Working with Fractions

Multiplying and dividing fractions and mixed numbers, reciprocals, and finding a fraction of an amount.

Key ideas

Multiply fractions by multiplying the numerators and multiplying the denominators; cancel common factors first.
Change mixed numbers to improper fractions before multiplying or dividing.
“Of” means multiply: 2/3 of 60 = 2/3 × 60 = 40.
The reciprocal of a/b is b/a; a number times its reciprocal is 1.
To divide by a fraction, multiply by its reciprocal.
Multiplying by a proper fraction makes a number smaller; dividing by it makes the number bigger.

Remember

Multiplying	a/b × c/d = (a × c)/(b × d)
Dividing	a/b ÷ c/d = a/b × d/c
Mixed number	2 1/3 = (2 × 3 + 1)/3 = 7/3

Watch out

Multiplying the whole numbers and fractions of mixed numbers separately.
Turning the first fraction upside down instead of the second when dividing.
Taking the second fraction of the whole amount instead of what is left.

Worked example

A family earns Rs 34,740 a month. They spend 1/3 of it on rent and 1/2 of what is left on food. How much do they spend on rent, on food, and how much is left?

Working: 1/3 × 34740 = 11580; 1/2 × 23160 = 11580

Answer: rent Rs 11,580, food Rs 11,580, left Rs 11,580