Basic Math Examples

$\frac{1}{3} s - \frac{3}{4} s = \frac{1}{12}$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{3}$ and $s$ .

$\frac{s}{3} - \frac{3}{4} s = \frac{1}{12}$

Step 1.1.2

Combine $s$ and $\frac{3}{4}$ .

$\frac{s}{3} - \frac{s \cdot 3}{4} = \frac{1}{12}$

Step 1.1.3

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

$\frac{s}{3} - \frac{3 s}{4} = \frac{1}{12}$

Step 1.2

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

$\frac{s}{3} \cdot \frac{4}{4} - \frac{3 s}{4} = \frac{1}{12}$

Step 1.3

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

$\frac{s}{3} \cdot \frac{4}{4} - \frac{3 s}{4} \cdot \frac{3}{3} = \frac{1}{12}$

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

$\frac{s \cdot 4}{3 \cdot 4} - \frac{3 s}{4} \cdot \frac{3}{3} = \frac{1}{12}$

Step 1.4.2

Multiply $3$ by $4$ .

$\frac{s \cdot 4}{12} - \frac{3 s}{4} \cdot \frac{3}{3} = \frac{1}{12}$

Step 1.4.3

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

$\frac{s \cdot 4}{12} - \frac{3 s \cdot 3}{4 \cdot 3} = \frac{1}{12}$

Step 1.4.4

Multiply $4$ by $3$ .

$\frac{s \cdot 4}{12} - \frac{3 s \cdot 3}{12} = \frac{1}{12}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{s \cdot 4 - 3 s \cdot 3}{12} = \frac{1}{12}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $s$ out of $s \cdot 4 - 3 s \cdot 3$ .

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Step 1.6.1.1

Factor $s$ out of $s \cdot 4$ .

$\frac{s (4) - 3 s \cdot 3}{12} = \frac{1}{12}$

Step 1.6.1.2

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

$\frac{s (4) + s (- 3 \cdot 3)}{12} = \frac{1}{12}$

Step 1.6.1.3

Factor $s$ out of $s (4) + s (- 3 \cdot 3)$ .

$\frac{s (4 - 3 \cdot 3)}{12} = \frac{1}{12}$

Step 1.6.2

Multiply $- 3$ by $3$ .

$\frac{s (4 - 9)}{12} = \frac{1}{12}$

Step 1.6.3

Subtract $9$ from $4$ .

$\frac{s \cdot - 5}{12} = \frac{1}{12}$

Step 1.7

Simplify the expression.

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Step 1.7.1

Move $- 5$ to the left of $s$ .

$\frac{- 5 \cdot s}{12} = \frac{1}{12}$

Step 1.7.2

Move the negative in front of the fraction.

$- \frac{5 s}{12} = \frac{1}{12}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 5 s = 1$

Step 3

Divide each term in $- 5 s = 1$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 s = 1$ by $- 5$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $s$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$s = - 0.2$