Basic Math Examples

\frac{5}{12} + \frac{4}{15}

$\frac{5}{12} + \frac{4}{15}$

Step 1

To write

\frac{5}{12}

$\frac{5}{12}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5}{12} \cdot \frac{5}{5} + \frac{4}{15}

$\frac{5}{12} \cdot \frac{5}{5} + \frac{4}{15}$

Step 2

To write

\frac{4}{15}

$\frac{4}{15}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{5}{12} \cdot \frac{5}{5} + \frac{4}{15} \cdot \frac{4}{4}

$\frac{5}{12} \cdot \frac{5}{5} + \frac{4}{15} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of

60

$60$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{12}

$\frac{5}{12}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{5 \cdot 5}{12 \cdot 5} + \frac{4}{15} \cdot \frac{4}{4}

$\frac{5 \cdot 5}{12 \cdot 5} + \frac{4}{15} \cdot \frac{4}{4}$

Step 3.2

Multiply

12

$12$ by

5

$5$ .

\frac{5 \cdot 5}{60} + \frac{4}{15} \cdot \frac{4}{4}

$\frac{5 \cdot 5}{60} + \frac{4}{15} \cdot \frac{4}{4}$

Step 3.3

Multiply

\frac{4}{15}

$\frac{4}{15}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{5 \cdot 5}{60} + \frac{4 \cdot 4}{15 \cdot 4}

$\frac{5 \cdot 5}{60} + \frac{4 \cdot 4}{15 \cdot 4}$

Step 3.4

Multiply

15

$15$ by

4

$4$ .

\frac{5 \cdot 5}{60} + \frac{4 \cdot 4}{60}

$\frac{5 \cdot 5}{60} + \frac{4 \cdot 4}{60}$

\frac{5 \cdot 5}{60} + \frac{4 \cdot 4}{60}

$\frac{5 \cdot 5}{60} + \frac{4 \cdot 4}{60}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 5 + 4 \cdot 4}{60}

$\frac{5 \cdot 5 + 4 \cdot 4}{60}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

5

$5$ .

\frac{25 + 4 \cdot 4}{60}

$\frac{25 + 4 \cdot 4}{60}$

Step 5.2

Multiply

4

$4$ by

4

$4$ .

\frac{25 + 16}{60}

$\frac{25 + 16}{60}$

Step 5.3

Add

25

$25$ and

16

$16$ .

\frac{41}{60}

$\frac{41}{60}$

\frac{41}{60}

$\frac{41}{60}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{41}{60}

$\frac{41}{60}$

Decimal Form:

0.68\overline{3}

$0.68\overline{3}$