Basic Math Examples

$\frac{1}{5} y = - \frac{3}{7} - \frac{7}{10}$

Step 1

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} y) = 5 (- \frac{3}{7} - \frac{7}{10})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $5 (\frac{1}{5} y)$ .

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Step 2.1.1.1

Combine $\frac{1}{5}$ and $y$ .

$5 \frac{y}{5} = 5 (- \frac{3}{7} - \frac{7}{10})$

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

Cancel the common factor.

$5 \frac{y}{5} = 5 (- \frac{3}{7} - \frac{7}{10})$

Step 2.1.1.2.2

Rewrite the expression.

$y = 5 (- \frac{3}{7} - \frac{7}{10})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $5 (- \frac{3}{7} - \frac{7}{10})$ .

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Step 2.2.1.1

To write $- \frac{3}{7}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$y = 5 (- \frac{3}{7} \cdot \frac{10}{10} - \frac{7}{10})$

Step 2.2.1.2

To write $- \frac{7}{10}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$y = 5 (- \frac{3}{7} \cdot \frac{10}{10} - \frac{7}{10} \cdot \frac{7}{7})$

Step 2.2.1.3

Write each expression with a common denominator of $70$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.3.1

Multiply $\frac{3}{7}$ by $\frac{10}{10}$ .

$y = 5 (- \frac{3 \cdot 10}{7 \cdot 10} - \frac{7}{10} \cdot \frac{7}{7})$

Step 2.2.1.3.2

Multiply $7$ by $10$ .

$y = 5 (- \frac{3 \cdot 10}{70} - \frac{7}{10} \cdot \frac{7}{7})$

Step 2.2.1.3.3

Multiply $\frac{7}{10}$ by $\frac{7}{7}$ .

$y = 5 (- \frac{3 \cdot 10}{70} - \frac{7 \cdot 7}{10 \cdot 7})$

Step 2.2.1.3.4

Multiply $10$ by $7$ .

$y = 5 (- \frac{3 \cdot 10}{70} - \frac{7 \cdot 7}{70})$

Step 2.2.1.4

Combine the numerators over the common denominator.

$y = 5 \frac{- 3 \cdot 10 - 7 \cdot 7}{70}$

Step 2.2.1.5

Simplify the numerator.

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Step 2.2.1.5.1

Multiply $- 3$ by $10$ .

$y = 5 \frac{- 30 - 7 \cdot 7}{70}$

Step 2.2.1.5.2

Multiply $- 7$ by $7$ .

$y = 5 \frac{- 30 - 49}{70}$

Step 2.2.1.5.3

Subtract $49$ from $- 30$ .

$y = 5 (\frac{- 79}{70})$

Step 2.2.1.6

Cancel the common factor of $5$ .

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Step 2.2.1.6.1

Factor $5$ out of $70$ .

$y = 5 \frac{- 79}{5 (14)}$

Step 2.2.1.6.2

Cancel the common factor.

$y = 5 \frac{- 79}{5 \cdot 14}$

Step 2.2.1.6.3

Rewrite the expression.

$y = \frac{- 79}{14}$

Step 2.2.1.7

Move the negative in front of the fraction.

$y = - \frac{79}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{79}{14}$

Decimal Form:

$y = - 5.64285714 \dots$

Mixed Number Form:

$y = - 5 \frac{9}{14}$