Basic Math Examples

$\frac{6}{5} - \frac{1}{2} \div 2 + \sqrt{\frac{9}{100}}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

$\frac{6}{5} \cdot \frac{2}{2} - \frac{1}{2} \div 2 + \sqrt{\frac{9}{100}}$

Step 1.2

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

$\frac{6 \cdot 2}{5 \cdot 2} - \frac{1}{2} \div 2 + \sqrt{\frac{9}{100}}$

Step 1.3

Multiply $\frac{1}{2} \div 2$ by $\frac{5}{5}$ .

$\frac{6 \cdot 2}{5 \cdot 2} - (\frac{1}{2} \div 2 \cdot \frac{5}{5}) + \sqrt{\frac{9}{100}}$

Step 1.4

Multiply $\frac{1}{2} \div 2$ by $\frac{5}{5}$ .

$\frac{6 \cdot 2}{5 \cdot 2} - \frac{\frac{1}{2} \cdot 5}{2 \cdot 5} + \sqrt{\frac{9}{100}}$

Step 1.5

Write $\sqrt{\frac{9}{100}}$ as a fraction with denominator $1$ .

$\frac{6 \cdot 2}{5 \cdot 2} - \frac{\frac{1}{2} \cdot 5}{2 \cdot 5} + \frac{\sqrt{\frac{9}{100}}}{1}$

Step 1.6

Multiply $\frac{\sqrt{\frac{9}{100}}}{1}$ by $\frac{10}{10}$ .

$\frac{6 \cdot 2}{5 \cdot 2} - \frac{\frac{1}{2} \cdot 5}{2 \cdot 5} + \frac{\sqrt{\frac{9}{100}}}{1} \cdot \frac{10}{10}$

Step 1.7

Multiply $\frac{\sqrt{\frac{9}{100}}}{1}$ by $\frac{10}{10}$ .

$\frac{6 \cdot 2}{5 \cdot 2} - \frac{\frac{1}{2} \cdot 5}{2 \cdot 5} + \frac{\sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 1.8

Reorder the factors of $5 \cdot 2$ .

$\frac{6 \cdot 2}{2 \cdot 5} - \frac{\frac{1}{2} \cdot 5}{2 \cdot 5} + \frac{\sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 1.9

Multiply $2$ by $5$ .

$\frac{6 \cdot 2}{10} - \frac{\frac{1}{2} \cdot 5}{2 \cdot 5} + \frac{\sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 1.10

Multiply $2$ by $5$ .

$\frac{6 \cdot 2}{10} - \frac{\frac{1}{2} \cdot 5}{10} + \frac{\sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 2

Combine the numerators over the common denominator.

$\frac{6 \cdot 2 - \frac{1}{2} \cdot 5 + \sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 3

Simplify each term.

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Step 3.1

Multiply $6$ by $2$ .

$\frac{12 - \frac{1}{2} \cdot 5 + \sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 3.2

Multiply $- \frac{1}{2} \cdot 5$ .

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Step 3.2.1

Multiply $5$ by $- 1$ .

$\frac{12 - 5 (\frac{1}{2}) + \sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 3.2.2

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{12 + \frac{- 5}{2} + \sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 3.3

Move the negative in front of the fraction.

$\frac{12 - \frac{5}{2} + \sqrt{\frac{9}{100}} \cdot 10}{10}$

Step 3.4

Rewrite $\sqrt{\frac{9}{100}}$ as $\frac{\sqrt{9}}{\sqrt{100}}$ .

$\frac{12 - \frac{5}{2} + \frac{\sqrt{9}}{\sqrt{100}} \cdot 10}{10}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Rewrite $9$ as $3^{2}$ .

$\frac{12 - \frac{5}{2} + \frac{\sqrt{3^{2}}}{\sqrt{100}} \cdot 10}{10}$

Step 3.5.2

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

$\frac{12 - \frac{5}{2} + \frac{3}{\sqrt{100}} \cdot 10}{10}$

Step 3.6

Simplify the denominator.

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Step 3.6.1

Rewrite $100$ as $10^{2}$ .

$\frac{12 - \frac{5}{2} + \frac{3}{\sqrt{10^{2}}} \cdot 10}{10}$

Step 3.6.2

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

$\frac{12 - \frac{5}{2} + \frac{3}{10} \cdot 10}{10}$

Step 3.7

Cancel the common factor of $10$ .

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Step 3.7.1

Cancel the common factor.

$\frac{12 - \frac{5}{2} + \frac{3}{10} \cdot 10}{10}$

Step 3.7.2

Rewrite the expression.

$\frac{12 - \frac{5}{2} + 3}{10}$

Step 4

Find the common denominator.

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Step 4.1

Write $12$ as a fraction with denominator $1$ .

$\frac{\frac{12}{1} - \frac{5}{2} + 3}{10}$

Step 4.2

Multiply $\frac{12}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{12}{1} \cdot \frac{2}{2} - \frac{5}{2} + 3}{10}$

Step 4.3

Multiply $\frac{12}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{12 \cdot 2}{2} - \frac{5}{2} + 3}{10}$

Step 4.4

Write $3$ as a fraction with denominator $1$ .

$\frac{\frac{12 \cdot 2}{2} - \frac{5}{2} + \frac{3}{1}}{10}$

Step 4.5

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{12 \cdot 2}{2} - \frac{5}{2} + \frac{3}{1} \cdot \frac{2}{2}}{10}$

Step 4.6

Multiply $\frac{3}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{12 \cdot 2}{2} - \frac{5}{2} + \frac{3 \cdot 2}{2}}{10}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{12 \cdot 2 - 5 + 3 \cdot 2}{2}}{10}$

Step 6

Simplify each term.

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Step 6.1

Multiply $12$ by $2$ .

$\frac{\frac{24 - 5 + 3 \cdot 2}{2}}{10}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{\frac{24 - 5 + 6}{2}}{10}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Subtract $5$ from $24$ .

$\frac{\frac{19 + 6}{2}}{10}$

Step 7.2

Add $19$ and $6$ .

$\frac{\frac{25}{2}}{10}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{2} \cdot \frac{1}{10}$

Step 9

Cancel the common factor of $5$ .

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Step 9.1

Factor $5$ out of $25$ .

$\frac{5 (5)}{2} \cdot \frac{1}{10}$

Step 9.2

Factor $5$ out of $10$ .

$\frac{5 \cdot 5}{2} \cdot \frac{1}{5 \cdot 2}$

Step 9.3

Cancel the common factor.

$\frac{5 \cdot 5}{2} \cdot \frac{1}{5 \cdot 2}$

Step 9.4

Rewrite the expression.

$\frac{5}{2} \cdot \frac{1}{2}$

Step 10

Multiply $\frac{5}{2}$ by $\frac{1}{2}$ .

$\frac{5}{2 \cdot 2}$

Step 11

Multiply $2$ by $2$ .

$\frac{5}{4}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$