Algebra Examples

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

Step 1

Subtract $\frac{2}{3}$ from both sides of the equation.

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

Step 2

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

$y = \frac{1}{4} \cdot \frac{3}{3} - \frac{2}{3}$

Step 3

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{1}{4} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{4}{4}$

Step 4

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

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Step 4.1

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

$y = \frac{3}{4 \cdot 3} - \frac{2}{3} \cdot \frac{4}{4}$

Step 4.2

Multiply $4$ by $3$ .

$y = \frac{3}{12} - \frac{2}{3} \cdot \frac{4}{4}$

Step 4.3

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$y = \frac{3}{12} - \frac{2 \cdot 4}{3 \cdot 4}$

Step 4.4

Multiply $3$ by $4$ .

$y = \frac{3}{12} - \frac{2 \cdot 4}{12}$

Step 5

Combine the numerators over the common denominator.

$y = \frac{3 - 2 \cdot 4}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 2$ by $4$ .

$y = \frac{3 - 8}{12}$

Step 6.2

Subtract $8$ from $3$ .

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

Step 7

Move the negative in front of the fraction.

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 0.41\overline{6}$