COMPLEX FRACTIONS WORD PROBLEMS WORKSHEET
Problem 1 :
Maya wants to divide a 3/4 pound box of trail mix into small bags. Each bag will hold 1/12 pound of trail mix. How many bags of trail mix can Maya fill ?
Problem 2 :
Cooper's bird feeder holds 9/10 of a cup of birdseed. Cooper is filling the bird feeder with a scoop that holds 3/10 of a cup. How many scoops of birdseed will Cooper put into the feeder?
Problem 3 :
A cookie factory uses 1/6 of a bag of flour in each batch of cookies. The factory used 1/2 of a bag of flour yesterday. How many batches of cookies did the factory make?
Problem 4 :
Sharon uses 1/2 ounces of lemonade to make each cup of a recipe. If she uses 18 ounces of lemonade, how many cups of recipe can she make ?
Solutions
Problem 1 :
Maya wants to divide a 3/4 pound box of trail mix into small bags. Each bag will hold 1/12 pound of trail mix. How many bags of trail mix can Maya fill ?
Solution :
Amount of trail mix each bag holds = 1/12 pound
Given : Each bag will hold 1/12 pound of trail mix.
Then, the number bags required for 3/4 pounds of trail mix is
= (3/4) / (1/12)
In the above complex fraction, change the division as multiplication and take reciprocal of the fraction in denominator.
= 3/4 ⋅ 12/1
Simplify.
= (3 ⋅ 12) / (4 ⋅ 1)
= (3 ⋅ 3) / (1 ⋅ 1)
= 9 / 1
= 9
So, Maya can fill 3/4 pound of trail mix in 9 bags.
Problem 2 :
Cooper's bird feeder holds 9/10 of a cup of birdseed. Cooper is filling the bird feeder with a scoop that holds 3/10 of a cup. How many scoops of birdseed will Cooper put into the feeder?
Solution :
Amount of seeds bird feeder holds = 9/10 of a cup
Given : Cooper is filling the bird feeder with a scoop that holds 3/10 of a cup.
Then, the number of scoops of birdseed will Cooper put into the feeder is
= (9/10) / (3/10)
In the above complex fraction, change the division as multiplication and take reciprocal of the fraction in denominator.
= 9/10 ⋅ 10/3
Simplify.
= (9 ⋅ 10) / (10 ⋅ 3)
= (3 ⋅ 1) / (1 ⋅ 1)
= 3 / 1
= 3
So, Cooper will put 3 scoops of birdseed into the feeder.
Problem 3 :
A cookie factory uses 1/6 of a bag of flour in each batch of cookies. The factory used 1/2 of a bag of flour yesterday. How many batches of cookies did the factory make?
Solution :
Flour used in each batch of cookies = 1/6 of a bag
Given : The factory used 1/2 of a bag of flour yesterday.
Then, the number of batches of cookies the factory made yesterday :
= (1/2) / (1/6)
In the above complex fraction, change the division as multiplication and take reciprocal of the fraction in denominator.
= 1/2 ⋅ 6/1
Simplify.
= (1 ⋅ 6) / (2 ⋅ 1)
= (1 ⋅ 3) / (1 ⋅ 1)
= 3 / 1
= 3
So, 3 batches of cookies the factory made yesterday.
Problem 4 :
Sharon uses 1/2 ounces of lemonade to make each cup of a recipe. If she uses 18 ounces of lemonade, how many cups of recipe can she make ?
Solution :
Lemonade used for each cup of recipe = 1/2 ounces
Given : Sharon uses 18 ounces of lemonade
Then, the number of cups of recipe can be made with 18 ounces of lemonade is
= 18 / (1/2)
In the above complex fraction, change the division as multiplication and take reciprocal of the fraction in denominator.
18 / (1/2) = 18 ⋅ 2/1
Simplify.
18 / (1/2) = (18 ⋅ 2) / 1
18 / (1/2) = 36 / 1
18 / (1/2) = 36
So, Sharon can make 36 cups recipe with 18 ounces of lemonade.
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