Question

$\text{Choose the expression whose value is}1\frac{1}{8}$

• A. $2\frac{1}{4}+3\frac{1}{2}-4\frac{3}{8}$
• B. $2\frac{1}{4}+3\frac{1}{2}-4\frac{5}{8}$
• C. $2\frac{1}{4}+2\frac{1}{2}-4\frac{3}{8}$
• D. $2\frac{1}{4}+2\frac{1}{2}-4\frac{5}{8}$

Answer 1

The correct option is B $2\frac{1}{4}+3\frac{1}{2}-4\frac{5}{8}$

$\text{To find the correct expression, we}\text{calculate the value of each of the}\text{expressions.}$

$Expression1:$

$2\frac{1}{4}+3\frac{1}{2}-4\frac{3}{8}$

$=(2+3-4)+(\frac{1}{4}+\frac{1}{2}-\frac{3}{8})$

$=1+(\frac{2}{8}+\frac{4}{8}-\frac{3}{8})$

$=1+\frac{3}{8}=1\frac{3}{8}$

$\therefore 2\frac{1}{4}+3\frac{1}{2}-4\frac{3}{8}=1\frac{3}{8}$

$Expression2:$

$2\frac{1}{4}+3\frac{1}{2}-4\frac{5}{8}$

$=(2+3-4)+(\frac{1}{4}+\frac{1}{2}-\frac{5}{8})$

$=1+(\frac{2}{8}+\frac{4}{8}-\frac{5}{8})$

$=1+\frac{1}{8}=1\frac{1}{8}$

$\therefore 2\frac{1}{4}+3\frac{1}{2}-4\frac{5}{8}=1\frac{1}{8}$

$Expression3:$

$2\frac{1}{4}+2\frac{1}{2}-4\frac{3}{8}$

$=(2+2-4)+(\frac{1}{4}+\frac{1}{2}-\frac{3}{8})$

$=0+(\frac{2}{8}+\frac{4}{8}-\frac{3}{8})$

$=0+\frac{3}{8}=\frac{3}{8}$

$\therefore 2\frac{1}{4}+2\frac{1}{2}-4\frac{3}{8}=\frac{3}{8}$

$Expression4:$

$2\frac{1}{4}+2\frac{1}{2}-4\frac{5}{8}$

$=(2+2-4)+(\frac{1}{4}+\frac{1}{2}-\frac{5}{8})$

$=0+(\frac{2}{8}+\frac{4}{8}-\frac{5}{8})$

$=0+\frac{1}{8}=\frac{1}{8}$

$\therefore 2\frac{1}{4}+2\frac{1}{2}-4\frac{5}{8}=\frac{1}{8}$

$\text{Hence, the expression with the value}1\frac{1}{8}\text{is}2\frac{1}{4}+3\frac{1}{2}-4\frac{5}{8}$