Simplify the expression: -1/4 + 5/12. Class 9

Simplify the expression: -1/4 + 5/12. Class 9

Question 1.

Simplify the expression: $\left(-\frac{1}{4}\right)+\left(\frac{5}{12}\right)$. Class 9

Solution:

$-\frac{1}{4}+\frac{5}{12}=-\frac{1}{4} \times \frac{3}{3}+\frac{5}{12}$ ...[L.C.M. of 4 and 12 is 12]

$\begin{aligned} & =\frac{-3}{12}+\frac{5}{12} \\ & =\frac{-3+5}{12}=\frac{2}{12} \\ \therefore \quad-\frac{1}{4}+\frac{5}{12} & =\frac{1}{6}\end{aligned}$

Question 2.

A tailor has $15 \frac{3}{4}$ metres of fine silk. If making one kurta requires $2 \frac{1}{4}$ metres of silk, exactly how many kurtas can he make? Class 9

Solution:

Total silk = $15 \frac{3}{4}$ m = $\frac{15 \times 4+3}{4}$ m = $\frac{63}{4}$ m

Silk required for one kurta

$=2 \frac{1}{4} \mathrm{~m}=\frac{2 \times 4+1}{4} \mathrm{~m}=\frac{9}{4} \mathrm{~m}$

Number of kurtas that can be made

$\begin{aligned} & =\frac{\text { Total silk }}{\text { Silk required for one kurta }} \\ & =\frac{63}{4} \div \frac{9}{4} \\ & =\frac{63}{4} \times \frac{4}{9}=\frac{63 \times 1}{1 \times 9}=7\end{aligned}$

∴ 7 kurtas can be made from $15 \frac{3}{4}$ m silk.