Basic Math Examples

$\sqrt{49} - 3 \cdot 12 + 20 \div 4 \div 2$

Step 1

Find the common denominator.

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Step 1.1

Write $\sqrt{49}$ as a fraction with denominator $1$ .

$\frac{\sqrt{49}}{1} - 3 \cdot 12 + 20 \div 4 \div 2$

Step 1.2

Multiply $\frac{\sqrt{49}}{1}$ by $\frac{2}{2}$ .

$\frac{\sqrt{49}}{1} \cdot \frac{2}{2} - 3 \cdot 12 + 20 \div 4 \div 2$

Step 1.3

Multiply $\frac{\sqrt{49}}{1}$ by $\frac{2}{2}$ .

$\frac{\sqrt{49} \cdot 2}{2} - 3 \cdot 12 + 20 \div 4 \div 2$

Step 1.4

Write $- 3 \cdot 12$ as a fraction with denominator $1$ .

$\frac{\sqrt{49} \cdot 2}{2} + \frac{- 3 \cdot 12}{1} + 20 \div 4 \div 2$

Step 1.5

Multiply $\frac{- 3 \cdot 12}{1}$ by $\frac{2}{2}$ .

$\frac{\sqrt{49} \cdot 2}{2} + \frac{- 3 \cdot 12}{1} \cdot \frac{2}{2} + 20 \div 4 \div 2$

Step 1.6

Multiply $\frac{- 3 \cdot 12}{1}$ by $\frac{2}{2}$ .

$\frac{\sqrt{49} \cdot 2}{2} + \frac{- 3 \cdot 12 \cdot 2}{2} + 20 \div 4 \div 2$

Step 2

Combine the numerators over the common denominator.

$\frac{\sqrt{49} \cdot 2 - 3 \cdot 12 \cdot 2 + 20 \div 4}{2}$

Step 3

Find the common denominator.

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Step 3.1

Write $\sqrt{49} \cdot 2$ as a fraction with denominator $1$ .

$\frac{\frac{\sqrt{49} \cdot 2}{1} - 3 \cdot 12 \cdot 2 + 20 \div 4}{2}$

Step 3.2

Multiply $\frac{\sqrt{49} \cdot 2}{1}$ by $\frac{4}{4}$ .

$\frac{\frac{\sqrt{49} \cdot 2}{1} \cdot \frac{4}{4} - 3 \cdot 12 \cdot 2 + 20 \div 4}{2}$

Step 3.3

Multiply $\frac{\sqrt{49} \cdot 2}{1}$ by $\frac{4}{4}$ .

$\frac{\frac{\sqrt{49} \cdot 2 \cdot 4}{4} - 3 \cdot 12 \cdot 2 + 20 \div 4}{2}$

Step 3.4

Write $- 3 \cdot 12 \cdot 2$ as a fraction with denominator $1$ .

$\frac{\frac{\sqrt{49} \cdot 2 \cdot 4}{4} + \frac{- 3 \cdot 12 \cdot 2}{1} + 20 \div 4}{2}$

Step 3.5

Multiply $\frac{- 3 \cdot 12 \cdot 2}{1}$ by $\frac{4}{4}$ .

$\frac{\frac{\sqrt{49} \cdot 2 \cdot 4}{4} + \frac{- 3 \cdot 12 \cdot 2}{1} \cdot \frac{4}{4} + 20 \div 4}{2}$

Step 3.6

Multiply $\frac{- 3 \cdot 12 \cdot 2}{1}$ by $\frac{4}{4}$ .

$\frac{\frac{\sqrt{49} \cdot 2 \cdot 4}{4} + \frac{- 3 \cdot 12 \cdot 2 \cdot 4}{4} + 20 \div 4}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{\frac{\sqrt{49} \cdot 2 \cdot 4 - 3 \cdot 12 \cdot 2 \cdot 4 + 20}{4}}{2}$

Step 5

Simplify each term.

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Step 5.1

Rewrite $49$ as $7^{2}$ .

$\frac{\frac{\sqrt{7^{2}} \cdot 2 \cdot 4 - 3 \cdot 12 \cdot 2 \cdot 4 + 20}{4}}{2}$

Step 5.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{\frac{7 \cdot 2 \cdot 4 - 3 \cdot 12 \cdot 2 \cdot 4 + 20}{4}}{2}$

Step 5.3

Multiply $7 \cdot 2 \cdot 4$ .

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Step 5.3.1

Multiply $7$ by $2$ .

$\frac{\frac{14 \cdot 4 - 3 \cdot 12 \cdot 2 \cdot 4 + 20}{4}}{2}$

Step 5.3.2

Multiply $14$ by $4$ .

$\frac{\frac{56 - 3 \cdot 12 \cdot 2 \cdot 4 + 20}{4}}{2}$

Step 5.4

Multiply $- 3 \cdot 12 \cdot 2 \cdot 4$ .

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Step 5.4.1

Multiply $- 3$ by $12$ .

$\frac{\frac{56 - 36 \cdot 2 \cdot 4 + 20}{4}}{2}$

Step 5.4.2

Multiply $- 36$ by $2$ .

$\frac{\frac{56 - 72 \cdot 4 + 20}{4}}{2}$

Step 5.4.3

Multiply $- 72$ by $4$ .

$\frac{\frac{56 - 288 + 20}{4}}{2}$

Step 6

Simplify the expression.

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Step 6.1

Subtract $288$ from $56$ .

$\frac{\frac{- 232 + 20}{4}}{2}$

Step 6.2

Add $- 232$ and $20$ .

$\frac{\frac{- 212}{4}}{2}$

Step 6.3

Divide $- 212$ by $4$ .

$\frac{- 53}{2}$

Step 6.4

Move the negative in front of the fraction.

$- \frac{53}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{53}{2}$

Decimal Form:

$- 26.5$

Mixed Number Form:

$- 26 \frac{1}{2}$