Basic Math Examples

$\frac{\frac{1}{3}}{\frac{1}{5}} + \frac{\frac{3}{6}}{\frac{6}{15}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{3} \cdot 5 + \frac{\frac{3}{6}}{\frac{6}{15}}$

Step 1.2

Combine $\frac{1}{3}$ and $5$ .

$\frac{5}{3} + \frac{\frac{3}{6}}{\frac{6}{15}}$

Step 1.3

Cancel the common factor of $3$ and $6$ .

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Step 1.3.1

Factor $3$ out of $3$ .

$\frac{5}{3} + \frac{\frac{3 (1)}{6}}{\frac{6}{15}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $3$ out of $6$ .

$\frac{5}{3} + \frac{\frac{3 \cdot 1}{3 \cdot 2}}{\frac{6}{15}}$

Step 1.3.2.2

Cancel the common factor.

$\frac{5}{3} + \frac{\frac{3 \cdot 1}{3 \cdot 2}}{\frac{6}{15}}$

Step 1.3.2.3

Rewrite the expression.

$\frac{5}{3} + \frac{\frac{1}{2}}{\frac{6}{15}}$

Step 1.4

Cancel the common factor of $6$ and $15$ .

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Step 1.4.1

Factor $3$ out of $6$ .

$\frac{5}{3} + \frac{\frac{1}{2}}{\frac{3 (2)}{15}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $3$ out of $15$ .

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

Step 1.4.2.2

Cancel the common factor.

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

Step 1.4.2.3

Rewrite the expression.

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

Step 1.5

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.6

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

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Step 1.6.1

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

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

Step 1.6.2

Multiply $2$ by $2$ .

$\frac{5}{3} + \frac{5}{4}$

Step 2

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 3

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

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 $\frac{5}{3}$ by $\frac{4}{4}$ .

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

Step 4.2

Multiply $3$ by $4$ .

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

Step 4.3

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

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

Step 4.4

Multiply $4$ by $3$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $4$ .

$\frac{20 + 5 \cdot 3}{12}$

Step 6.2

Multiply $5$ by $3$ .

$\frac{20 + 15}{12}$

Step 6.3

Add $20$ and $15$ .

$\frac{35}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{12}$

Decimal Form:

$2.91\overline{6}$

Mixed Number Form:

$2 \frac{11}{12}$