Algebra Examples

$\frac{3}{4} = y - \frac{1}{5} \cdot 8$

Step 1

Rewrite the equation as $y - \frac{1}{5} \cdot 8 = \frac{3}{4}$ .

$y - \frac{1}{5} \cdot 8 = \frac{3}{4}$

Step 2

Simplify each term.

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Step 2.1

Multiply $- \frac{1}{5} \cdot 8$ .

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Step 2.1.1

Multiply $8$ by $- 1$ .

$y - 8 (\frac{1}{5}) = \frac{3}{4}$

Step 2.1.2

Combine $- 8$ and $\frac{1}{5}$ .

$y + \frac{- 8}{5} = \frac{3}{4}$

Step 2.2

Move the negative in front of the fraction.

$y - \frac{8}{5} = \frac{3}{4}$

Step 3

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

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Step 3.1

Add $\frac{8}{5}$ to both sides of the equation.

$y = \frac{3}{4} + \frac{8}{5}$

Step 3.2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{3}{4} \cdot \frac{5}{5} + \frac{8}{5}$

Step 3.3

To write $\frac{8}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{3}{4} \cdot \frac{5}{5} + \frac{8}{5} \cdot \frac{4}{4}$

Step 3.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$y = \frac{3 \cdot 5}{4 \cdot 5} + \frac{8}{5} \cdot \frac{4}{4}$

Step 3.4.2

Multiply $4$ by $5$ .

$y = \frac{3 \cdot 5}{20} + \frac{8}{5} \cdot \frac{4}{4}$

Step 3.4.3

Multiply $\frac{8}{5}$ by $\frac{4}{4}$ .

$y = \frac{3 \cdot 5}{20} + \frac{8 \cdot 4}{5 \cdot 4}$

Step 3.4.4

Multiply $5$ by $4$ .

$y = \frac{3 \cdot 5}{20} + \frac{8 \cdot 4}{20}$

Step 3.5

Combine the numerators over the common denominator.

$y = \frac{3 \cdot 5 + 8 \cdot 4}{20}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $3$ by $5$ .

$y = \frac{15 + 8 \cdot 4}{20}$

Step 3.6.2

Multiply $8$ by $4$ .

$y = \frac{15 + 32}{20}$

Step 3.6.3

Add $15$ and $32$ .

$y = \frac{47}{20}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{47}{20}$

Decimal Form:

$y = 2.35$

Mixed Number Form:

$y = 2 \frac{7}{20}$