Basic Math Examples

\frac{4}{5} = \frac{1}{3} + y

$\frac{4}{5} = \frac{1}{3} + y$

Step 1

Rewrite the equation as

\frac{1}{3} + y = \frac{4}{5}

$\frac{1}{3} + y = \frac{4}{5}$ .

\frac{1}{3} + y = \frac{4}{5}

$\frac{1}{3} + y = \frac{4}{5}$

Step 2

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 2.1

Subtract

\frac{1}{3}

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

y = \frac{4}{5} - \frac{1}{3}

$y = \frac{4}{5} - \frac{1}{3}$

Step 2.2

To write

\frac{4}{5}

$\frac{4}{5}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

y = \frac{4}{5} \cdot \frac{3}{3} - \frac{1}{3}

$y = \frac{4}{5} \cdot \frac{3}{3} - \frac{1}{3}$

Step 2.3

To write

- \frac{1}{3}

$- \frac{1}{3}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

y = \frac{4}{5} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{5}{5}

$y = \frac{4}{5} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{5}{5}$

Step 2.4

Write each expression with a common denominator of

15

$15$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 2.4.1

Multiply

\frac{4}{5}

$\frac{4}{5}$ by

\frac{3}{3}

$\frac{3}{3}$ .

y = \frac{4 \cdot 3}{5 \cdot 3} - \frac{1}{3} \cdot \frac{5}{5}

$y = \frac{4 \cdot 3}{5 \cdot 3} - \frac{1}{3} \cdot \frac{5}{5}$

Step 2.4.2

Multiply

5

$5$ by

3

$3$ .

y = \frac{4 \cdot 3}{15} - \frac{1}{3} \cdot \frac{5}{5}

$y = \frac{4 \cdot 3}{15} - \frac{1}{3} \cdot \frac{5}{5}$

Step 2.4.3

Multiply

\frac{1}{3}

$\frac{1}{3}$ by

\frac{5}{5}

$\frac{5}{5}$ .

y = \frac{4 \cdot 3}{15} - \frac{5}{3 \cdot 5}

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

Step 2.4.4

Multiply

3

$3$ by

5

$5$ .

y = \frac{4 \cdot 3}{15} - \frac{5}{15}

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

y = \frac{4 \cdot 3}{15} - \frac{5}{15}

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

Step 2.5

Combine the numerators over the common denominator.

y = \frac{4 \cdot 3 - 5}{15}

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

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply

4

$4$ by

3

$3$ .

y = \frac{12 - 5}{15}

$y = \frac{12 - 5}{15}$

Step 2.6.2

Subtract

5

$5$ from

12

$12$ .

y = \frac{7}{15}

$y = \frac{7}{15}$

y = \frac{7}{15}

$y = \frac{7}{15}$

y = \frac{7}{15}

$y = \frac{7}{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

y = \frac{7}{15}

$y = \frac{7}{15}$

Decimal Form:

y = 0.4 ¯ 6

$y = 0.4\overline{6}$