Basic Math Examples

$\frac{1}{3} w + \frac{1}{5} w = \frac{4}{9}$

Step 1

Simplify $\frac{1}{3} w + \frac{1}{5} w$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{w}{3} + \frac{1}{5} w = \frac{4}{9}$

Step 1.1.2

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

$\frac{w}{3} + \frac{w}{5} = \frac{4}{9}$

Step 1.2

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

$\frac{w}{3} \cdot \frac{5}{5} + \frac{w}{5} = \frac{4}{9}$

Step 1.3

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

$\frac{w}{3} \cdot \frac{5}{5} + \frac{w}{5} \cdot \frac{3}{3} = \frac{4}{9}$

Step 1.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

$\frac{w \cdot 5}{3 \cdot 5} + \frac{w}{5} \cdot \frac{3}{3} = \frac{4}{9}$

Step 1.4.2

Multiply $3$ by $5$ .

$\frac{w \cdot 5}{15} + \frac{w}{5} \cdot \frac{3}{3} = \frac{4}{9}$

Step 1.4.3

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

$\frac{w \cdot 5}{15} + \frac{w \cdot 3}{5 \cdot 3} = \frac{4}{9}$

Step 1.4.4

Multiply $5$ by $3$ .

$\frac{w \cdot 5}{15} + \frac{w \cdot 3}{15} = \frac{4}{9}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{w \cdot 5 + w \cdot 3}{15} = \frac{4}{9}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Move $5$ to the left of $w$ .

$\frac{5 \cdot w + w \cdot 3}{15} = \frac{4}{9}$

Step 1.6.2

Move $3$ to the left of $w$ .

$\frac{5 w + 3 \cdot w}{15} = \frac{4}{9}$

Step 1.6.3

Add $5 w$ and $3 w$ .

$\frac{8 w}{15} = \frac{4}{9}$

Step 2

Multiply both sides of the equation by $\frac{15}{8}$ .

$\frac{15}{8} \cdot \frac{8 w}{15} = \frac{15}{8} \cdot \frac{4}{9}$

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 $\frac{15}{8} \cdot \frac{8 w}{15}$ .

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Step 3.1.1.1

Cancel the common factor of $15$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{15}{8} \cdot \frac{8 w}{15} = \frac{15}{8} \cdot \frac{4}{9}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{8} (8 w) = \frac{15}{8} \cdot \frac{4}{9}$

Step 3.1.1.2

Cancel the common factor of $8$ .

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Step 3.1.1.2.1

Factor $8$ out of $8 w$ .

$\frac{1}{8} (8 (w)) = \frac{15}{8} \cdot \frac{4}{9}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{8} (8 w) = \frac{15}{8} \cdot \frac{4}{9}$

Step 3.1.1.2.3

Rewrite the expression.

$w = \frac{15}{8} \cdot \frac{4}{9}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{15}{8} \cdot \frac{4}{9}$ .

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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 $15$ .

$w = \frac{3 (5)}{8} \cdot \frac{4}{9}$

Step 3.2.1.1.2

Factor $3$ out of $9$ .

$w = \frac{3 \cdot 5}{8} \cdot \frac{4}{3 \cdot 3}$

Step 3.2.1.1.3

Cancel the common factor.

$w = \frac{3 \cdot 5}{8} \cdot \frac{4}{3 \cdot 3}$

Step 3.2.1.1.4

Rewrite the expression.

$w = \frac{5}{8} \cdot \frac{4}{3}$

Step 3.2.1.2

Cancel the common factor of $4$ .

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Step 3.2.1.2.1

Factor $4$ out of $8$ .

$w = \frac{5}{4 (2)} \cdot \frac{4}{3}$

Step 3.2.1.2.2

Cancel the common factor.

$w = \frac{5}{4 \cdot 2} \cdot \frac{4}{3}$

Step 3.2.1.2.3

Rewrite the expression.

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

Step 3.2.1.3

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

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

Step 3.2.1.4

Multiply $2$ by $3$ .

$w = \frac{5}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$w = \frac{5}{6}$

Decimal Form:

$w = 0.8\overline{3}$