Basic Math Examples

$2 (5 a - \frac{1}{3}) = \frac{7}{3}$

Step 1

Divide each term in $2 (5 a - \frac{1}{3}) = \frac{7}{3}$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 (5 a - \frac{1}{3}) = \frac{7}{3}$ by $2$ .

$\frac{2 (5 a - \frac{1}{3})}{2} = \frac{\frac{7}{3}}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 (5 a - \frac{1}{3})}{2} = \frac{\frac{7}{3}}{2}$

Step 1.2.1.2

Divide $5 a - \frac{1}{3}$ by $1$ .

$5 a - \frac{1}{3} = \frac{\frac{7}{3}}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply the numerator by the reciprocal of the denominator.

$5 a - \frac{1}{3} = \frac{7}{3} \cdot \frac{1}{2}$

Step 1.3.2

Multiply $\frac{7}{3} \cdot \frac{1}{2}$ .

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Step 1.3.2.1

Multiply $\frac{7}{3}$ by $\frac{1}{2}$ .

$5 a - \frac{1}{3} = \frac{7}{3 \cdot 2}$

Step 1.3.2.2

Multiply $3$ by $2$ .

$5 a - \frac{1}{3} = \frac{7}{6}$

Step 2

Move all terms not containing $a$ to the right side of the equation.

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Step 2.1

Add $\frac{1}{3}$ to both sides of the equation.

$5 a = \frac{7}{6} + \frac{1}{3}$

Step 2.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 a = \frac{7}{6} + \frac{1}{3} \cdot \frac{2}{2}$

Step 2.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

$5 a = \frac{7}{6} + \frac{2}{3 \cdot 2}$

Step 2.3.2

Multiply $3$ by $2$ .

$5 a = \frac{7}{6} + \frac{2}{6}$

Step 2.4

Combine the numerators over the common denominator.

$5 a = \frac{7 + 2}{6}$

Step 2.5

Add $7$ and $2$ .

$5 a = \frac{9}{6}$

Step 2.6

Cancel the common factor of $9$ and $6$ .

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Step 2.6.1

Factor $3$ out of $9$ .

$5 a = \frac{3 (3)}{6}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $3$ out of $6$ .

$5 a = \frac{3 \cdot 3}{3 \cdot 2}$

Step 2.6.2.2

Cancel the common factor.

$5 a = \frac{3 \cdot 3}{3 \cdot 2}$

Step 2.6.2.3

Rewrite the expression.

$5 a = \frac{3}{2}$

Step 3

Divide each term in $5 a = \frac{3}{2}$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 a = \frac{3}{2}$ by $5$ .

$\frac{5 a}{5} = \frac{\frac{3}{2}}{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 a}{5} = \frac{\frac{3}{2}}{5}$

Step 3.2.1.2

Divide $a$ by $1$ .

$a = \frac{\frac{3}{2}}{5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$a = \frac{3}{2} \cdot \frac{1}{5}$

Step 3.3.2

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

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Step 3.3.2.1

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

$a = \frac{3}{2 \cdot 5}$

Step 3.3.2.2

Multiply $2$ by $5$ .

$a = \frac{3}{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{3}{10}$

Decimal Form:

$a = 0.3$