Basic Math Examples

$\frac{| 15 - 26 |}{3} + \frac{| - 8 + 19 |}{2}$

Step 1

Simplify by adding and subtracting.

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Step 1.1

Subtract $26$ from $15$ .

$\frac{| - 11 |}{3} + \frac{| - 8 + 19 |}{2}$

Step 1.2

Add $- 8$ and $19$ .

$\frac{| - 11 |}{3} + \frac{| 11 |}{2}$

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 $- 11$ and $0$ is $11$ .

$\frac{11}{3} + \frac{| 11 |}{2}$

Step 2.2

The absolute value is the distance between a number and zero. The distance between $0$ and $11$ is $11$ .

$\frac{11}{3} + \frac{11}{2}$

Step 3

To write $\frac{11}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11}{3} \cdot \frac{2}{2} + \frac{11}{2}$

Step 4

To write $\frac{11}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11}{3} \cdot \frac{2}{2} + \frac{11}{2} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{11}{3}$ by $\frac{2}{2}$ .

$\frac{11 \cdot 2}{3 \cdot 2} + \frac{11}{2} \cdot \frac{3}{3}$

Step 5.2

Multiply $3$ by $2$ .

$\frac{11 \cdot 2}{6} + \frac{11}{2} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{11}{2}$ by $\frac{3}{3}$ .

$\frac{11 \cdot 2}{6} + \frac{11 \cdot 3}{2 \cdot 3}$

Step 5.4

Multiply $2$ by $3$ .

$\frac{11 \cdot 2}{6} + \frac{11 \cdot 3}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{11 \cdot 2 + 11 \cdot 3}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $11$ by $2$ .

$\frac{22 + 11 \cdot 3}{6}$

Step 7.2

Multiply $11$ by $3$ .

$\frac{22 + 33}{6}$

Step 7.3

Add $22$ and $33$ .

$\frac{55}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{55}{6}$

Decimal Form:

$9.1\overline{6}$

Mixed Number Form:

$9 \frac{1}{6}$