A mixed number is an addition of its whole and fractional parts.

Add <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>9</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>27</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

A mixed number is an addition of its whole and fractional parts.

Add <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>8</mn></mrow><mrow><mn>31</mn></mrow></mfrac></mstyle></math> .

To write <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>31</mn></mrow><mrow><mn>31</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>31</mn></mrow><mrow><mn>31</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>31</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>217</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>8</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>31</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>225</mn></mrow><mrow><mn>31</mn></mrow></mfrac></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>225</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

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