Question

use >, <, or = to make the statement true.
$4 \frac{9}{10} - 1 \frac{1}{8} \square 2 \frac{1}{2} + \frac{2}{7}$
$\boldsymbol{>}$ $\boldsymbol{<}$ $\boldsymbol{=}$

Explanation:

Step1: Convert mixed numbers to improper fractions

Left side: $4\frac{9}{10} = \frac{49}{10}$, $1\frac{1}{8} = \frac{9}{8}$
Right side: $2\frac{1}{2} = \frac{5}{2}$, $\frac{2}{7}$ remains as is

Step2: Calculate left side difference

Find common denominator (40):
$\frac{49}{10} - \frac{9}{8} = \frac{49\times4}{40} - \frac{9\times5}{40} = \frac{196 - 45}{40} = \frac{151}{40} = 3.775$

Step3: Calculate right side sum

Find common denominator (14):
$\frac{5}{2} + \frac{2}{7} = \frac{5\times7}{14} + \frac{2\times2}{14} = \frac{35 + 4}{14} = \frac{39}{14} \approx 2.786$

Step4: Compare the two results

$3.775 > 2.786$

Answer:

$4\frac{9}{10} - 1\frac{1}{8} > 2\frac{1}{2} + \frac{2}{7}$
The correct symbol is $>$