COMPLEX FRACTIONS
About "Complex fractions"
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
Complex-fractions - Practice problems
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.
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