Question

choose the correct symbol to make the following statement true. $5\frac{4}{5}+2\frac{1}{3}\square 8\frac{3}{4}$ with options =, <, >

Explanation:

Step1: Convert mixed numbers to improper fractions

$5\frac{4}{5}=\frac{5\times5 + 4}{5}=\frac{29}{5}$, $2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3}$, $8\frac{3}{4}=\frac{8\times4 + 3}{4}=\frac{35}{4}$

Step2: Add the first two fractions

Find a common denominator (15) for $\frac{29}{5}$ and $\frac{7}{3}$:
$\frac{29}{5}+\frac{7}{3}=\frac{29\times3}{15}+\frac{7\times5}{15}=\frac{87 + 35}{15}=\frac{122}{15}$

Step3: Compare $\frac{122}{15}$ and $\frac{35}{4}$

Find a common denominator (60):
$\frac{122}{15}=\frac{122\times4}{60}=\frac{488}{60}$, $\frac{35}{4}=\frac{35\times15}{60}=\frac{525}{60}$
Since $\frac{488}{60}<\frac{525}{60}$

Answer:

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