Basic Math Examples

$\frac{5}{12} \div \frac{3}{4} + \frac{1}{3} \cdot \frac{2}{5}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{12} \cdot \frac{4}{3} + \frac{1}{3} \cdot \frac{2}{5}$

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Factor $4$ out of $12$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

$\frac{5}{3} \cdot \frac{1}{3} + \frac{1}{3} \cdot \frac{2}{5}$

Step 1.3

Multiply $\frac{5}{3}$ by $\frac{1}{3}$ .

$\frac{5}{3 \cdot 3} + \frac{1}{3} \cdot \frac{2}{5}$

Step 1.4

Multiply $3$ by $3$ .

$\frac{5}{9} + \frac{1}{3} \cdot \frac{2}{5}$

Step 1.5

Multiply $\frac{1}{3} \cdot \frac{2}{5}$ .

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Step 1.5.1

Multiply $\frac{1}{3}$ by $\frac{2}{5}$ .

$\frac{5}{9} + \frac{2}{3 \cdot 5}$

Step 1.5.2

Multiply $3$ by $5$ .

$\frac{5}{9} + \frac{2}{15}$

Step 2

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5}{9} \cdot \frac{5}{5} + \frac{2}{15}$

Step 3

To write $\frac{2}{15}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{9} \cdot \frac{5}{5} + \frac{2}{15} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{9}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 5}{9 \cdot 5} + \frac{2}{15} \cdot \frac{3}{3}$

Step 4.2

Multiply $9$ by $5$ .

$\frac{5 \cdot 5}{45} + \frac{2}{15} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{2}{15}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 5}{45} + \frac{2 \cdot 3}{15 \cdot 3}$

Step 4.4

Multiply $15$ by $3$ .

$\frac{5 \cdot 5}{45} + \frac{2 \cdot 3}{45}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 2 \cdot 3}{45}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $5$ .

$\frac{25 + 2 \cdot 3}{45}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{25 + 6}{45}$

Step 6.3

Add $25$ and $6$ .

$\frac{31}{45}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{31}{45}$

Decimal Form:

$0.6\overline{8}$