Basic Math Examples

$1.6 = \frac{4}{5} \cdot (y - 5)$

Step 1

Rewrite the equation as $\frac{4}{5} \cdot (y - 5) = 1.6$ .

$\frac{4}{5} \cdot (y - 5) = 1.6$

Step 2

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} (\frac{4}{5} \cdot (y - 5)) = \frac{5}{4} \cdot 1.6$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{5}{4} (\frac{4}{5} \cdot (y - 5))$ .

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Step 3.1.1.1

Apply the distributive property.

$\frac{5}{4} (\frac{4}{5} y + \frac{4}{5} \cdot - 5) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.2

Combine $\frac{4}{5}$ and $y$ .

$\frac{5}{4} (\frac{4 y}{5} + \frac{4}{5} \cdot - 5) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.3

Cancel the common factor of $5$ .

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Step 3.1.1.3.1

Factor $5$ out of $- 5$ .

$\frac{5}{4} (\frac{4 y}{5} + \frac{4}{5} \cdot (5 (- 1))) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{5}{4} (\frac{4 y}{5} + \frac{4}{5} \cdot (5 \cdot - 1)) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.3.3

Rewrite the expression.

$\frac{5}{4} (\frac{4 y}{5} + 4 \cdot - 1) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.4

Multiply $4$ by $- 1$ .

$\frac{5}{4} (\frac{4 y}{5} - 4) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.5

Apply the distributive property.

$\frac{5}{4} \cdot \frac{4 y}{5} + \frac{5}{4} \cdot - 4 = \frac{5}{4} \cdot 1.6$

Step 3.1.1.6

Cancel the common factor of $5$ .

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Step 3.1.1.6.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 y}{5} + \frac{5}{4} \cdot - 4 = \frac{5}{4} \cdot 1.6$

Step 3.1.1.6.2

Rewrite the expression.

$\frac{1}{4} (4 y) + \frac{5}{4} \cdot - 4 = \frac{5}{4} \cdot 1.6$

Step 3.1.1.7

Cancel the common factor of $4$ .

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Step 3.1.1.7.1

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) + \frac{5}{4} \cdot - 4 = \frac{5}{4} \cdot 1.6$

Step 3.1.1.7.2

Cancel the common factor.

$\frac{1}{4} (4 y) + \frac{5}{4} \cdot - 4 = \frac{5}{4} \cdot 1.6$

Step 3.1.1.7.3

Rewrite the expression.

$y + \frac{5}{4} \cdot - 4 = \frac{5}{4} \cdot 1.6$

Step 3.1.1.8

Cancel the common factor of $4$ .

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Step 3.1.1.8.1

Factor $4$ out of $- 4$ .

$y + \frac{5}{4} \cdot (4 (- 1)) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.8.2

Cancel the common factor.

$y + \frac{5}{4} \cdot (4 \cdot - 1) = \frac{5}{4} \cdot 1.6$

Step 3.1.1.8.3

Rewrite the expression.

$y + 5 \cdot - 1 = \frac{5}{4} \cdot 1.6$

Step 3.1.1.9

Multiply $5$ by $- 1$ .

$y - 5 = \frac{5}{4} \cdot 1.6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5}{4} \cdot 1.6$ .

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Step 3.2.1.1

Multiply $\frac{5}{4} \cdot 1.6$ .

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Step 3.2.1.1.1

Combine $\frac{5}{4}$ and $1.6$ .

$y - 5 = \frac{5 \cdot 1.6}{4}$

Step 3.2.1.1.2

Multiply $5$ by $1.6$ .

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

Step 3.2.1.2

Divide $8$ by $4$ .

$y - 5 = 2$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$y = 2 + 5$

Step 4.2

Add $2$ and $5$ .

$y = 7$