Download 7-1 Period 5

SUMMER MATH
PACKET
7th Grade
Southampton Township School #3
Name: ______________________________________
Summer Packet Directions
Packet Due: September 4, 2013
 Complete each problem.
 Work is expected to be shown in the actual packet neatly for EVERY
problem. Points will be deducted if work is not shown. Additional
lined paper may be added if necessary.
 All final answers must be recorded on the Answer Sheet (second to
last page of the packet).
 Label answers when necessary.
 Do NOT use a calculator.
 A NJASK reference sheet has been provided to assist with some
information.
 This packet will be graded and counted as a part of your homework
grade. A quiz will be given during the second week of school
reflecting the topics covered.
 If you are stuck on a particular problem, check out some of the math
websites posted below. Parents or classmates may also be used to
help.
http://www.aplusmath.com
http://amathsdictionaryforkids.com
http://funbrain.com
http://math.com
FRACTIONS
Adding and Subtracting Fractions
The denominators need to be the same when adding and subtracting fractions. Also, sometimes
you will need to rename fractions in order to subtract. Always reduce answers to lowest terms.
Examples:
1)
11 9

12 12
1 1 1 2 3 1
    
6 3 6 6 6 2
2)
19 9

20 20
1 7
4 7 12 7 5
1  1    
2 8
8 8 8 8 8
3) 1
23 8

25 25
Multiplication and Division of Fractions and Mixed Numbers
When multiplying fractions and mixed numbers there is no need to have a common
denominator, just multiply straight across. However, you do need to change all mixed numbers
into improper fractions before you multiply. Always reduce answers to lowest terms.
When dividing fractions you need to change the problem into a multiplication problem. Change
the division sign to a multiplication sign and invert (flip-flop) the second fraction.
Examples:
4)
3 2

5 4
7) 9÷
3
7
1 2 9 2 18 3
1
2    
 1
4 3 4 3 12 2
2
*Multiply across*
2
1 11 9 11 2 22
3 4     
3
2 3 2 3 9 27
*Keep, Change, Flip*
5)
4 2

5 6
4 2
6) 2  2
5 3
8)
3 10
÷
5 12
4
9) 2 ÷ 2
5
FRACTIONS, DECIMALS, AND PERCENTS
Fractions to Decimals: Use your division skills to turn a fraction into a decimal – remember to
divide the numerator by the denominator.
3
Example:  3  4  0.75
4
Decimals to Fractions: Read the number using place value, decide if the number ends in the
tenths, hundredths, thousandths, etc., that will be your denominator. Reduce your fraction.
5 1

Example: 0.5 reads 5 tenths which is the fraction
10 2
Decimals to Percents: Multiply your decimal by 100 (which moves the decimal 2 places to the
right) and then add the percent sign.
Example: 0.32 = 32%
Percents to Decimals: Divide your percentage by 100 (which moves the decimal 2 places to the
left) and then take away the percent sign.
Example: 45% = 0.45
Fraction
10)
Decimal
Percent
11)
25%
12)
13)
1
2
14)
15)
0.6
16)
17)
90%
5
8
18)
19)
Comparing and Ordering Fractions and Decimals
Order the following lists in order from least to greatest. To solve, it may be helpful for you to
create a number line, put all of the fractions over their Least Common Denominator, and/or
change all of the fractions to decimals. **The higher the negative, the lower it is on a number
line!! **Just number them 1-5 in order.
20)
2 1 3 1 2
,- , ,- ,
3 6 4 8 5
5 3 3 2 1
21) - , , - , ,8 5 4 6 4
22)
4
4
4
, - 0.35 , - , 0.72 ,9
6
5
23)
7
1 5 8 3
, -1 , , - ,
8
3 4 9 2
24) - 0.79 , - 0.8 , - 0.08 , - 0.81 , - 0.079
Absolute Value
Absolute Value is a number’s distance from zero. The symbol for
absolute value is  6 = 6. The answer is always positive!!
25)
 18 =
26)
9 =
27) 25  15 =
DECIMALS
Adding and Subtracting Decimals
When adding and subtracting decimals, always be sure to line up the decimal points. Add or
subtract as usual then bring the decimal straight down into your answer. In a whole number, the
decimal is located at the end of the number. Fill in zeros as placeholders when needed.
28) 43.5 + 92.1
29) 84.52 - 7.348
30) 74.3 + 6.65 + 2.008
Multiplying Decimals
Multiplying Decimals is the same as multiplying whole numbers. The key is to count the decimal
places in each factor (the numbers you are multiplying together).
Step 1: Line up the digits (not the decimal points!)
Step 2: Multiply as with whole numbers
Step 3: Add together the decimal places in each factor. The product (answer) has the same
number of decimal places
31) 2.08 x 0.9
32) 14.2 x 9.7
33) 0.84 x 3.15
Dividing Decimals
Example 1: Dividing a decimal by a whole number.
5.92 ÷ 7 = 0.85
Step 1: Rewrite the problem as a long division problem and bring the decimal straight up into
the quotient (answer). Remember, the first number (dividend) goes under the long
division sign. The second number (divisor) goes on the outside.
Step 2: Divide as needed. Remember, no remainders.
Example 2: Dividing a decimal by a decimal.
20.8 ÷ 2.6 = 8
Step 1: Rewrite the problem as a long division problem.
Step 2: If the divisor (outside number) is a decimal, you must move the decimal point to the
right until it becomes a whole number.
Step 3: Move the decimal in the dividend to the right the same number of times.
Step 4: Bring the decimal straight up into the quotient.
Step 5: Divide as needed. Remember, no remainders.
34) 3.54 ÷ 6
35) 9.12 ÷ 1.6
36) 15.12 ÷ 9
Comparing Fractions and Decimals
Insert < (less than), > (greater than), or = (equal to) into the following comparisons. To solve, it
may be helpful for you to create a number line, put the fractions over their Least Common
Denominator, and/or change the fractions to decimals.
37)
2
7
____
5
15
38) _
5
3
____ 
6
4
2
4
39) - ____
3
6
Order of Operations
Use the order of operations to simplify each expression. To help you figure out what step to complete
first please refer to the example.
P – Parenthesis
(4 + 5 )
E- Exponents
62
M or D – Multiplication OR Division (left to right)
A or S – Addition OR Subtraction (left to right)
Example:
( 4 + 5)  4 – 33 + 9(2)
9  4 – 33 + 9(2)
Parenthesis
9  4 – 27 + 9(2)
Exponents
36 – 27 + 18
Multiplication
9 + 18
Subtraction (left to right)
27
Addition (left to right)
40) 64 − 4 • 23 + 7
41) 9.4+(1.5 + 6.5)  6.7 – 4.5
42) {(3.8-0.6)  2}  (2.2  4.4)
43) 4 ÷ {5 + 9  1 - (3+10)}
44) (6-4)2 – (25 + 3)2 + 18
Area and Perimeter
Find the area perimeter of the following polygons. Use the reference sheet if needed.
45) Area = ______________________
46) Perimeter = __________________
47) Area = ______________________
48) Perimeter = __________________
49) Area = ______________________
50) Circumference = ______________
*use 3.14 for π*
Name: ______________________________________
Summer Packet Answer Sheet
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