Question

Simplify:
$2\frac{1}{4}+\frac{13}{5}÷2\frac{3}{5}-1\frac{1}{3}$
(3 Marks)

Answer 1

Solution:
$1\frac{11}{12}$

Explanation:
Let us convert all the mixed fractions to improper fractions.
$2\frac{1}{4}$ = $\frac{2\times 4+1}{4}$ = $\frac{9}{4}$
$2\frac{3}{5}$ = $\frac{2\times 5+3}{5}$ = $\frac{13}{5}$
$1\frac{1}{3}$ = $\frac{1\times 3+1}{3}$ = $\frac{4}{3}$
(1 Mark)

We will perform division first followed by addition and at last we will perform the subtraction.
$2\frac{1}{4}+\frac{13}{5}÷2\frac{3}{5}-1\frac{1}{3}$ = $\frac{9}{4}+\frac{13}{5}÷\frac{13}{5}-\frac{4}{3}$
= $\frac{9}{4}+1-\frac{4}{3}$

We will make the denominators the same.
The common denominator is 12.
$\frac{9}{4}=\frac{9\times 3}{4\times 3}=\frac{27}{12}$
$1=\frac{1}{1}=\frac{12}{12}$
$\frac{4}{3}=\frac{4\times 4}{3\times 4}=\frac{16}{12}$
(1 Mark)

$2\frac{1}{4}+\frac{13}{5}÷2\frac{3}{5}-1\frac{1}{3}$ = $\frac{27}{12}+\frac{12}{12}-\frac{16}{12}$
= $\frac{27+12-16}{12}$
=$\frac{23}{12}$
=$1\frac{11}{12}$
(1 Mark)