Question

$\text{Help Anna with her homework by finding the}\text{correct expression whose final value is}$
$2\frac{1}{4}$ .

• A. $7\frac{7}{8}-5\frac{1}{4}$
• B. $7\frac{5}{8}-6\frac{1}{8}$
• C. $8\frac{3}{4}-5\frac{1}{8}$
• D. $7\frac{7}{8}-5\frac{5}{8}$

Answer 1

The correct option is D $7\frac{7}{8}-5\frac{5}{8}$

To find the correct expression, we need to calculate the difference of each pair of fractions.

For the first option, we see:
$\text{Calculating}7\frac{7}{8}-5\frac{1}{4}\text{, we get:}$

$Wholenumberpart=7-5=2$

$Fractionalpart=\frac{7}{8}-\frac{1}{4}=\frac{7}{8}-\frac{1\times 2}{4\times 2}=\frac{7}{8}-\frac{2}{8}=\frac{5}{8}$

Combining the two parts, we get:
$7\frac{7}{8}-5\frac{1}{4}=2\frac{5}{8}$


For the second option, we see:
$\text{Calculating}7\frac{5}{8}-6\frac{1}{8}\text{, we get:}$

$Wholenumberpart=7-6=1$

$Fractionalpart=\frac{5}{8}-\frac{1}{8}=\frac{6}{8}=\frac{3}{4}$

Combining the whole number and the fractional parts, we get:
$7\frac{5}{8}-6\frac{1}{8}=1\frac{3}{4}$


For the third option, we see:
$\text{Calculating}8\frac{3}{4}-5\frac{1}{8}\text{, we get:}$

$Wholenumberpart=8-5=3$

$Fractionalpart=\frac{3}{4}-\frac{1}{8}=\frac{3\times 2}{4\times 2}-\frac{1}{8}=\frac{6}{8}-\frac{1}{8}=\frac{5}{8}$

Combining the whole number and the fractional parts, we get:
$8\frac{3}{4}-5\frac{1}{8}=3\frac{5}{8}$


$\text{Finally, calculating}7\frac{7}{8}-5\frac{5}{8}\text{we get:}$

$Wholenumberpart=7-5=2$

$Fractionalpart=\frac{7}{8}-\frac{5}{8}=\frac{2}{8}=\frac{2÷2}{8÷2}=\frac{1}{4}$

Combining the whole number and the fractional parts, we get:
$7\frac{7}{8}-5\frac{5}{8}=2\frac{1}{4}$

$\therefore \text{The expression with the final value}$
$\text{as}2\frac{1}{4}\text{is}7\frac{7}{8}-5\frac{5}{8}$