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.
Page 2
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
•
Step 2: Multiply the dividend (first fraction) by the reciprocal of the divisor.
•
!
"
is
"
!
Step 3: Simplify the “new” fraction that comes out after multiplication by reducing it to
lowest term.
Page 3
REVIEW OF OPERATIONS OF FRACTIONS
Reduce to lowest terms.
1.
3
12
5.
9
15
6.
9.
8
20
10.
2.
6
18
3.
8
14
8
10
7.
12
16
11.
20
25
20
45
4.
14
21
8.
10
12
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
27. 7
3
5
28. 4
3
7
29. 2
3
4
30. 7
1
8
31. 6
1
5
32. 1
4
7
Page 4
33. 4
2
3
4
5
34. 7
1
2
35. 6
Compute. Answer should be in lowest terms.
37.
3
8
1
+ 4
8
5
40.
11
3
1
+4
2
43.
46.
38.
44.
1
4
1
–3
2
47.
5
39.
5
6
3
+2
4
42. 7
9
–4
3
4
1
+5
2
8
1
8
7
+5
8
41. 6
4
5
2
–3
5
8
2
5
3
+9
10
8
45.
7
9
2
–3
3
48.
1
8
5
–4
6
1
4
2
7
3
–4
4
8
Page 5
6
7
36. 7
4
9
49.
4
x 80
5
50.
1
x 60
4
51.
2
5
x
3
9
52.
3
1
x6
4
2
53. 7
1
2
x 3
2
3
55. 32 ÷ 2
54. 8 x 7
2
3
56. 3
1
4
1
÷4
2
57. 3
2
2
÷1
3
7
58. 16 ÷ 2
2
3
59. 8
1
1
÷
3
2
60. 40 ÷ 4
4
5
Page 6
EVALUATING A FRACTION OF A NUMBER
Solve the following story problems.
1. Last year
3
of the Ladies Auxiliary baked brownies for the year-end
5
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 the
time, 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
3
of his money
5
on two books. How much did he spend on these two books?
Page 7
6. At Beecher City High School,
4
of the senior class plan on attending
5
college at Lake Land Junior College. If there are 85 seniors at Beecher
City H.S., how many plan on attending Lake Land?
7. Jake bought 4 ½ pounds of hamburger for the cookout. How much did it
cost him if hamburger is $1.80 per pound?
8. Surveys indicate that two-thirds of all voters in Ward 5 plan on choosing
Spike Jones for commissioner. If there are 500 voters in Ward 5, about
how many will be voting for Spike Jones?
9. A recipe calls for 2½ cups of milk. How much milk will you need to make
three times the recipe?
A.
B.
C.
D.
E.
5 cups
6½ cups
7 cups
7½ cups
9 cups
10. A recipe calls for 3½ cups of milk. How much milk will you need to double
the recipe?
A.
B.
C.
D.
E.
5 cups
5½ cups
6½ cups
7 cups
7½ cups
Page 8
11. Which of the following fractions has the largest value?
A.)
B.)
C.)
D.)
E.)
11
23
10
21
9
19
8
17
6
13
12. Which of the following fractions has the largest value?
A.)
B.)
C.)
D.)
E.)
11
25
7
20
21
50
2
5
41
100
13. Which group of fractions is listed from smallest to greatest?
A.)
B.)
C.)
D.)
E.)
9 2 3
, ,
10 3 5
3 1 2
, , ,
4 5 3
2 1 3
, ,
5 3 4
2 3 4
, ,
3 10 5
7 3 4
, ,
10 4 5
Page 9
What is the difference between EXPRESSIONS and EQUATIONS?
EXPRESSIONS
EQUATIONS
Things to remember:
alone on the left side of =
 Your goal is to get the variable _______________________________________!
both
 Do the same thing to ________________sides!
 Do the ________________(inverse
operation) of what is being done in order to move terms across the equal
opposite
sign.
same side
 Combine like terms when they are on the ______________of
the equal sign. (CLT)
addition
subtraction
 Always undo _________________
or ___________________
before multiplication and division!
Other Helpful Tips:



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.
Page 10
Solve and Check the following equations
Page 11
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?
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.
11 of the original number." Write and solve an equation
5. The sum of 2 consecutive numbers is 113. Find the numbers
Page 12
Fraction and Equation Skills For Students
Entering Math 8 - Answers
REVIEW OF OPERATIONS OF FRACTIONS
Page 13