Basic Math Examples

$\frac{\frac{3}{4} + \frac{1}{6}}{\frac{2}{5}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{3}{4} + \frac{1}{6}) \frac{5}{2}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{3}{4} \cdot \frac{3}{3} + \frac{1}{6}) \frac{5}{2}$

Step 3

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{3}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2}) \frac{5}{2}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$(\frac{3 \cdot 3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2}) \frac{5}{2}$

Step 4.2

Multiply $4$ by $3$ .

$(\frac{3 \cdot 3}{12} + \frac{1}{6} \cdot \frac{2}{2}) \frac{5}{2}$

Step 4.3

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$(\frac{3 \cdot 3}{12} + \frac{2}{6 \cdot 2}) \frac{5}{2}$

Step 4.4

Multiply $6$ by $2$ .

$(\frac{3 \cdot 3}{12} + \frac{2}{12}) \frac{5}{2}$

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $3$ .

$\frac{9 + 2}{12} \cdot \frac{5}{2}$

Step 6.2

Add $9$ and $2$ .

$\frac{11}{12} \cdot \frac{5}{2}$

Step 7

Multiply $\frac{11}{12} \cdot \frac{5}{2}$ .

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Step 7.1

Multiply $\frac{11}{12}$ by $\frac{5}{2}$ .

$\frac{11 \cdot 5}{12 \cdot 2}$

Step 7.2

Multiply $11$ by $5$ .

$\frac{55}{12 \cdot 2}$

Step 7.3

Multiply $12$ by $2$ .

$\frac{55}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{55}{24}$

Decimal Form:

$2.291\overline{6}$

Mixed Number Form:

$2 \frac{7}{24}$