Basic Math Examples

$\frac{| 15 - 12 |}{4} - \frac{| - 21 + 9 |}{8}$

Step 1

Subtract $12$ from $15$ .

$\frac{| 3 |}{4} - \frac{| - 21 + 9 |}{8}$

Step 2

Simplify each term.

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Step 2.1

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{3}{4} - \frac{| - 21 + 9 |}{8}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Add $- 21$ and $9$ .

$\frac{3}{4} - \frac{| - 12 |}{8}$

Step 2.2.2

The absolute value is the distance between a number and zero. The distance between $- 12$ and $0$ is $12$ .

$\frac{3}{4} - \frac{12}{8}$

Step 2.3

Cancel the common factor of $12$ and $8$ .

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Step 2.3.1

Factor $4$ out of $12$ .

$\frac{3}{4} - \frac{4 (3)}{8}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $4$ out of $8$ .

$\frac{3}{4} - \frac{4 \cdot 3}{4 \cdot 2}$

Step 2.3.2.2

Cancel the common factor.

$\frac{3}{4} - \frac{4 \cdot 3}{4 \cdot 2}$

Step 2.3.2.3

Rewrite the expression.

$\frac{3}{4} - \frac{3}{2}$

Step 3

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

$\frac{3}{4} - \frac{3}{2} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{3}{4} - \frac{3 \cdot 2}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$\frac{3}{4} - \frac{3 \cdot 2}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 - 3 \cdot 2}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $2$ .

$\frac{3 - 6}{4}$

Step 6.2

Subtract $6$ from $3$ .

$\frac{- 3}{4}$

Step 7

Move the negative in front of the fraction.

$- \frac{3}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{4}$

Decimal Form:

$- 0.75$