Download Fraction Operations Unit Test

Section A
Adding and Subtracting Fractions
5-1 Least Common Multiple (LCM)
5-2 Adding and Subtracting with Unlike Denominators
5-3a Adding and Subtracting Mixed Numbers
5-3b Regrouping to Subtract Mixed Numbers
5-4 Solving Fraction Equations: Addition and Subtraction
Section A Quiz
Section B
Multiplying and Dividing Fractions
5-5a Multiplying Fractions
5-5b Multiplying Mixed Numbers
5-6 Dividing Fractions and Mixed Numbers
5-7 Solving Fraction Equations: Multiplication and Division
Section B Quiz
Fraction Operations Unit Test
5-1 Least Common Multiple
Vocabulary
__________ ____________ ________________ - the smallest number that is a multiple of two or
more numbers (LCM)
Example 1: Consumer Application
English muffins come in packs of 8, and eggs come in cartons of 12. If there are 24 students, what is
the least number of packs and cartons needed so that each student has a muffin sandwich with one
egg?
Draw muffins in groups of _____
Draw eggs in groups of _____
Stop when you have drawn the same number in each!
muffins
eggs
There are _____ total muffins and _____ total eggs.
So _____ packs of muffins and _____ cartons of eggs are needed
Example 2: Using Multiples to Find the LCM
METHOD 1 – Use a number line and skip count by the given numbers
Find the LCM of 3 and 4
LCM = _____
Find the LCM of 6 and 9
LCM = _____
METHOD 2 – Use a list
List multiples for each number. Then find the __________ number found on all lists.
Find the LCM of 3, 5, and 6
Find the LCM of 4, 5, and 8
3:
4:
5:
5:
6:
8:
LCM = _____
LCM = _____
METHOD 3 – Use prime factorization
Without using exponents
1. Write the prime factorization of each number
2. Line up the common factors
3. To find the LCM, multiply one number from each column.
Find the LCM of 8 and 12 using prime factorization
8
12
8=
12 =
LCM = _____
Using exponents
1. Write the prime factorization of each number in exponential form.
2. To find the LCM, multiply each prime factor once with the greatest exponent used in any of the
prime factorizations.
Find the LCM of 12, 10, and 15 using prime factorization
8
12
15
8=
12 =
15 =
LCM = _____
Practice
1. Pencils are sold in packs of 12, and erasers in packs of 9. Mr. Joplin wants to give each of 36
students a pencil and an eraser. What is the least number of packs he should buy so there are none
left over?
Find the Least Common Multiple (LCM) using the method of your choice.
2) 2 and 8
3) 3 and 7
4) 4 and 10
5) 3 and 9
6) 3, 6, and 9
7) 4, 8, and 10
8) 4, 6, and 12
9) 4, 6, and 7
10) 3, 8, and 12
11) 3, 7, and 10
12) 2, 6, and 11
13) 3, 4, and 5
14) 10 and 11
15) 2, 4, 5, and 6
16) 4, 5, and 7
17. During its grand opening weekend, a restaurant offered every 8th customer a free appetizer and
every 12th customer a free drink. Which customer was the first to receive and free appetizer AND a
free drink?
5-2 Adding and Subtracting with Unlike Denominators
Vocabulary
__________ ____________ ________________ - the least common multiple of the denominators
Example 1: Social Studies Application
The Pacific Ocean covers
!
!
of Earth’s surface. The Atlantic Ocean covers
!
!
Earth’s surface.
What fraction of Earth’s surface is covered by the Pacific and Atlantic Oceans?
Add
!
!
and
!
3:
!
5:
1. Find a common denominator for 3 and 5.
2. Write equivalent fractions with _____ as the common denominator
3. Add the numerators. Keep the common denominator.
!
!
→
!
+!→
________
You can use any common denominator or the least common denominator to add & subtract
unlike fractions.
Example 2: Adding and Subtracting Unlike Fractions
Add or Subtract. Write each answer in simplest form
METHOD 1: Multiply the denominators to find a common denominator
!
!
−!=
!"
!
!
+!=
!
METHOD 2: Use the LCD
!
!"
!
−!=
!
8:
!
10:
Evaluate each expression for x =
!
!
!
+!=
8:
6:
Write your answer in simplest form.
!
!
𝑥+!
!
−𝑥
!
𝑥 − !!
Practice: Find each sum or difference. Write your answer in simplest form. Circle your answer.
1)
!
!"
+
!
!
2)
!
3)
!
!
−!
!
!
6)
!
!
!
!
9)
!
!
!
−
!
!
4)
!
+!
!
!
5)
7)
!
!
8) !! + !
−!
!
!
!
!
−
!
!
+!
!
!
+!+!
!
10. Bailey spent ! of his allowance at the movies and ! on baseball cards. What fraction of Bailey’s
allowance is left?
Adding and Subtracting with Unlike Denominators
PRACTICE
Add or subtract. Write each answer in simplest form. NO CALCULATORS
1. 6 + 1
7
3
2. 3 − 2
5
7
3. 1 + 3
8
4
4. 7 − 2
3
8
5.
1 3
+
5
6
6. 5 − 2
3
6
7. 5 − 1
9 3
8. 7 + 3
8
4
9.
10. 4 − 7
5 11
11. 4 + 5
9
6
12. 5 + 2
3
8
5 − 1
6
12
Evaluate each expression for b = 1 . Write your answer in simplest form. NO CALCULATORS
3
13. b + 5
8
14. 7 − b
9
15. 2 + b
7
16. b + b
17. 11 − b
12
18. 3 − b
4
19. Kyle is making a dessert that calls for 4 cup of crushed cookies. If he has already crushed 7
5
10
cup, how much more does he need?
5-3a Adding and Subtracting Mixed Numbers
3
1
2 +1
4
6
1. add the fractions first
(don’t forget to find a common denominator)
2. add the whole numbers
3. combine the two parts
More Examples: Find each sum or difference. Write the answer in simplest form.
!
!
!
!
1) 4 − 2
!
!
!
!"
2) 8 − 6
!
!
!
!
3) 3 + 7
!
4) The length of a Parsons chameleon’s body is 23 inches. The chameleon can extend its tongue
!
!
35 ! inches. What is the total length of its body and its tongue?
!
Evaluate each expression for 𝑛 = 2 . Write your answer in simplest form.
!
!
5) 2 ! + 𝑛
!
6) 𝑛 − 1 !
!
7) 5 − (1 ! + 𝑛)
Practice: Find each sum or difference. Write the answer in simplest form.
!
!
!
1) 7 !" + 3 !
4) 6 − 1
!
!
!
!
!
!
5) 19
!
!"
!
6) 3
!
!
!
!
!
!
−1
!"
!
8) 5 !! + 5 !
10) 6 !" + 3 !
!
3) 8 ! − 2 !
+ 10
!
7) 2 ! + 4 !"
!
!
2) 2 ! + 2 !
!
!
9) 9 ! − 3 !
!
!
11) 10 ! − 2 !"
!
12) 14 ! − 6 !"
!
!
13) A sea turtle traveled 7 hours in two days. It traveled 3 hours on the first day.
!
!
How many hours did it travel on the second day?
!
!
!
!
14) The drama club rehearsed 1 hours Friday and 3 hours Saturday.
How many total hours did the students rehearse?
!
Adding and Subtracting Mixed Numbers
PRACTICE
Find each sum or difference. Write the answer in simplest form. NO CALCULATORS
1. 1 1 + 3 1
2
4
2. 10 3 − 8 1
10
5
3. 3 1 + 2 5
6
4
4. 3 2 − 1 1
6
3
5. 10 2 − 9 1
3
4
6. 4 2 + 1 1
15
5
7. 4 3 + 5 1
4
8
8. 11 2 − 8 1
5
3
9. 7 1 + 3 2
3
9
10. 22 5 − 17 1
4
6
11. 32 4 − 14 1
3
7
12. 12 1 + 5 1
4
12
13. 8 1 + 2 2
10
25
14. 3 1 − 110
17
2
15. 2 1 − 1 1
6
16
16. Jack babysat for 4 1 hours on Friday night. He babysat for 3 2 hours on Saturday night. How
3
4
many hours did he babysit in all?
17. Bonita planted an oak tree and an elm tree in her backyard. Three years later, the oak tree was
51
71
6 feet tall, and the elm tree was 2 feet tall. How much taller was the elm tree?
Adding and Subtracting Mixed Numbers
HOMEWORK
Find each sum or difference. Write the answer in simplest form. NO CALCULATORS
1. 8 1 + 2 1
3
2
2. 12 1 − 10 1
8
2
3. 7 1 + 1 1
8
6
4. 2 7 + 1 1
8
12
5. 4 1 − 1 1
6
9
6. 3 1 + 3 1
3
7
7. 29 1 − 14 1
3
6
8. 5 3 − 1 7
4
11
9. 21 1 + 1 3
6
8
10. 15 7 − 14 3
8
12
11. 5 6 + 4 3
15
10
12. 25 1 + 25 2
5
7
13. 6 5 + 14 1
9
6
14. 11 7 − 5 3
8
12
15. 4 2 + 3 1
13
2
16. Donald is making a party mix. He bought 2 1 pounds of pecans and 3 1 pounds of walnuts. How
5
4
many pounds of nuts did Donald buy in all?
17. Mrs. Watson’s cookie recipe calls for 3 4 cups of sugar. Mr. Clark’s cookie recipe calls for 4 2
3
7
cups of sugar. How much more sugar does Mr. Clark’s recipe use?
18. Tasha’s cat weighs 15 5 lb. Naomi’s cat weighs 11 1 lb. Can they bring both of their cats to the
3
12
vet in a carrier that can hold up to 27 pounds? Explain.
5-3b Regrouping to Subtract Mixed Numbers
1
3
2 −1
4
4
1.
2.
3.
4.
5.
make sure you have a common denominator
check the fractions to see if you need to borrow or regroup
subtract fraction part
subtract whole numbers
combine the two parts
Subtract using borrowing
6
Subtract using regrouping
5
7
−2
12
12
6
5
7
−2
12
12
Examples: Subtract. Write each answer in simplest form.
!
!
1) 8 − 5 !
!
2) 17 − 1 !
3) 5 − 4 !
More Examples: Find each sum or difference. Write the answer in simplest form.
!
!
4) 13 ! − 11 !
!
!
5) 10 ! − 6 !
!
!
6) 20 ! − 7 !
Practice: Subtract. Write each answer in simplest form.
1) 2 − 1
!
!
!
!
!
!!
5) 5 !" − 3 !
!
!
6) 6 !! − 3 !!
!
!
8) 4 !" − 3 !
!
!
9) 10 ! − 2 !
!
!
!
!
12) 6 − 2
4) 7 ! − 4 !"
7) 9 ! − 5 !
!
!
!
!
10) 11 − 9
!
!
!
!
2) 8 − 2
11) 7 − 2
!
!
!
!
3) 3 − 1
!
!"
!
!
!
!
!
13) Mr. Jones purchased a 4-pound bag of flour. He used 1 pounds of the flour to make bread.
How many pounds of flour are left?
!
!
14) A standard piece of notebook paper has a length of 11 inches and a width of 8 inches.
!
What is the difference between these two measures.
Regrouping to Subtract Mixed Numbers
PRACTICE
Subtract. Write each answer in simplest form. NO CALCULATORS
1. 2 − 2
3
2. 1 − 1
4
3. 5 1 − 3 1
4
2
4. 2 1 − 1 5
3
6
5. 1 4 − 2
9
3
6. 2 1 − 1 7
8
4
7. 4 − 2 3
8
8. 5 1 − 2 2
6
3
9. 14 − 8 2
9
10. 7 − 3 11
12
11. 14 5 − 3 7
8
12
12. 5 1 − 2 2
3
7
13. At the pie-eating contest, Dina ate 3 1 pies. Mason ate 2 5 pies. How much more pie did Dina
3
6
eat than Mason?
14. When Latoya bought her angel fish, it was 1 1 inches long. Now it is 2 1 inches long. How much
3
2
did her angel fish grow?
15. Tim had 6 feet of wrapping paper for Kylie’s birthday present. He used 3 3 feet of the paper to
8
wrap her gift. How much paper did Tim have left?
5-4 Solving Fraction Equations: Addition and Subtraction
Solving Equations Review
𝑥 + 62 = 93
81 = 17 + 𝑦
52 + 𝑏 = 71
𝑝−2=5
40 = 𝑥 − 11
𝑥 − 56 = 19
Solving Fraction Equations - Solve each equation. Write the solution in lowest terms.
A. 𝑥 + 6
C. 5
!
!
!
= 11
!
=𝑚+
!
!"
!
check
B. 2
check
D. 𝑤 −
!
= 𝑥 − 3!
!
!
!
=2
!
!
check
check
!
E. On average, a person in Costa Rica consumes 132 pounds of sugar per year. If the average
!
!
person in Costa Rica consumes 24 pounds less than the average person in the US, what is the
!
average sugar consumption per year by a person in the US? Write an equation and solve.
!
!
!
!
F. 𝑚 + 4 = 6 − 1
!
!
!
!
G. 3 − 1
=𝑝−5
!
!
Practice: Solve each equation. Write the solution in simplest form.
!
1) 𝑥 + 2 ! = 7
!
!
3) 9 ! = 𝑥 + 4 !
!
!
6) 8 !" = 𝑥 − 4 !
2) 3 ! = 𝑥 − 5 !
!
!
5) 3 ! + 𝑥 = 7 !
!
!
!
!"
8) 𝑥 + 5 = 9
4) 𝑥 + 1 ! = 5 !"
7) 𝑥 − 4 = 1
!
!
!
!
!
!
!
!
!
!
!
!
9) 𝑞 − 4 = 1 + 1
!
10) A tailor increased the length of a robe by 2 inches. The new length of the robe is 60 inches.
!
What was the original length?
!
11) Robert is taking a movie-making class in school. He edited his short video and cut 3 minutes.
The new length of the video is 12
!
!"
!
minutes. How long was his video before he cut it?
Solving Fraction Equations: Addition and Subtraction
PRACTICE #1
Solve each equation. Write the solution in simplest form. NO CALCULATOR
1. k + 1 1 = 3
2
2. m − 2 1 = 1 1
3
2
3. 1 1 − 2 = p
3
4
4. n + 3 7 = 5 1
8
8
5. 3 1 = y − 1 1
3
6
6. 2 1 + d = 3 1
5
2
7. 2 1 + q = 4 3
14
7
8. z − 1 2 = 1 7
10
5
9. f + 2 = 1 1
3
9
10. b = 1 5 − 3
8
4
11. t + 1 1 = 3 3
5
10
12. 3 1 + w = 5 7
2
12
13. c − 8 1 = 10 3
5
10
14. h + 1 = 2 1
3
6
15. 1 5 = g − 3 5
18
9
16. Joey beat Frank in the swim race by 2 1 minutes. Frank’s time was 8 3 minutes. What was
10
5
Joey’s time in the race?
17. Sabrina bought 8 gallons of paint. After she painted her shed, she had 4 1 gallons left over. How
6
much paint did Sabrina use on her shed?
Solving Fraction Equations: Addition and Subtraction
PRACTICE #2
Solve each equation. Write the solution in simplest form. NO CALCULATOR
1. 5 1 = x + 7
16
4
2. 6 1 = z + 1 5
4
8
3. 2 2 = n − 4 2
3
7
4. a − 2 2 = 2 5
22
11
5. k + 3 3 = 5 2
3
4
6. r + 6 = 9 2
5
7. 11 2 = q − 4 2
5
7
8. 4 2 = p + 3
5
10
9. 3 = c − 4 5
6
8
10. 2 1 + c = 2 1 + 1 1
3
6
4
11. 3 1 − 1 3 = p + 5
6
5
10
12. A seamstress raised the hem on Helen’s skirt by 1 1 inches. The skirt’s original length was 16
3
inches. What is the new length?
13. The bike trail is 5 1 miles long. Jessie has already cycled 2 5 miles of the trail. How much farther
4
8
does she need to go to finish the trail?
14. Carol wants each of the curtains she makes to be the same length. She started with two pieces
of cloth measuring 6 1 feet and 7 3 feet. She cut 1 5 feet off the 6 1 -foot piece. How much
3
3
4
8
should she cut from the second piece?
5-5a Multiplying Fractions
1. Multiply the numerators
2. Multiply the denominators
3. Put answer in simplest form
1)
! !
∙
2)
! !
! !
∙
! !
3)
! !
∙
! !
Fractions can be simplified before multiplying by using common factors
4)
! !
7)
!
∙
! !
!
∙
!" !
Evaluate the expression 𝑎 ∙
!
!
! !
∙!
6)
! !
8)
! !
9)
!
!
∙
! !
!
!
∙
!" !
!
11) 𝑎 = !"
!
∙
! !
for each value of 𝑎 . Write the answer in simplest form.
!
10) 𝑎 = !
13) Jim spent
!
5)
of an hour doing chores. He spent
12) 𝑎 = !
!
!
of that time washing dishes.
What fraction of an hour did he spend washing dishes?
Practice: Multiply – write each answer in simplest form
1)
! !
∙
2)
! !
∙
3)
! !
4)
! !
5)
! !
∙
6)
! !
7)
!
8)
! !
9)
! !
! !
∙
! !
∙
!
!" !
Evaluate the expression 𝑥 ∙
!
!
! !
! !
!
∙
!
∙
! !
∙
! !
∙
! !
for each value of 𝑥 . Write the answer in simplest form.
!
!
10) 𝑥 = !
11) 𝑥 = !
!
!
12) 𝑥 = !
!
13. A walnut muffin recipe calls for cup walnuts. Mrs. Hooper wants to make ! of the recipe.
!
What fraction of a cup of walnuts will she need?
Multiplying Fractions
HOMEWORK
Multiply. Write each answer in simplest form. NO CALCULATOR
1. 1 • 2
2 5
2. 1 • 7
3 8
3. 2 • 4
3 6
4. 1 • 10
4 11
5. 3 • 2
5 3
6. 8 • 3
9 4
7. 3 • 4
8 5
8. 2 • 3
7 4
9. 1 • 2
6 3
Evaluate the expression x • 1 for each value of x. Write the answer in simplest form.
5
10. x = 3
7
11. x = 5
6
12. x = 2
3
13. x = 10
11
14. x = 5
8
15. x = 4
5
16. A cookie recipe calls for 2 cup of brown sugar. Jesse is making 1 of the recipe. How much
3
4
brown sugar will he need?
17. Nancy spent 7 hour working out at the gym. She spent 5 of that time lifting weights. What
8
7
fraction of an hour did she spend lifting weights?
5-5b Multiplying Mixed Numbers
Mixed number to improper fraction review (MAD Wheel)
!
!
1) 1 ! =
!
2) 3 ! =
!
3) 4 ! =
4) 6 !" =
Multiplying Mixed Numbers
1. change the mixed numbers into improper fractions
2. multiply
3. put answer in simplest form
1)
!
!
! !
∙ 1!
!
2) 1 ! ∙ !
!
!
!
!
4) 2 ∙ 1
3)
!
!
!
!
5) 1 ∙ 1
!
!
∙ 2!
!
!
!
!
!
6) 2 ∙ 3
Sometimes the distributive property can be used to solve multiplication problems
!
!
7) 5 ∙ 3 !!
!
8) 3 ∙ 2 !
!
9) 8 ∙ 2 !
!
Milo is making 1 batches of muffins. If one batch calls for 1 cups flour, how much flour will he
!
!
need?
Practice: Find each product – write each answer in simplest form
! !
2) 2 ! ∙ !
! !
! !
5)
1) 1 ! ∙ !
4) 1 ∙
! !
!
!
!
∙1
!
7) 1 ! ∙ 1 !
!
!
3)
!
!"
!
!
!
!
∙ 1!
!
6) 2
!
∙
!
!! !
!
8) 2 ! ∙ 1 !"
10) 2 ! ∙ 1 !
!
9) 4 ∙ 5 !
!
!
11) 2 ! ∙ 5 !
!
12) 10 ! ∙ 1 !
Evaluate each expression
13)
!
!
!
∙ 𝑐 for 𝑐 = 4 !
!
!
14) 1 ! ∙ 𝑥 for 𝑥 = !
!
!
15) 1 ! ∙ 𝑏 for 𝑏 = 1 !
!
16) Josh is training to run in a half-marathon. So far this week, he has run 6 miles on each of three
days. What is the total distance Josh has run this week?
!
Multiplying Mixed Numbers
PRACTICE #1
Multiply. Write each answer in simplest form.
1. 1 • 1 1
3
2
2. 1 1 • 4
5 5
3. 1 1 • 2
4 3
4. 1 1 • 2
8 5
5. 2 • 1 1
5
2
6. 1 3 • 1
5 3
7. 2 • 1 1
4
7
8. 2 • 1 1
3
10
9. 1 • 1 1
8
2
Find each product. Write the answer in simplest form.
10. 4 • 1 1
5
6
11. 3 • 1 1
5
4
12. 1 3 • 1
4 3
13. 2 • 1 1
2
14. 4 • 2 1
4
15. 5 • 1 1
5
16. Lin Li makes two and a half dollars per hour baby-sitting her little brother. How much money will
she make if she baby-sits for 5 hours?
17. Andrea is baking 2 batches of cookies. The recipe calls for 4 1 cups of flour for each batch. How
2
many cups of flour will she use?
Multiplying Mixed Numbers
PRACTICE #2
Multiply. Write each answer in simplest form.
1. 1 2 • 4
3 5
2. 1 7 • 4
8 5
3. 2 3 • 1
4 5
4. 2 1 • 2
6 3
5. 2 2 • 3
5 8
6. 1 3 • 5
4 6
7. 1 1 • 3
6 5
8. 2 • 2 1
9
7
9. 2 3 • 7
11 10
Find each product. Write the answer in simplest form.
10. 6 • 1 1
7
4
11. 5 • 1 3
8
5
12. 2 4 • 1
9 6
13. 1 3 • 1 1
3
10
14. 2 1 • 2 1
2
2
15. 1 2 • 3 1
3
2
16. Dominick lives 1 3 miles from his school. If his mother drives him half the way, how far will
4
Dominick have to walk to get to school?
17. Katoni bought 2 1 dozen donuts to bring to the office. Since there are 12 donuts in a dozen, how
2
many donuts did Katoni buy?
5-6 Dividing Fractions and Mixed Numbers
Vocabulary
__________________ - one of two numbers whose product is 1
Find the reciprocal of the following
1)
!
5)
!
!
=
=
!
2)
!
!
=
3)
6) 5 =
!
!
!
=
4)
!
8) 1 !" =
!"
!
7) 2 ! =
Using Reciprocals to Divide Fractions and Mixed Numbers
*** Dividing by a number is the same as multiplying by its reciprocal ***
𝟏
𝟐𝟒 ÷ 𝟒 = 𝟔
𝟐𝟒 ∙ 𝟒 = 𝟔
Divide: Write each answer in simplest form
1)
!
÷5
2)
!
!
!
÷!
3) 2 ! ÷ 1 !
4)
!
÷7
!
5)
!
!
6) 4 ! ÷ 2 !
!
÷!
!
=
!
!
!
!
!
7. Lisa had some wood that was 12 feet long. She cut it into 5 pieces that are equal in length.
!
How long is each piece of wood?
Practice
Find the reciprocal
1)
!
!
=
2)
!
!
=
!
3)
!
=
4)
!
!!
!
=
5) 2 =
!
Divide: Write each answer in simplest form
6)
!
!
!
!
!
10)
!
!
!
÷
!
!
!
÷ 1!
!
!
!
7) 2 ! ÷ 1 !
!
9) 1 ÷
12)
!
÷3
!
13) 4 ÷ !
!
15) 2 ! ÷ 1 !
16)
!
÷ 12
!
8)
11)
14)
!
!"
÷5
!
!"
!
!
÷1
÷4
!
17) 9 ÷ !
!
!
!
18) Rhula bought 12 lb of raisins. She packed them into freezer bags so that each bag weighs lb.
!
How many freezer bags did she pack?
Dividing Fractions and Mixed Numbers
PRACTICE #1
Find the reciprocal.
1. 1
2
2. 2
3
3. 1
5
4. 1
3
5. 3
5
6. 1 1
4
7. 2
5
8. 3
7
9. 1 1
2
Divide. Write each answer in simplest form.
10. 2 ÷ 2
3
11. 1 ÷ 3
4
2
12. 5 ÷ 1
6
4
13. 3 ÷ 1
5
5
14. 7 ÷ 3
9
15. 1 1 ÷ 1
2
2
16. 8 ÷ 1 5
10
6
17. 8 ÷ 6
9
7
18. 3 3 ÷ 2 1
5
4
19. Stella has 6 pounds of chocolate. She will use 2 pound of the chocolate to make one cake.
3
How many cakes can she make?
20. Todd has 8 pound of clay. He will use 1 pound to make each action figure. How many action
3
9
figures can he make?
21. Dylan gives his two guinea pigs a total of 3 cup of food every day. If each guinea pig gets the
4
same amount of food, how much do they each get each day?
Dividing Fractions and Mixed Numbers
PRACTICE #2
Find the reciprocal.
1. 5
7
2. 9
8
3. 3
5
4. 1
10
5. 4
9
6. 13
14
7. 1 1
3
8. 2 4
5
9. 3 1
6
Divide. Write each answer in simplest form.
10. 5 ÷ 5
6
11. 2 3 ÷ 1 4
4
7
13. 3 1 ÷ 2 3
4
4
14.
16. 2 6 ÷ 6
9
7
17. 5 ÷ 2 3
10
6
9 ÷3
10
12. 7 ÷ 2
8
3
15. 3 ÷ 9
4
18. 2 1 ÷ 3 1
8
4
19. The rope in the school gymnasium is 10 1 feet long. To make it easier to climb, the gym teacher
2
tied a knot in the rope every 3 foot. How many knots are in the rope?
4
20. Mr. Fulton bought 12 1 pounds of ground beef for the cookout. He plans on using 1 pound of
2
4
beef for each hamburger. How many hamburgers can he make?
21. Mrs. Marks has 9 1 ounces of fertilizer for her plants. She plans on using 3 ounce of fertilizer for
4
4
each plant. How many plants can she fertilize?
5-7 Solving Fraction Equations: Multiplication and Division
Solving Equations Review
3𝑥 = 12 8 = 4𝑤 135 = 3𝑦 Solving Fraction Equations - Solve each equation. Write the solution in lowest terms.
A.
!
𝑥 = 14
!
C. 2𝑥 =
E.
!!
!
!
!
=4
!
𝑗 = 25
check
B.
check
D. 7𝑤 =
check
F.
!
!!
!
check
!
check
!
=6
check
!
G. Dexter makes dog biscuits for the animal shelter. He makes of a recipe and uses 15 cups of
!
powdered milk. How many cups of powdered milk are in the recipe?
Practice: Solve each equation. Write the solution in simplest form.
1)
!
!
4) 2𝑐 =
7)
!
𝑧 = 12
2) 4𝑛 = !
!
5)
!"
!
𝑥=3
!
10)
8)
! !
∙ = 4𝑑
! !
!
!
!!
!
!!
3)
!
=5
!
𝑗 = 10
6) 3𝑡 =
=9
9) 8𝑥 = !
!
!
!
!
11) 2𝑦 = ! ÷ !
12) In PE class,
!
!
of the students want to play volleyball. If 9 students want to play volleyball, how
many students are in the class?
Solving Fraction Equations: Multiplication and Division
PRACTICE #1
Solve each equation. Write the answer in simplest form.
1. 1 x = 2
2
2. 2t = 2
3
3. 1 a = 3
3
4. r = 4
2
5. b = 6
3
6. 2y = 1
5
7. 1 d = 2
4
8. b = 6
5
9.
10. 1 s = 4
3
11. h = 2
2
12. 1 c = 1
4
Circle the correct answer.
q
= 1
5
10
13. Tate earned $9 for working 3 of an hour.
4
Which equation can be used to
find Tate’s hourly rate?
A 9h = 3
4
C 3h=9
4
B 9+ 3 =h
4
D 9− 3 =h
4
14. Which operation should you use to solve the
equation 5x = 2?
F addition
G subtraction
H multiplication
J division
15. A number n is divided by 2, and the quotient is 1 . Write an equation to model this problem.
3
16. A number n is multiplied by 1 , and the product is 5. Write and solve an equation to model this
4
problem.
Solving Fraction Equations: Multiplication and Division
PRACTICE #2
Solve each equation. Write the answer in simplest form.
1. 1 x = 6
4
2. 2t = 4
7
3. 3 a = 3
5
4. r = 8
6
5. 2b = 4
9
6. 3y = 4
5
7. 2 d = 5
3
8. 2f = 1
6
9. 4q = 2
9
10. 1 s = 2
2
11. h = 5
7
12. 1 c = 9
4
13. 5g = 5
6
14. 3k = 1
9
15. 3 x = 6
5
16. It takes 3 buckets of water to fill 1 of a fish tank. How many buckets are needed to fill the whole
3
tank?
17. Jenna got 12, or 3 , of her answers on the test right. How many questions were on the test?
5
18. It takes Charles 2 minutes to run 1 of a mile. How long will it take Charles to run a mile?
4