Basic Math Examples

$\frac{3}{5} g - \frac{1}{3} = - \frac{10}{3}$

Step 1

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

$\frac{3 g}{5} - \frac{1}{3} = - \frac{10}{3}$

Step 2

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

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Step 2.1

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

$\frac{3 g}{5} = - \frac{10}{3} + \frac{1}{3}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{3 g}{5} = \frac{- 10 + 1}{3}$

Step 2.3

Add $- 10$ and $1$ .

$\frac{3 g}{5} = \frac{- 9}{3}$

Step 2.4

Divide $- 9$ by $3$ .

$\frac{3 g}{5} = - 3$

Step 3

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} \cdot \frac{3 g}{5} = \frac{5}{3} \cdot - 3$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{5}{3} \cdot \frac{3 g}{5}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 g}{5} = \frac{5}{3} \cdot - 3$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 g) = \frac{5}{3} \cdot - 3$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 g$ .

$\frac{1}{3} (3 (g)) = \frac{5}{3} \cdot - 3$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 g) = \frac{5}{3} \cdot - 3$

Step 4.1.1.2.3

Rewrite the expression.

$g = \frac{5}{3} \cdot - 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{5}{3} \cdot - 3$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Factor $3$ out of $- 3$ .

$g = \frac{5}{3} \cdot (3 (- 1))$

Step 4.2.1.1.2

Cancel the common factor.

$g = \frac{5}{3} \cdot (3 \cdot - 1)$

Step 4.2.1.1.3

Rewrite the expression.

$g = 5 \cdot - 1$

Step 4.2.1.2

Multiply $5$ by $- 1$ .

$g = - 5$