Question

Solve:
$\left(iii\right)$ $\frac{z}{7}+1=2\frac{1}{2}$

Answer 1

Convert mixed fraction into improper fraction

Given,

$\frac{z}{7}+1=2\frac{1}{2}$

$\Rightarrow \frac{z}{7}+1=\frac{(2\times 2)+1}{2}$

$\Rightarrow \frac{z}{7}+1=\frac{4+1}{2}$

$\Rightarrow \frac{z}{7}+1=\frac{5}{2}$

Subtracting each side by $1$

$\frac{z}{7}+1-1=\frac{5}{2}-1$

$\Rightarrow \frac{z}{7}=\frac{5-(1\times 2)}{2}$

$\Rightarrow \frac{z}{7}=\frac{5-2}{2}$

$\frac{z}{7}=\frac{3}{2}$

Multiplying each side by $7$

$\frac{z}{7}\times 7=\frac{3}{2}\times 7$

$\Rightarrow z=\frac{3\times 7}{2}=\frac{21}{2}$

$\Rightarrow z=10\frac{1}{2}$

Hence, the value of $z$ is $10\frac{1}{2}.$