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$3$ $+$ $7 \frac{2}{9}$

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Solution

The given expression contains a whole number and a mixed fraction. To add a whole number and a fraction we express the whole number in a fraction by writing $1$ in the denominator. Then we add the two fractions by converting them into like fractions (or by cross multiplication )
Here, the given whole number is $3$ and fraction is $7 \frac{2}{9}$ . First, converting $7 \frac{2}{9}$ into improper fraction, we have
$7 \frac{2}{9}$ $=$ $\frac{(9 \times 7) + 2}{9} = \frac{65}{9}$
Now, $3$ $+$ $7 \frac{2}{9}$ $=$ $3$ $+$ $\frac{65}{9}$
$=$ $\frac{3}{1} + \frac{65}{9}$ [converting the whole number $3$ into a fraction by taking $1$ as its denominator]
$=$ $\frac{3 \times 9 + 65}{9}$ [ cross multiplying]
$=$ $\frac{27 + 65}{9}$
$=$ $\frac{92}{9}$
Therefore, $3$ $+$ $7 \frac{2}{9}$ $=$ $\frac{92}{9}$

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