Pre-Algebra Examples

$\frac{2 h}{3} - \frac{1}{4} = \frac{1}{3}$

Step 1

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

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Step 1.1

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{2 h}{3} = \frac{1}{3} + \frac{1}{4}$

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 h}{3} = \frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4}$

Step 1.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 h}{3} = \frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{3}{3}$

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{2 h}{3} = \frac{4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3}$

Step 1.4.2

Multiply $3$ by $4$ .

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

Step 1.4.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{2 h}{3} = \frac{4}{12} + \frac{3}{4 \cdot 3}$

Step 1.4.4

Multiply $4$ by $3$ .

$\frac{2 h}{3} = \frac{4}{12} + \frac{3}{12}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 h}{3} = \frac{4 + 3}{12}$

Step 1.6

Add $4$ and $3$ .

$\frac{2 h}{3} = \frac{7}{12}$

Step 2

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 h}{3} = \frac{3}{2} \cdot \frac{7}{12}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{3}{2} \cdot \frac{2 h}{3}$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 h}{3} = \frac{3}{2} \cdot \frac{7}{12}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 h) = \frac{3}{2} \cdot \frac{7}{12}$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 h$ .

$\frac{1}{2} (2 (h)) = \frac{3}{2} \cdot \frac{7}{12}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 h) = \frac{3}{2} \cdot \frac{7}{12}$

Step 3.1.1.2.3

Rewrite the expression.

$h = \frac{3}{2} \cdot \frac{7}{12}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3}{2} \cdot \frac{7}{12}$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Factor $3$ out of $12$ .

$h = \frac{3}{2} \cdot \frac{7}{3 (4)}$

Step 3.2.1.1.2

Cancel the common factor.

$h = \frac{3}{2} \cdot \frac{7}{3 \cdot 4}$

Step 3.2.1.1.3

Rewrite the expression.

$h = \frac{1}{2} \cdot \frac{7}{4}$

Step 3.2.1.2

Multiply $\frac{1}{2}$ by $\frac{7}{4}$ .

$h = \frac{7}{2 \cdot 4}$

Step 3.2.1.3

Multiply $2$ by $4$ .

$h = \frac{7}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$h = \frac{7}{8}$

Decimal Form:

$h = 0.875$