FRACTIONS Packet - Review Exercises

Summer Math Packet

Fraction and Equation Skills For Students Entering Math 8

At the beginning of our Math 8 course, you will be assessed on the prerequisite skills outlined in this packet. The packet will not be graded; however, you are responsible for the material. The answers are provided at the end of the packet; please check your answers. On the first day of school, you will submit an online form detailing your understanding of each of the topics in this packet. That form will be available in Google Classroom beginning on June 1.

The assessment will count as a full test grade in your first quarter average. We will spend the first week of school going over this packet and answering questions. You may email me over the summer if you have questions.

Add and Subtract Fractions with Different or Unlike Denominators

To add or subtract fractions with different denominators, we need to do some extra steps. The general approach is discussed below. We will go over a few examples in this lesson to make sure you get comfortable with the procedure.

Steps How to Add or Subtract Fractions with Different Denominators

Step 1: Given two unlike fractions where the denominators are NOT the same.

Step 2: Make the denominators the same by finding the Least Common Multiple (LCM) of their denominators. This step is exactly the same as finding the Least Common Denominator (LCD).

Step 3: Rewrite each fraction into its equivalent fraction with a denominator which is equal to the Least Common Multiple that you found in step #2.

Step 4: Now, add or subtract the "new" fractions from step #3. Always reduce the answer to its lowest terms.

Multiplying Fractions

To multiply fractions is as easy as following the 3 suggested steps below. It's understood that no fraction can have a denominator of 0 because it will be an undefined term.

Steps in Multiplying Fractions Given two fractions with nonzero denominators:

Step 1: Multiply the numerators. ? This will be the numerator of the "new" fraction.

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Step 2: Multiply the denominators. ? This will be the denominator of the "new" fraction.

Step 3: Simplify the resulting fraction by reducing it to the lowest term, if needed.

Divide Fractions by Converting to Multiplication of Fractions

To

divide

fractions,

we

need

to

know

these

3

basic

parts.

Suppose

we

want

to

divide

! "

by

% &

the

setup should look like this.

? Dividend ? the number being divided or partitioned by the divisor. It is found to

the left of the division symbol.

? Divisor ? the number that is dividing the dividend. It is located to the right of the

division symbol.

Now, apply the following simple steps to divide these fractions.

General Steps on How to Divide Fractions

?

Step

1:

Find

the

reciprocal

of

the

divisor

(second

fraction)

The

reciprocal

of

! "

is

" !

? Step 2: Multiply the dividend (first fraction) by the reciprocal of the divisor.

? Step 3: Simplify the "new" fraction that comes out after multiplication by reducing it to lowest term.

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REVIEW OF OPERATIONS OF FRACTIONS

Reduce to lowest terms.

1. 3

12

2. 6

18

3. 8

10

4. 14

21

5. 9

15

6. 8

14

7. 20

25

8. 10

12

9. 8

20

10. 12

16

11. 20

45

12. 6

16

Change each improper fraction to a mixed number or whole number.

13. 13

2

14. 11

4

15. 18

3

16. 7

4

17. 40

8

18. 10

7

19. 16

3

20. 22

9

21. 35

7

22. 19

5

23. 11

3

24. 30

10

Change to an improper fraction.

25. 3 1

7

26. 5 2

3

29. 2 3

4

30. 7 1

8

27. 7 3

5

31. 6 1

5

28. 4 3

7

32. 1 4

7

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33. 4 2

3

34. 7 4

5

35. 6 1

2

Compute. Answer should be in lowest terms.

37. 5 3

8

+ 41

8

38. 8 2

5

+9 3

10

39. 8 3

4

+5 1

2

40. 11

3

+4 1

2

41. 6 5

6

+2 3

4

42. 7 1

8

+5 7

8

36. 7 4

9

43. 8 4

5

?3 2

5

44. 9 ?4 1

4

45. 6 7

9

?3 2

3

46. 5 1

4

?3 1

2

47. 8 2

7

?4 3

4

48. 7 1

8

?4 5

6

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