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 tolowest term.

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REVIEW OF OPERATIONS OF FRACTIONS

Reduce to lowest terms.

1. 312

2. 618

3. 810

4. 1421

5. 915

6. 814

7. 2025

8. 1012

9. 820

10. 1216

11. 2045

12. 616

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

13. 132

14. 114

15. 183

16. 74

17. 408

18. 107

19. 163

20. 229

21. 357

22. 195

23. 113

24. 3010

Change to an improper fraction.

25. 3 17

26. 5 23

27. 7 35

28. 4 37

29. 2 34

30. 7 18

31. 6 15

32. 1 47

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33. 4 23

34. 7 45

35. 6 12

36. 7 49

Compute. Answer should be in lowest terms.

37. 5 38

38. 8 25

39. 8 34

+ 4 18

+ 9 310

+ 5 12

40. 113

41. 6 56

42. 7 18

+ 4 12

+ 2 34

+ 5 78

43. 8 45

44. 9 45. 6 79

–3 25

– 4 14

– 3 23

46. 5 14

47. 8 27

48. 7 18

– 3 12

– 4 34

– 4 56

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49. 45

x 80 50. 14

x 60

51. 23

x 59

52. 34

x 6 12

53. 7 12

x 3 23

54. 8 x 7 14

55. 32 ÷ 2 23

56. 3 12

÷ 4

57. 3 23

÷ 1 27

58. 16 ÷ 2 23

59. 8 13

÷ 12

60. 40 ÷ 4 45

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EVALUATING A FRACTION OF A NUMBER

Solve the following story problems.

1. Last year 35

of the Ladies Auxiliary baked brownies for the year-end

fundraiser. If there were 120 members of the Ladies Auxiliary last year,how many baked brownies?

2. It has been cloudy 4 out of 5 days for the last month. If there were 30 days in the month, how many days were cloudy?

3. The student council surveyed the ticket buyers at last week’s football game found that 12.5% were freshmen. If there were 2,472 people who bought tickets for the game, how many were freshmen?

4. Jared spent 8 hours at his factory job last Monday. Two-thirds of thetime, he worked on the Flex Line assembling air conditioners. How much time did he end up working on the Flex Line? Give your answer is hours and minutes, no fractional hours.

5. Mark earned $40 mowing lawns last week. He spent 35

of his money

on two books. How much did he spend on these two books?

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6. At Beecher City High School, 45

of the senior class plan on attending

college at Lake Land Junior College. If there are 85 seniors at BeecherCity H.S., how many plan on attending Lake Land?

7. Jake bought 4 ½ pounds of hamburger for the cookout. How much did itcost him if hamburger is $1.80 per pound?

8. Surveys indicate that two-thirds of all voters in Ward 5 plan on choosingSpike Jones for commissioner. If there are 500 voters in Ward 5, abouthow many will be voting for Spike Jones?

9. A recipe calls for 2½ cups of milk. How much milk will you need to makethree times the recipe?

A. 5 cupsB. 6½ cupsC. 7 cupsD. 7½ cupsE. 9 cups

10. A recipe calls for 3½ cups of milk. How much milk will you need to doublethe recipe?

A. 5 cupsB. 5½ cupsC. 6½ cupsD. 7 cupsE. 7½ cups

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11. Which of the following fractions has the largest value?

A.) 1123

B.) 1021

C.) 919

D.) 817

E.) 613

12. Which of the following fractions has the largest value?

A.) 1125

B.) 720

C.) 2150

D.) 25

E.) 41100

13. Which group of fractions is listed from smallest to greatest?

A.) 9 ,10

2 ,335

B.) 34

, 15

, 2 ,3

C.) 2 ,51 ,3

34

D.) 2 ,3310

, 45

E.) 710

, 34

, 45

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Your goal is to get the variable _______________________________________!

Do the same thing to ________________sides! Do the ________________(inverse operation) of what is being done in order to move terms across the equal

sign.

Combine like terms when they are on the ______________of the equal sign. (CLT)

Always undo _________________ or ___________________ before multiplication and division!

alone on the left side of =

both

opposite

same side

addition subtraction

What is the difference between EXPRESSIONS and EQUATIONS?

EXPRESSIONS EQUATIONS

Draw a vertical line down through the equal sign.

Multiply by the multiplicative inverse or reciprocal of a fraction in order to remove it.

Move all of the constants (numbers without variables) to one side and all of the terms with variable to

the other side.

Use the distributive property and combine like terms before moving things across the equal sign.

Things to remember:

Other Helpful Tips:

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Solve and Check the following equations

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2. The length of a rectangular garden is 3 yards more than twice its width. The perimeter of

the garden is 36 yards. What are the width and length?

3. An athlete runs an equal distance 5 days a week. The other 2 days of the week, she runs

a total of 13 miles. Write an equation to represent the total numbers of miles run in a week,

R, and the number of miles, x, run each of the 5 days. If the athlete ran 53 miles last week,

how far did she run each of the first 5 days?

4. Peter has to use the following information to find the original number: "If you double a

number and then add 36, you get .i. of the original number." Write and solve an equation

Write and Solve an Equation to answer the question

1. A town has accumulated 2 inches of snow, and the snow depth is increasing by 4 inches

every hour. A nearby town has accumulated 7 inches, and the depth is increasing by 2

inches every hour. In about how many hours will the snowfall of the towns be equal?

5. The sum of 2 consecutive numbers is 113. Find the numbers

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REVIEW OF OPERATIONS OF FRACTIONS

Fraction and Equation Skills For Students Entering Math 8 - Answers

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