Basic Math Examples

$\frac{1}{4} s - \frac{3}{10} s = \frac{1}{4}$

Step 1

Simplify $\frac{1}{4} s - \frac{3}{10} s$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{4}$ and $s$ .

$\frac{s}{4} - \frac{3}{10} s = \frac{1}{4}$

Step 1.1.2

Combine $s$ and $\frac{3}{10}$ .

$\frac{s}{4} - \frac{s \cdot 3}{10} = \frac{1}{4}$

Step 1.1.3

Move $3$ to the left of $s$ .

$\frac{s}{4} - \frac{3 s}{10} = \frac{1}{4}$

Step 1.2

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

$\frac{s}{4} \cdot \frac{5}{5} - \frac{3 s}{10} = \frac{1}{4}$

Step 1.3

To write $- \frac{3 s}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{s}{4} \cdot \frac{5}{5} - \frac{3 s}{10} \cdot \frac{2}{2} = \frac{1}{4}$

Step 1.4

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

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Step 1.4.1

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

$\frac{s \cdot 5}{4 \cdot 5} - \frac{3 s}{10} \cdot \frac{2}{2} = \frac{1}{4}$

Step 1.4.2

Multiply $4$ by $5$ .

$\frac{s \cdot 5}{20} - \frac{3 s}{10} \cdot \frac{2}{2} = \frac{1}{4}$

Step 1.4.3

Multiply $\frac{3 s}{10}$ by $\frac{2}{2}$ .

$\frac{s \cdot 5}{20} - \frac{3 s \cdot 2}{10 \cdot 2} = \frac{1}{4}$

Step 1.4.4

Multiply $10$ by $2$ .

$\frac{s \cdot 5}{20} - \frac{3 s \cdot 2}{20} = \frac{1}{4}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{s \cdot 5 - 3 s \cdot 2}{20} = \frac{1}{4}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $s$ out of $s \cdot 5 - 3 s \cdot 2$ .

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Step 1.6.1.1

Factor $s$ out of $s \cdot 5$ .

$\frac{s (5) - 3 s \cdot 2}{20} = \frac{1}{4}$

Step 1.6.1.2

Factor $s$ out of $- 3 s \cdot 2$ .

$\frac{s (5) + s (- 3 \cdot 2)}{20} = \frac{1}{4}$

Step 1.6.1.3

Factor $s$ out of $s (5) + s (- 3 \cdot 2)$ .

$\frac{s (5 - 3 \cdot 2)}{20} = \frac{1}{4}$

Step 1.6.2

Multiply $- 3$ by $2$ .

$\frac{s (5 - 6)}{20} = \frac{1}{4}$

Step 1.6.3

Subtract $6$ from $5$ .

$\frac{s \cdot - 1}{20} = \frac{1}{4}$

Step 1.7

Simplify the expression.

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Step 1.7.1

Move $- 1$ to the left of $s$ .

$\frac{- 1 \cdot s}{20} = \frac{1}{4}$

Step 1.7.2

Move the negative in front of the fraction.

$- \frac{s}{20} = \frac{1}{4}$

Step 2

Multiply both sides of the equation by $- 20$ .

$- 20 (- \frac{s}{20}) = - 20 (\frac{1}{4})$

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 $- 20 (- \frac{s}{20})$ .

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Step 3.1.1.1

Cancel the common factor of $20$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{s}{20}$ into the numerator.

$- 20 \frac{- s}{20} = - 20 (\frac{1}{4})$

Step 3.1.1.1.2

Factor $20$ out of $- 20$ .

$20 (- 1) \frac{- s}{20} = - 20 (\frac{1}{4})$

Step 3.1.1.1.3

Cancel the common factor.

$20 \cdot - 1 \frac{- s}{20} = - 20 (\frac{1}{4})$

Step 3.1.1.1.4

Rewrite the expression.

$- - s = - 20 (\frac{1}{4})$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 s = - 20 (\frac{1}{4})$

Step 3.1.1.2.2

Multiply $s$ by $1$ .

$s = - 20 (\frac{1}{4})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Factor $4$ out of $- 20$ .

$s = 4 (- 5) \frac{1}{4}$

Step 3.2.1.2

Cancel the common factor.

$s = 4 \cdot - 5 \frac{1}{4}$

Step 3.2.1.3

Rewrite the expression.

$s = - 5$