**Complex fractions :**

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

**Problem 1 : **

Find the value of (2/5) / (7/15)

**Solution : **

**Step 1 : **

Determine the sign of the quotient.

The quotient will be positive, because the signs of both numerator (2/5) and denominator (7/15) are same.

**Step 2 : **

Write the complex fraction as division :

(2/5) / (7/15) = (2/5) ÷ (7/15)

**Step 3 : **

Rewrite the above division as multiplication by taking the reciprocal of the second fraction.

(2/5) ÷ (7/15) = (2/5) x (15/7)

**Step 4 : **

Simplify

(2/5) x (15/7) = (2/1) x (3/7)

(2/5) x (15/7) = 6/7

**Problem 2 : **

Find the value of (7/10) / (-1/5)

**Solution : **

**Step 1 : **

Determine the sign of the quotient.

The quotient will be negative, because the signs are different.

**Step 2 : **

Write the complex-fraction as division :

(7/10) / (-1/5) = (7/10) ÷ (-1/5)

**Step 3 : **

Rewrite the above division as multiplication by taking the reciprocal of the second fraction.

(7/10) ÷ (-1/5) = (7/10) x (-5/1)

**Step 4 : **

Simplify

(7/10) x (-5/1) = (7/2) x (-1/1)

(7/10) x (-5/1) = -7/2

**Problem 3 : **

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.

After having gone through the stuff given above, we hope that the students would have understood "Complex-fraction".

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