Basic Math Examples

\frac{3}{5} + \frac{5}{8}

$\frac{3}{5} + \frac{5}{8}$

Step 1

To write

\frac{3}{5}

$\frac{3}{5}$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{3}{5} \cdot \frac{8}{8} + \frac{5}{8}

$\frac{3}{5} \cdot \frac{8}{8} + \frac{5}{8}$

Step 2

To write

\frac{5}{8}

$\frac{5}{8}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3}{5} \cdot \frac{8}{8} + \frac{5}{8} \cdot \frac{5}{5}

$\frac{3}{5} \cdot \frac{8}{8} + \frac{5}{8} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of

40

$40$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{5}

$\frac{3}{5}$ by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{3 \cdot 8}{5 \cdot 8} + \frac{5}{8} \cdot \frac{5}{5}

$\frac{3 \cdot 8}{5 \cdot 8} + \frac{5}{8} \cdot \frac{5}{5}$

Step 3.2

Multiply

5

$5$ by

8

$8$ .

\frac{3 \cdot 8}{40} + \frac{5}{8} \cdot \frac{5}{5}

$\frac{3 \cdot 8}{40} + \frac{5}{8} \cdot \frac{5}{5}$

Step 3.3

Multiply

\frac{5}{8}

$\frac{5}{8}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{3 \cdot 8}{40} + \frac{5 \cdot 5}{8 \cdot 5}

$\frac{3 \cdot 8}{40} + \frac{5 \cdot 5}{8 \cdot 5}$

Step 3.4

Multiply

8

$8$ by

5

$5$ .

\frac{3 \cdot 8}{40} + \frac{5 \cdot 5}{40}

$\frac{3 \cdot 8}{40} + \frac{5 \cdot 5}{40}$

\frac{3 \cdot 8}{40} + \frac{5 \cdot 5}{40}

$\frac{3 \cdot 8}{40} + \frac{5 \cdot 5}{40}$

Step 4

Combine the numerators over the common denominator.

\frac{3 \cdot 8 + 5 \cdot 5}{40}

$\frac{3 \cdot 8 + 5 \cdot 5}{40}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

3

$3$ by

8

$8$ .

\frac{24 + 5 \cdot 5}{40}

$\frac{24 + 5 \cdot 5}{40}$

Step 5.2

Multiply

5

$5$ by

5

$5$ .

\frac{24 + 25}{40}

$\frac{24 + 25}{40}$

Step 5.3

Add

24

$24$ and

25

$25$ .

\frac{49}{40}

$\frac{49}{40}$

\frac{49}{40}

$\frac{49}{40}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{49}{40}

$\frac{49}{40}$

Decimal Form:

1.225

$1.225$

Mixed Number Form:

1 \frac{9}{40}

$1 \frac{9}{40}$