Basic Math Examples

3 \frac{2}{5} + 5 \frac{2}{3}

$3 \frac{2}{5} + 5 \frac{2}{3}$

Step 1

Convert

3 \frac{2}{5}

$3 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

3 + \frac{2}{5} + 5 \frac{2}{3}

$3 + \frac{2}{5} + 5 \frac{2}{3}$

Step 1.2

Add

3

$3$ and

\frac{2}{5}

$\frac{2}{5}$ .

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Step 1.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

3 \cdot \frac{5}{5} + \frac{2}{5} + 5 \frac{2}{3}

$3 \cdot \frac{5}{5} + \frac{2}{5} + 5 \frac{2}{3}$

Step 1.2.2

Combine

3

$3$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 \cdot 5}{5} + \frac{2}{5} + 5 \frac{2}{3}

$\frac{3 \cdot 5}{5} + \frac{2}{5} + 5 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{3 \cdot 5 + 2}{5} + 5 \frac{2}{3}

$\frac{3 \cdot 5 + 2}{5} + 5 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

5

$5$ .

\frac{15 + 2}{5} + 5 \frac{2}{3}

$\frac{15 + 2}{5} + 5 \frac{2}{3}$

Step 1.2.4.2

Add

15

$15$ and

2

$2$ .

\frac{17}{5} + 5 \frac{2}{3}

$\frac{17}{5} + 5 \frac{2}{3}$

\frac{17}{5} + 5 \frac{2}{3}

$\frac{17}{5} + 5 \frac{2}{3}$

\frac{17}{5} + 5 \frac{2}{3}

$\frac{17}{5} + 5 \frac{2}{3}$

\frac{17}{5} + 5 \frac{2}{3}

$\frac{17}{5} + 5 \frac{2}{3}$

Step 2

Convert

5 \frac{2}{3}

$5 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

\frac{17}{5} + 5 + \frac{2}{3}

$\frac{17}{5} + 5 + \frac{2}{3}$

Step 2.2

Add

5

$5$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{17}{5} + 5 \cdot \frac{3}{3} + \frac{2}{3}

$\frac{17}{5} + 5 \cdot \frac{3}{3} + \frac{2}{3}$

Step 2.2.2

Combine

5

$5$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{17}{5} + \frac{5 \cdot 3}{3} + \frac{2}{3}

$\frac{17}{5} + \frac{5 \cdot 3}{3} + \frac{2}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{17}{5} + \frac{5 \cdot 3 + 2}{3}

$\frac{17}{5} + \frac{5 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

5

$5$ by

3

$3$ .

\frac{17}{5} + \frac{15 + 2}{3}

$\frac{17}{5} + \frac{15 + 2}{3}$

Step 2.2.4.2

Add

15

$15$ and

2

$2$ .

\frac{17}{5} + \frac{17}{3}

$\frac{17}{5} + \frac{17}{3}$

\frac{17}{5} + \frac{17}{3}

$\frac{17}{5} + \frac{17}{3}$

\frac{17}{5} + \frac{17}{3}

$\frac{17}{5} + \frac{17}{3}$

\frac{17}{5} + \frac{17}{3}

$\frac{17}{5} + \frac{17}{3}$

Step 3

To write

\frac{17}{5}

$\frac{17}{5}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{17}{5} \cdot \frac{3}{3} + \frac{17}{3}

$\frac{17}{5} \cdot \frac{3}{3} + \frac{17}{3}$

Step 4

To write

\frac{17}{3}

$\frac{17}{3}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{17}{5} \cdot \frac{3}{3} + \frac{17}{3} \cdot \frac{5}{5}

$\frac{17}{5} \cdot \frac{3}{3} + \frac{17}{3} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{17}{5}

$\frac{17}{5}$ by

$\frac{3}{3}$ .

$\frac{17 \cdot 3}{5 \cdot 3} + \frac{17}{3} \cdot \frac{5}{5}$

Step 5.2

Multiply

$5$ by

$3$ .

$\frac{17 \cdot 3}{15} + \frac{17}{3} \cdot \frac{5}{5}$

Step 5.3

Multiply

$\frac{17}{3}$ by

$\frac{5}{5}$ .

$\frac{17 \cdot 3}{15} + \frac{17 \cdot 5}{3 \cdot 5}$

Step 5.4

Multiply

$3$ by

$5$ .

$\frac{17 \cdot 3}{15} + \frac{17 \cdot 5}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{17 \cdot 3 + 17 \cdot 5}{15}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$17$ by

$3$ .

$\frac{51 + 17 \cdot 5}{15}$

Step 7.2

Multiply

$17$ by

$5$ .

$\frac{51 + 85}{15}$

Step 7.3

Add

$51$ and

$85$ .

$\frac{136}{15}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{136}{15}$

Decimal Form:

$9.0\overline{6}$

Mixed Number Form:

$9 \frac{1}{15}$