Basic Math Examples

\frac{7}{8} + \frac{5}{12}

$\frac{7}{8} + \frac{5}{12}$

Step 1

To write

\frac{7}{8}

$\frac{7}{8}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7}{8} \cdot \frac{3}{3} + \frac{5}{12}

$\frac{7}{8} \cdot \frac{3}{3} + \frac{5}{12}$

Step 2

To write

\frac{5}{12}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7}{8} \cdot \frac{3}{3} + \frac{5}{12} \cdot \frac{2}{2}

$\frac{7}{8} \cdot \frac{3}{3} + \frac{5}{12} \cdot \frac{2}{2}$

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{7}{8}

$\frac{7}{8}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{7 \cdot 3}{8 \cdot 3} + \frac{5}{12} \cdot \frac{2}{2}

$\frac{7 \cdot 3}{8 \cdot 3} + \frac{5}{12} \cdot \frac{2}{2}$

Step 3.2

Multiply

8

$8$ by

3

$3$ .

\frac{7 \cdot 3}{24} + \frac{5}{12} \cdot \frac{2}{2}

$\frac{7 \cdot 3}{24} + \frac{5}{12} \cdot \frac{2}{2}$

Step 3.3

Multiply

\frac{5}{12}

$\frac{5}{12}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{7 \cdot 3}{24} + \frac{5 \cdot 2}{12 \cdot 2}

$\frac{7 \cdot 3}{24} + \frac{5 \cdot 2}{12 \cdot 2}$

Step 3.4

Multiply

12

$12$ by

2

$2$ .

\frac{7 \cdot 3}{24} + \frac{5 \cdot 2}{24}

$\frac{7 \cdot 3}{24} + \frac{5 \cdot 2}{24}$

\frac{7 \cdot 3}{24} + \frac{5 \cdot 2}{24}

$\frac{7 \cdot 3}{24} + \frac{5 \cdot 2}{24}$

Step 4

Combine the numerators over the common denominator.

\frac{7 \cdot 3 + 5 \cdot 2}{24}

$\frac{7 \cdot 3 + 5 \cdot 2}{24}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

7

$7$ by

3

$3$ .

\frac{21 + 5 \cdot 2}{24}

$\frac{21 + 5 \cdot 2}{24}$

Step 5.2

Multiply

5

$5$ by

2

$2$ .

\frac{21 + 10}{24}

$\frac{21 + 10}{24}$

Step 5.3

Add

21

$21$ and

10

$10$ .

\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}

$1 \frac{7}{24}$