Basic Math Examples

$\frac{6}{10 a} - \frac{3}{9 a} + \frac{4}{5 a}$

Step 1

Cancel the common factor of $3$ and $9$ .

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Step 1.1

Factor $3$ out of $3$ .

$\frac{6}{10 a} - \frac{3 (1)}{9 a} + \frac{4}{5 a}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $9 a$ .

$\frac{6}{10 a} - \frac{3 (1)}{3 (3 a)} + \frac{4}{5 a}$

Step 1.2.2

Cancel the common factor.

$\frac{6}{10 a} - \frac{3 \cdot 1}{3 (3 a)} + \frac{4}{5 a}$

Step 1.2.3

Rewrite the expression.

$\frac{6}{10 a} - \frac{1}{3 a} + \frac{4}{5 a}$

Step 2

To write $\frac{6}{10 a}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{6}{10 a} \cdot \frac{3}{3} - \frac{1}{3 a} + \frac{4}{5 a}$

Step 3

To write $- \frac{1}{3 a}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{6}{10 a} \cdot \frac{3}{3} - \frac{1}{3 a} \cdot \frac{10}{10} + \frac{4}{5 a}$

Step 4

Write each expression with a common denominator of $30 a$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{6}{10 a}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 3}{10 a \cdot 3} - \frac{1}{3 a} \cdot \frac{10}{10} + \frac{4}{5 a}$

Step 4.2

Multiply $3$ by $10$ .

$\frac{6 \cdot 3}{30 a} - \frac{1}{3 a} \cdot \frac{10}{10} + \frac{4}{5 a}$

Step 4.3

Multiply $\frac{1}{3 a}$ by $\frac{10}{10}$ .

$\frac{6 \cdot 3}{30 a} - \frac{10}{3 a \cdot 10} + \frac{4}{5 a}$

Step 4.4

Multiply $10$ by $3$ .

$\frac{6 \cdot 3}{30 a} - \frac{10}{30 a} + \frac{4}{5 a}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 - 10}{30 a} + \frac{4}{5 a}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $6$ by $3$ .

$\frac{18 - 10}{30 a} + \frac{4}{5 a}$

Step 6.2

Subtract $10$ from $18$ .

$\frac{8}{30 a} + \frac{4}{5 a}$

Step 7

To write $\frac{4}{5 a}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{8}{30 a} + \frac{4}{5 a} \cdot \frac{6}{6}$

Step 8

Write each expression with a common denominator of $30 a$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{4}{5 a}$ by $\frac{6}{6}$ .

$\frac{8}{30 a} + \frac{4 \cdot 6}{5 a \cdot 6}$

Step 8.2

Multiply $6$ by $5$ .

$\frac{8}{30 a} + \frac{4 \cdot 6}{30 a}$

Step 9

Combine the numerators over the common denominator.

$\frac{8 + 4 \cdot 6}{30 a}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $4$ by $6$ .

$\frac{8 + 24}{30 a}$

Step 10.2

Add $8$ and $24$ .

$\frac{32}{30 a}$

Step 11

Reduce the expression $\frac{32}{30 a}$ by cancelling the common factors.

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Step 11.1

Factor $2$ out of $32$ .

$\frac{2 (16)}{30 a}$

Step 11.2

Factor $2$ out of $30 a$ .

$\frac{2 (16)}{2 (15 a)}$

Step 11.3

Cancel the common factor.

$\frac{2 \cdot 16}{2 (15 a)}$

Step 11.4

Rewrite the expression.

$\frac{16}{15 a}$