6
36) (5.04)(0.16)
40) (23)(1.05)
44) 357.2 ÷ 15
33) 200 + 85.7
37) 20.7 + 207
41) 6.5 ÷ 0.5
45) 140 – 0.98
34) 78 ÷ 0.16
38) 86.4 – 30
42) 14.65(0.33)
46) 5000 ÷ 120
Ordering: Write the following in order from least to greatest by converting each number to a
decimal!
5 7
11 4
,
,– ,
6 10 15 5
47) –
48) –9, – 49 , –
4
, –0.08
5
49)
50)
225 , –
30
, –1.5 , 1.15
2
–0.085, –0.8, –0.058, –0.008
Convert the following:
51) 65% to a decimal and fraction
52) 0.12 to a fraction and percent
1
53) 3 to a percent, an improper fraction, and a decimal
2
54) 1.5 to a fraction and percent
55) 5 yards to inches
56) 650 millimeters to meters
11
57) to a percent, a mixed number, and a decimal
8
Translations. Translate the following into an algebraic expression:
58) “Twice a number”
62) “Two more than three times a number”
59) “Two more than a number”
63) “Four less than a number squared”
60) “Three-fifths of 90”
64) “The quotient of a and b”
61) “Double the sum of a and b”
65) “8% of 20 is what number?”
Vocabulary:
66) List all factors of the following in order from least to greatest: 36, 50, and 80.
List the first five multiples of 9, 15, 20, and 30.
67) Find the prime factorization of 80 and 120 using a factor tree.
Summer Practice: p. 3
68) Find the GCF (Greatest Common Factor) by listing all the factors:
A) 18 and 30
B) 20 and 36
C) 32 and 40
69) Find the LCM (Least Common Multiple) by listing multiples of each:
A) 4 and 6
B) 9 and 15
C) 12 and 16
1
70) Identify 5 different “Common FDPs” ; For Example: 100% = 1.0 =
1
71) Write the perfect squares of the numbers 4-10.
72) Find the pattern. What are the next 3 numbers in the sequence? 5, 15, 45, 135…
Geometry:
73) What is the name of a quadrilateral in which all sides are equal and parallel?
What is the name of a polygon with 7 equal sides? 11 equal sides?
74) What is the difference between the following terms? Use a ruler to draw
pictures to illustrate.
A) equilateral and isosceles
B) complementary and supplementary
C) congruent and similar
D) transformation and tessellation
E) parallel and perpendicular
F) major arc and semicircle
G) prism and pyramid
75) Use formulas to find the Perimeter of:
A) A rectangle whose length is 20.5 yd and whose width is 24.6 yd.
B) An equilateral triangle whose sides measure 8.5 m.
C) A circle whose diameter is 16 m. (Find the Circumference)
76) Find the Area of:
A) A triangle whose base is 8.5 and height is 12.3.
B) A square whose sides measure 11 yards.
C) A circle whose radius is 10 in.
77) Calculate the:
A) Area of a Trapezoid whose bases are 6 in and 8 in and whose height is 3 in.
B) Circumference of a circle whose radius is 15 m.
C) Measure of the third angle of triangle whose other angles measure 63º and 24º.
D) Find the Surface Area and Volume of a cube whose sides are 15 yd.
Word Problems:
78) There are 25 children and 80 adults in a theater. If there are 315 total people in the
theater, what is the ratio of children to all adults? Your answer should be in reduced form.
79) Find the mean, median, mode, and range of the following data: 90, 100, 105, 108, 200
Summer Practice: p. 4
80) Your mother bought you an outfit that cost $41.99. If the tax was $5.60, how much did
she owe in all? How much change did she receive if she gave the cashier $50?
81) A bug was flying aimlessly in the sky. It flew in straight lines. It began by flying east for
8 miles, then west on the same exact path for 12 miles. It turned again and flew east for
another 17 miles, and lastly west for 21 miles until it stopped. Where did it finally land?
(Be specific. EX: 20 miles east.)
82) A bag of 25 large strawberries sold for $5.00. If there were 150 strawberries, how much
would they cost?
83) There were 9 chaperones who could attend the 7th grade field trip. Students were
grouped evenly with one chaperone. If there were 60 students total, how many students
were there at maximum in each group?
84) Find the mean, median, mode, and range for the following data:
Average Monthly Texts from Students
Grade
Month
Texts
4
January
50
5
February
150
6
March
125
7
April
200
8
May
500
85) Display the data in #34 using 2 different graphs. For example, histogram.
86) What is 2% of 80 gallons?
87) Show which is the better buy: an 8-pack of soda for $6.99 or a 12 pack of soda for $10.99
Solve:
88) Solve using the Order of Operations: 20 + 3[52 – (10 – 6)]
89) Solve using the Order of Operations:
90) If x = 2, y = 3, and z = 4, solve using the Order of Operations: z2 + y2 – 5(6 – x)
91) Find the value of the variable, algebraically, in the following one-step equations:
A) M – 9 = 21
92) 150 − (8 + 4) 2
20 − 3 2 − 5
B) 55 = 8 + C
C) 100 = 2.5M
Find the value of the variable in the following proportions using cross products:
A)
20 4
=
25 y
B)
3 15
=
m 35
C)
x 72
=
9 81
Summer Practice: p. 5
93) 94) 95) 96) a + b
when a = –7 and b = –8
2a + 80 = 144
x + 0.12 = 16.82
x 8
=
4 9
97)
105 + 8 – 33[5 – (4 – 2)]
98)
8 + (4 − 2)(24 ÷ 4)
2 2 + (7 − 12 )
99)
(2)100 – 4(9 + 32)