COMPLEX FRACTIONS WORD PROBLEMS

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. 

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