Question

Fill in the blanks with $>,=$or $<$ sign.

$7\frac{1}{3}\square 1\frac{1}{3}$

Answer 1

Given : $7\frac{1}{3}\square 1\frac{1}{3}$

Here we have two mixed fractions, so converting them into an improper fraction

$7\frac{1}{3}$ $=$$\frac{3\times 7+1}{3}$$=$$\frac{21+1}{3}$$=$$\frac{22}{3}$

$1\frac{1}{3}$ $=$$\frac{1\times 3+1}{3}$$=$$\frac{3+1}{3}$$=$$\frac{4}{3}$

Now according to the question we have to compare the two fractions.

$7\frac{1}{3}\square 1\frac{1}{3}$

$\frac{22}{3}$ $\square$$\frac{4}{3}$ $\left(\therefore 7\frac{1}{3}=\frac{22}{3},1\frac{1}{3}=\frac{4}{3}\right)$

Using the cross product method

$22\times 3\square 4\times 3$

$$\begin{gathered} 66\square 12 \\ 66>12 \end{gathered}$$

Therefore, $7\frac{1}{3}>1\frac{1}{3}$