Solve for a a/20+4/15=9/15

$\frac{a}{20} + \frac{4}{15} = \frac{9}{15}$

Step 1

Cancel the common factor of $9$ and $15$ .

Factor $3$ out of $9$ .

$\frac{a}{20} + \frac{4}{15} = \frac{3 (3)}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$\frac{a}{20} + \frac{4}{15} = \frac{3 \cdot 3}{3 \cdot 5}$

Cancel the common factor.

$\frac{a}{20} + \frac{4}{15} = \frac{3 \cdot 3}{3 \cdot 5}$

Rewrite the expression.

$\frac{a}{20} + \frac{4}{15} = \frac{3}{5}$

Step 2

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

Subtract $\frac{4}{15}$ from both sides of the equation.

$\frac{a}{20} = \frac{3}{5} - \frac{4}{15}$

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

$\frac{a}{20} = \frac{3}{5} \cdot \frac{3}{3} - \frac{4}{15}$

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

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

$\frac{a}{20} = \frac{3 \cdot 3}{5 \cdot 3} - \frac{4}{15}$

Multiply $5$ by $3$ .

$\frac{a}{20} = \frac{3 \cdot 3}{15} - \frac{4}{15}$

Combine the numerators over the common denominator.

$\frac{a}{20} = \frac{3 \cdot 3 - 4}{15}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{a}{20} = \frac{9 - 4}{15}$

Subtract $4$ from $9$ .

$\frac{a}{20} = \frac{5}{15}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5$ .

$\frac{a}{20} = \frac{5 (1)}{15}$

Cancel the common factors.

Factor $5$ out of $15$ .

$\frac{a}{20} = \frac{5 \cdot 1}{5 \cdot 3}$

Cancel the common factor.

$\frac{a}{20} = \frac{5 \cdot 1}{5 \cdot 3}$

Rewrite the expression.

$\frac{a}{20} = \frac{1}{3}$

Step 3

Multiply both sides of the equation by $20$ .

$20 \frac{a}{20} = 20 (\frac{1}{3})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$20 \frac{a}{20} = 20 (\frac{1}{3})$

Rewrite the expression.

$a = 20 (\frac{1}{3})$

Simplify the right side.

Combine $20$ and $\frac{1}{3}$ .

$a = \frac{20}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = \frac{20}{3}$

Decimal Form:

$a = 6.\overline{6}$

Mixed Number Form:

$a = 6 \frac{2}{3}$

Solve for a a/20+4/15=9/15

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