Question

A family spends 1/3 of its income for the mortgage and 1/6 of its income for food. What proportion of its income remains?

Answer 1

Answer:

1/2

Step-by-step explanation:

Since we're dealing with fractions, the total fraction is 1

Mortgage =1/3

Food =1/6

Fraction of income left=x

So we equate everything above to 1

$\frac{1}{3} + \frac{1}{6} + x = 1$

$\frac{1}{3} + \frac{1}{6} + x = 1 \\ lcm = 6 \\ multiply \: each \: term \: by \: 6 \\ 6 \times \frac{1}{3} + 6 \times \frac{1}{6} + 6(x) = 6(1)$

$= > 2(1) + 1(1) + 6x = 6 \\ 2 + 1 + 6x = 6 \\ 3 + 6x = 6$

$6x = 6 - 3 \\ 6x = 3 \\ x = \frac{3}{6} = \frac{1}{2}$

Answer 2

Answer: 1/2

Step-by-step explanation:

1/3 = 2/6 so 2/6 + 1/6 = 3/6

3/6 = 1/2