**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.

**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.

After having gone through the stuff given above, we hope that the students would have understood "Complex fractions word problems".

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