Basic Math Examples

5 \frac{1}{3} + \frac{2}{5}

$5 \frac{1}{3} + \frac{2}{5}$

Step 1

Convert

$5 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$5 + \frac{1}{3} + \frac{2}{5}$

Step 1.2

Add

$5$ and

$\frac{1}{3}$ .

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Step 1.2.1

To write

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

$\frac{3}{3}$ .

$5 \cdot \frac{3}{3} + \frac{1}{3} + \frac{2}{5}$

Step 1.2.2

Combine

$5$ and

$\frac{3}{3}$ .

$\frac{5 \cdot 3}{3} + \frac{1}{3} + \frac{2}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 1}{3} + \frac{2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$5$ by

$3$ .

$\frac{15 + 1}{3} + \frac{2}{5}$

Step 1.2.4.2

Add

$15$ and

$1$ .

$\frac{16}{3} + \frac{2}{5}$

Step 2

To write

$\frac{16}{3}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{16}{3} \cdot \frac{5}{5} + \frac{2}{5}$

Step 3

To write

$\frac{2}{5}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{16}{3} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of

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

$1$ .

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Step 4.1

Multiply

$\frac{16}{3}$ by

$\frac{5}{5}$ .

$\frac{16 \cdot 5}{3 \cdot 5} + \frac{2}{5} \cdot \frac{3}{3}$

Step 4.2

Multiply

$3$ by

$5$ .

$\frac{16 \cdot 5}{15} + \frac{2}{5} \cdot \frac{3}{3}$

Step 4.3

Multiply

$\frac{2}{5}$ by

$\frac{3}{3}$ .

$\frac{16 \cdot 5}{15} + \frac{2 \cdot 3}{5 \cdot 3}$

Step 4.4

Multiply

$5$ by

$3$ .

$\frac{16 \cdot 5}{15} + \frac{2 \cdot 3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{16 \cdot 5 + 2 \cdot 3}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$16$ by

$5$ .

$\frac{80 + 2 \cdot 3}{15}$

Step 6.2

Multiply

$2$ by

$3$ .

$\frac{80 + 6}{15}$

Step 6.3

Add

$80$ and

$6$ .

$\frac{86}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{86}{15}$

Decimal Form:

$5.7\overline{3}$

Mixed Number Form:

$5 \frac{11}{15}$