Basic Math Examples

\frac{5}{8} + \frac{2}{3}

$\frac{5}{8} + \frac{2}{3}$

Step 1

To write

\frac{5}{8}

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5}{8} \cdot \frac{3}{3} + \frac{2}{3}

$\frac{5}{8} \cdot \frac{3}{3} + \frac{2}{3}$

Step 2

To write

\frac{2}{3}

$\frac{2}{3}$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{5}{8} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{8}{8}

$\frac{5}{8} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{8}{8}$

Step 3

Write each expression with a common denominator of

24

$24$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{5}{8}

$\frac{5}{8}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{5 \cdot 3}{8 \cdot 3} + \frac{2}{3} \cdot \frac{8}{8}

$\frac{5 \cdot 3}{8 \cdot 3} + \frac{2}{3} \cdot \frac{8}{8}$

Step 3.2

Multiply

8

$8$ by

3

$3$ .

\frac{5 \cdot 3}{24} + \frac{2}{3} \cdot \frac{8}{8}

$\frac{5 \cdot 3}{24} + \frac{2}{3} \cdot \frac{8}{8}$

Step 3.3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{5 \cdot 3}{24} + \frac{2 \cdot 8}{3 \cdot 8}

$\frac{5 \cdot 3}{24} + \frac{2 \cdot 8}{3 \cdot 8}$

Step 3.4

Multiply

3

$3$ by

8

$8$ .

\frac{5 \cdot 3}{24} + \frac{2 \cdot 8}{24}

$\frac{5 \cdot 3}{24} + \frac{2 \cdot 8}{24}$

\frac{5 \cdot 3}{24} + \frac{2 \cdot 8}{24}

$\frac{5 \cdot 3}{24} + \frac{2 \cdot 8}{24}$

Step 4

Combine the numerators over the common denominator.

\frac{5 \cdot 3 + 2 \cdot 8}{24}

$\frac{5 \cdot 3 + 2 \cdot 8}{24}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

5

$5$ by

3

$3$ .

\frac{15 + 2 \cdot 8}{24}

$\frac{15 + 2 \cdot 8}{24}$

Step 5.2

Multiply

2

$2$ by

8

$8$ .

\frac{15 + 16}{24}

$\frac{15 + 16}{24}$

Step 5.3

Add

15

$15$ and

16

$16$ .

\frac{31}{24}

$\frac{31}{24}$

\frac{31}{24}

$\frac{31}{24}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{31}{24}

$\frac{31}{24}$

Decimal Form:

1.291 ¯ 6

$1.291\overline{6}$

Mixed Number Form:

1 \frac{7}{24}

$1 \frac{7}{24}$