Montgomery County Public Schools, Rockville, MD

Answer Key

Sail into Summer with Math!

For Students Entering

Investigations into Mathematics

This summer math booklet was developed to provide

students in kindergarten through the eighth grade an

opportunity to review grade level math objectives

and to improve math performance.

THIS IS NOT A REQUIRED ASSIGNMENT

IM Summer Mathematics Packet

Table of Contents

Page

Objective

Suggested Completion Date

1

Rename Fractions, Decimals, and Percents. . . . . . . . . . . . . June 22nd

2

Fraction Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . June 25th

3

Multiply Fractions and Solve Proportions . . . . . . . . . . . . . June 29th

4

Add Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . July 6th

5

Subtract Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . July 9th

6

Multiply Mixed Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . July 13th

7

Divide Mixed Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . July 16th

8

Decimal Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . July 20th

9

Find Percent of a Number . . . . . . . . . . . . . . . . . . . . . . . . . . July 23rd

10

Solve Problems using Percent . . . . . . . . . . . . . . . . . . . . . . August 3rd

11

Mean, Median, and Mode . . . . . . . . . . . . . . . . . . . . . . . . . August 6th

12

Integers I . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . August 13th

13

Integers II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . August 17th

14

Solving Equations I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . August 20th

15

Solving Equations II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .August 24th

Summer Mathematics Packet

Rename Fractions, Percents, and Decimals

Hints/Guide:

3

, and divide the numerator

5

(the top number of a fraction) by the denominator (the bottom number of a fraction). So:

To convert fractions into decimals, we start with a fraction, such as

6

5 | 3.0

- 30

0

and the fraction

3

is equivalent to the decimal 0.6

5

To convert a decimal to a percent, we multiply the decimal by 100 (percent means a ratio of a

number compared to 100). A short-cut is sometimes used of moving the decimal point two

places to the right (which is equivalent to multiplying a decimal by 100, so 0.6 x 100 = 60 and

3

= 0.6 = 60%

5

To convert a percent to a decimal, we divide the percent by 100, 60% ¡Â 100 = 0.6 so 60% = 0.6

To convert a fraction into a percent, we can use a proportion to solve,

3

x

, so 5x = 300 which means that x = 60 = 60%

=

5 100

Exercises:

No Calculators!

Rename each fraction as a decimal:

1.

1

=

5

4.

1

=

3

2.

3

=

4

0.75

3.

1

=

2

0.5

5.

8

=

10

0.8

6.

2

=

3

0.6666....

20%

8.

3

=

4

9.

1

=

2

33.33...%

11.

0.2

0.3333...

Rename each fraction as a percent:

7.

10.

1

=

5

1

=

3

75%

8

=

10

80%

12.

2

=

3

50%

66.66....%

Rename each percent as a decimal:

0.08

16. 12% = 0.12

13. 8% =

IM

0.6

17. 40% = 0.4

14. 60% =

Page 1

15. 11% =

18. 95% =

0.11

0.95

Summer Mathematics Packet

Fraction Operations

Hints/Guide:

When adding and subtracting fractions, we need to be sure that each fraction has the same

denominator, then add or subtract the numerators together. For example:

1 3 1 6 1+ 6 7

+ = + =

=

8 4 8 8

8

8

That was easy because it was easy to see what the new denominator should be, but what about if

7 8

it is not so apparent? For example:

+

12 15

For this example we must find the Lowest Common Denominator (LCM) for the two

denominators.

12 and 15

12 = 12, 24, 36, 48, 60, 72, 84, ....

15 = 15, 30, 45, 60, 75, 90, 105, .....

LCM (12, 15) = 60

7 8 35 32 35 + 32 67

7

So,

Note: Be sure answers are in lowest terms

+ =

+

=

=

=1

12 15 60 60

60

60

60

To multiply fractions, we multiply the numerators together and the denominators together, and

then simplify the product. To divide fractions, we find the reciprocal of the second fraction (flip

the numerator and the denominator) and then multiply the two together. For example:

2 1 2 1

2 3 2 4 8

? =

=

and

¡Â = ? =

3 4 12 6

3 4 3 3 9

Exercises: Perform the indicated operation:

No calculators!

SHOW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.

1.

1 3

+ =

4 5

2.

6 2

+ =

7 3

3.

2 8

+ =

5 9

4.

3 2

! =

4 3

5.

2 2

! =

5 9

6.

9 2

! =

11 5

7.

1 2

? =

3 3

8.

3 3

? =

4 5

9.

7 2

? =

8 5

10.

IM

3 3

¡Â =

8 4

11.

1 1

¡Â =

4 4

Page 2

12.

7 3

¡Â =

11 5

Summer Mathematics Packet

Multiply Fractions and Solve Proportions

Hints/Guide:

To solve problems involving multiplying fractions and whole numbers, we must first place a one

under the whole number, then multiply the numerators together and the denominators together.

Then we simplify the answer:

6

6 4 24

3

?4 = ? =

=3

7

7 1

7

7

To solve proportions, one method is to determine the multiplying factor of the two equal ratios.

For example:

4 24

4 24

since 4 is multiplied by 6 to get 24, we multiply 9 by 6, so =

.

=

9

x

9 54

Since the numerator of the fraction on the right must be multiplied by 6 to get the numerator on

the left, then we must multiply the denominator of 9 by 6 to get the missing denominator, which

must be 54.

Exercises: Solve (For problems 8 - 15, solve for N):

No Calculators!

SHOW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.

IM

1. 4 ?

3

=

4

2.

1

?7 =

5

3. 8 ?

4. 6 ?

3

=

7

5.

4

?4 =

5

6.

2

?6 =

3

7. 7 ?

1

=

4

8.

1 n

=

5 20

9.

3 12

=

n 28

10.

1

5

=

n 25

11.

n 3

=

4 12

12.

3 12

=

7 n

13.

n 12

=

9 27

14.

2 18

=

3 n

15.

2 n

=

7 21

Page 3

1

=

5

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