COMPLEX FRACTIONS WORD PROBLEMS
About "Complex fractions word problems"
Complex fractions word problems :
A complex-fraction is a fraction that has a fraction in its numerator, denominator, or both.
Example : (a/b) / (c/d) or a/b ÷ c/d
In this section, we are going to see how word problems on complex fractions can be solved.
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 :
Step 1 :
To get answer for the above question, we have to divide 3/4 by 1/12.
That is, we have to find the value of (3/4) / (1/12).
Step 2 :
Determine the sign of the quotient.
The quotient will be positive, because the signs of both numerator (3/4) and denominator (1/12) are same.
Step 3 :
Write the complex fraction as division :
(3/4) / (1/12) = (3/4) ÷ (1/12)
Step 4 :
Rewrite the above division as multiplication by taking the reciprocal of the second fraction.
(3/4) ÷ (1/12) = (3/4) x (12/1)
Step 5 :
Simplify
(3/4) x (12/1) = (3/1) x (3/1)
(3/4) x (12/1) = 9
Hence, Maya can fill 9 bags of trail mix.
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 :
Step 1 :
To get answer for the above question, divide the total amount of birdseed by the size of each scoop.
That is, we have to find the value of (9/10) / (3/10).
Step 2 :
Determine the sign of the quotient.
The quotient will be positive, because the signs of both numerator (9/10) and denominator (3/10) are same.
Step 3 :
Write the complex fraction as division :
(9/10) / (3/10) = (9/10) ÷ (3/10)
Step 4 :
Rewrite the above division as multiplication by taking the reciprocal of the second fraction.
(9/10) ÷ (3/10) = (9/10) x (10/3)
Step 5 :
Simplify
(9/10) x (10/3) = (3/1) x (1/1)
(9/10) x (10/3) = 3
Hence, 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 :
Step 1 :
To get answer for the above question, divide the total amount of flour used by the amount used in each batch.
That is, we have to find the value of (1/2) / (1/6).
Step 2 :
Determine the sign of the quotient.
The quotient will be positive, because the signs of both numerator (1/2) and denominator (1/6) are same.
Step 3 :
Write the complex fraction as division :
(1/2) / (1/6) = (1/2) ÷ (1/6)
Step 4 :
Rewrite the above division as multiplication by taking the reciprocal of the second fraction.
(1/2) ÷ (1/6) = (1/2) x (6/1)
Step 5 :
Simplify
(1/2) x (6/1) = (1/1) x (3/1)
(1/2) x (6/1) = 3
Hence, the factory made 3 batches of cookies yesterday.
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