Algebra Examples

$45 \div 5 \div 3 + 8 \times 3 \div 2 - 2^{3}$

Step 1

Multiply $8$ by $3$ .

$45 \div 5 \div 3 + 24 \div 2 - 2^{3}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $45 \div 5 \div 3$ by $\frac{2}{2}$ .

$45 \div 5 \div 3 \cdot \frac{2}{2} + 24 \div 2 - 2^{3}$

Step 2.2

Multiply $45 \div 5 \div 3$ by $\frac{2}{2}$ .

$\frac{45 \div 5 \cdot 2}{3 \cdot 2} + 24 \div 2 - 2^{3}$

Step 2.3

Multiply $24 \div 2$ by $\frac{3}{3}$ .

$\frac{45 \div 5 \cdot 2}{3 \cdot 2} + 24 \div 2 \cdot \frac{3}{3} - 2^{3}$

Step 2.4

Multiply $24 \div 2$ by $\frac{3}{3}$ .

$\frac{45 \div 5 \cdot 2}{3 \cdot 2} + \frac{24 \cdot 3}{2 \cdot 3} - 2^{3}$

Step 2.5

Write $- 2^{3}$ as a fraction with denominator $1$ .

$\frac{45 \div 5 \cdot 2}{3 \cdot 2} + \frac{24 \cdot 3}{2 \cdot 3} + \frac{- 2^{3}}{1}$

Step 2.6

Multiply $\frac{- 2^{3}}{1}$ by $\frac{6}{6}$ .

$\frac{45 \div 5 \cdot 2}{3 \cdot 2} + \frac{24 \cdot 3}{2 \cdot 3} + \frac{- 2^{3}}{1} \cdot \frac{6}{6}$

Step 2.7

Multiply $\frac{- 2^{3}}{1}$ by $\frac{6}{6}$ .

$\frac{45 \div 5 \cdot 2}{3 \cdot 2} + \frac{24 \cdot 3}{2 \cdot 3} + \frac{- 2^{3} \cdot 6}{6}$

Step 2.8

Reorder the factors of $3 \cdot 2$ .

$\frac{45 \div 5 \cdot 2}{2 \cdot 3} + \frac{24 \cdot 3}{2 \cdot 3} + \frac{- 2^{3} \cdot 6}{6}$

Step 2.9

Multiply $2$ by $3$ .

$\frac{45 \div 5 \cdot 2}{6} + \frac{24 \cdot 3}{2 \cdot 3} + \frac{- 2^{3} \cdot 6}{6}$

Step 2.10

Multiply $2$ by $3$ .

$\frac{45 \div 5 \cdot 2}{6} + \frac{24 \cdot 3}{6} + \frac{- 2^{3} \cdot 6}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{45 \div 5 \cdot 2 + 24 \cdot 3 - 2^{3} \cdot 6}{6}$

Step 4

Simplify each term.

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Step 4.1

Divide $45$ by $5$ .

$\frac{9 \cdot 2 + 24 \cdot 3 - 2^{3} \cdot 6}{6}$

Step 4.2

Multiply $9$ by $2$ .

$\frac{18 + 24 \cdot 3 - 2^{3} \cdot 6}{6}$

Step 4.3

Multiply $24$ by $3$ .

$\frac{18 + 72 - 2^{3} \cdot 6}{6}$

Step 4.4

Raise $2$ to the power of $3$ .

$\frac{18 + 72 - 1 \cdot 8 \cdot 6}{6}$

Step 4.5

Multiply $- 1 \cdot 8 \cdot 6$ .

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Step 4.5.1

Multiply $- 1$ by $8$ .

$\frac{18 + 72 - 8 \cdot 6}{6}$

Step 4.5.2

Multiply $- 8$ by $6$ .

$\frac{18 + 72 - 48}{6}$

Step 5

Simplify the expression.

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Step 5.1

Add $18$ and $72$ .

$\frac{90 - 48}{6}$

Step 5.2

Subtract $48$ from $90$ .

$\frac{42}{6}$

Step 5.3

Divide $42$ by $6$ .

$7$