Basic Math Examples

$\frac{4}{5} + 3 y = 0.4$

Step 1

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

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Step 1.1

Subtract $\frac{4}{5}$ from both sides of the equation.

$3 y = 0.4 - \frac{4}{5}$

Step 1.2

To write $0.4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$3 y = 0.4 \cdot \frac{5}{5} - \frac{4}{5}$

Step 1.3

Combine $0.4$ and $\frac{5}{5}$ .

$3 y = \frac{0.4 \cdot 5}{5} - \frac{4}{5}$

Step 1.4

Combine the numerators over the common denominator.

$3 y = \frac{0.4 \cdot 5 - 4}{5}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $0.4$ by $5$ .

$3 y = \frac{2 - 4}{5}$

Step 1.5.2

Subtract $4$ from $2$ .

$3 y = \frac{- 2}{5}$

Step 1.6

Cancel the common factor of $- 2$ and $5$ .

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Step 1.6.1

Rewrite $- 2$ as $1 (- 2)$ .

$3 y = \frac{1 (- 2)}{5}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Rewrite $5$ as $1 (5)$ .

$3 y = \frac{1 \cdot - 2}{1 \cdot 5}$

Step 1.6.2.2

Cancel the common factor.

$3 y = \frac{1 \cdot - 2}{1 \cdot 5}$

Step 1.6.2.3

Rewrite the expression.

$3 y = \frac{- 2}{5}$

Step 1.7

Move the negative in front of the fraction.

$3 y = - \frac{2}{5}$

Step 2

Divide each term in $3 y = - \frac{2}{5}$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 y = - \frac{2}{5}$ by $3$ .

$\frac{3 y}{3} = \frac{- \frac{2}{5}}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- \frac{2}{5}}{3}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{2}{5}}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{2}{5} \cdot \frac{1}{3}$

Step 2.3.2

Multiply $- \frac{2}{5} \cdot \frac{1}{3}$ .

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Step 2.3.2.1

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

$y = - \frac{2}{3 \cdot 5}$

Step 2.3.2.2

Multiply $3$ by $5$ .

$y = - \frac{2}{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{2}{15}$

Decimal Form:

$y = - 0.1\overline{3}$