Basic Math Examples

\frac{12}{10} \div 36 + \frac{12}{10} \div \frac{25}{100} - \frac{21}{16}

$\frac{12}{10} \div 36 + \frac{12}{10} \div \frac{25}{100} - \frac{21}{16}$

Step 1

Find the common denominator.

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Step 1.1

Cancel the common factor of

25

$25$ and

$100$ .

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Step 1.1.1

Factor

$25$ out of

$25$ .

$\frac{12}{10} \div 36 + \frac{12}{10} \div \frac{25 (1)}{100} - \frac{21}{16}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor

$25$ out of

$100$ .

$\frac{12}{10} \div 36 + \frac{12}{10} \div \frac{25 \cdot 1}{25 \cdot 4} - \frac{21}{16}$

Step 1.1.2.2

Cancel the common factor.

$\frac{12}{10} \div 36 + \frac{12}{10} \div \frac{25 \cdot 1}{25 \cdot 4} - \frac{21}{16}$

Step 1.1.2.3

Rewrite the expression.

$\frac{12}{10} \div 36 + \frac{12}{10} \div \frac{1}{4} - \frac{21}{16}$

Step 1.2

Multiply

$\frac{12}{10} \div 36$ by

$\frac{\frac{4}{4}}{\frac{4}{4}}$ .

$\frac{12}{10} \div 36 \cdot \frac{\frac{4}{4}}{\frac{4}{4}} + \frac{12}{10} \div \frac{1}{4} - \frac{21}{16}$

Step 1.3

Multiply

$\frac{12}{10} \div 36$ by

$\frac{\frac{4}{4}}{\frac{4}{4}}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{36 (\frac{4}{4})} + \frac{12}{10} \div \frac{1}{4} - \frac{21}{16}$

Step 1.4

Multiply

$\frac{12}{10} \div \frac{1}{4}$ by

$\frac{144}{144}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{36 (\frac{4}{4})} + \frac{12}{10} \div \frac{1}{4} \cdot \frac{144}{144} - \frac{21}{16}$

Step 1.5

Multiply

$\frac{12}{10} \div \frac{1}{4}$ by

$\frac{144}{144}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{36 (\frac{4}{4})} + \frac{\frac{12}{10} \cdot 144}{\frac{1}{4} \cdot 144} - \frac{21}{16}$

Step 1.6

Multiply

$\frac{21}{16}$ by

$\frac{\frac{9}{4}}{\frac{9}{4}}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{36 (\frac{4}{4})} + \frac{\frac{12}{10} \cdot 144}{\frac{1}{4} \cdot 144} - (\frac{21}{16} \cdot \frac{\frac{9}{4}}{\frac{9}{4}})$

Step 1.7

Multiply

$\frac{21}{16}$ by

$\frac{\frac{9}{4}}{\frac{9}{4}}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{36 (\frac{4}{4})} + \frac{\frac{12}{10} \cdot 144}{\frac{1}{4} \cdot 144} - \frac{21 (\frac{9}{4})}{16 (\frac{9}{4})}$

Step 1.8

Combine

$36$ and

$\frac{4}{4}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{\frac{36 \cdot 4}{4}} + \frac{\frac{12}{10} \cdot 144}{\frac{1}{4} \cdot 144} - \frac{21 (\frac{9}{4})}{16 (\frac{9}{4})}$

Step 1.9

Multiply

$36$ by

$4$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{\frac{144}{4}} + \frac{\frac{12}{10} \cdot 144}{\frac{1}{4} \cdot 144} - \frac{21 (\frac{9}{4})}{16 (\frac{9}{4})}$

Step 1.10

Reorder the factors of

$\frac{1}{4} \cdot 144$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{\frac{144}{4}} + \frac{\frac{12}{10} \cdot 144}{144 (\frac{1}{4})} - \frac{21 (\frac{9}{4})}{16 (\frac{9}{4})}$

Step 1.11

Combine

$144$ and

$\frac{1}{4}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{\frac{144}{4}} + \frac{\frac{12}{10} \cdot 144}{\frac{144}{4}} - \frac{21 (\frac{9}{4})}{16 (\frac{9}{4})}$

Step 1.12

Combine

$16$ and

$\frac{9}{4}$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{\frac{144}{4}} + \frac{\frac{12}{10} \cdot 144}{\frac{144}{4}} - \frac{21 (\frac{9}{4})}{\frac{16 \cdot 9}{4}}$

Step 1.13

Multiply

$16$ by

$9$ .

$\frac{\frac{12}{10} \cdot \frac{4}{4}}{\frac{144}{4}} + \frac{\frac{12}{10} \cdot 144}{\frac{144}{4}} - \frac{21 (\frac{9}{4})}{\frac{144}{4}}$

Step 2

Combine the numerators over the common denominator.

$\frac{\frac{12}{10} \cdot \frac{4}{4} + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of

$4$ .

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Step 3.1.1

Cancel the common factor.

$\frac{\frac{12}{10} \cdot \frac{4}{4} + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.1.2

Rewrite the expression.

$\frac{\frac{12}{10} \cdot 1 + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.2

Multiply

$\frac{12}{10}$ by

$1$ .

$\frac{\frac{12}{10} + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.3

Cancel the common factor of

$12$ and

$10$ .

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Step 3.3.1

Factor

$2$ out of

$12$ .

$\frac{\frac{2 (6)}{10} + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor

$2$ out of

$10$ .

$\frac{\frac{2 \cdot 6}{2 \cdot 5} + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.3.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot 6}{2 \cdot 5} + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{\frac{6}{5} + \frac{12}{10} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.4

Cancel the common factor of

$2$ .

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Step 3.4.1

Factor

$2$ out of

$10$ .

$\frac{\frac{6}{5} + \frac{12}{2 (5)} \cdot 144 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.4.2

Factor

$2$ out of

$144$ .

$\frac{\frac{6}{5} + \frac{12}{2 \cdot 5} \cdot (2 \cdot 72) - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.4.3

Cancel the common factor.

$\frac{\frac{6}{5} + \frac{12}{2 \cdot 5} \cdot (2 \cdot 72) - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.4.4

Rewrite the expression.

$\frac{\frac{6}{5} + \frac{12}{5} \cdot 72 - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.5

Combine

$\frac{12}{5}$ and

$72$ .

$\frac{\frac{6}{5} + \frac{12 \cdot 72}{5} - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.6

Multiply

$12$ by

$72$ .

$\frac{\frac{6}{5} + \frac{864}{5} - 21 (\frac{9}{4})}{\frac{144}{4}}$

Step 3.7

Multiply

$- 21 (\frac{9}{4})$ .

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Step 3.7.1

Combine

$- 21$ and

$\frac{9}{4}$ .

$\frac{\frac{6}{5} + \frac{864}{5} + \frac{- 21 \cdot 9}{4}}{\frac{144}{4}}$

Step 3.7.2

Multiply

$- 21$ by

$9$ .

$\frac{\frac{6}{5} + \frac{864}{5} + \frac{- 189}{4}}{\frac{144}{4}}$

Step 3.8

Move the negative in front of the fraction.

$\frac{\frac{6}{5} + \frac{864}{5} - \frac{189}{4}}{\frac{144}{4}}$

Step 4

Combine fractions.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{\frac{6 + 864}{5} + \frac{- 189}{4}}{\frac{144}{4}}$

Step 4.2

Add

$6$ and

$864$ .

$\frac{\frac{870}{5} + \frac{- 189}{4}}{\frac{144}{4}}$

Step 5

Simplify each term.

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Step 5.1

Divide

$870$ by

$5$ .

$\frac{174 + \frac{- 189}{4}}{\frac{144}{4}}$

Step 5.2

Move the negative in front of the fraction.

$\frac{174 - \frac{189}{4}}{\frac{144}{4}}$

Step 6

To write

$174$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{174 \cdot \frac{4}{4} - \frac{189}{4}}{\frac{144}{4}}$

Step 7

Combine

$174$ and

$\frac{4}{4}$ .

$\frac{\frac{174 \cdot 4}{4} - \frac{189}{4}}{\frac{144}{4}}$

Step 8

Combine the numerators over the common denominator.

$\frac{\frac{174 \cdot 4 - 189}{4}}{\frac{144}{4}}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply

$174$ by

$4$ .

$\frac{\frac{696 - 189}{4}}{\frac{144}{4}}$

Step 9.2

Subtract

$189$ from

$696$ .

$\frac{\frac{507}{4}}{\frac{144}{4}}$

Step 10

Cancel the common factor of

$144$ and

$4$ .

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Step 10.1

Factor

$4$ out of

$144$ .

$\frac{\frac{507}{4}}{\frac{4 \cdot 36}{4}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor

$4$ out of

$4$ .

$\frac{\frac{507}{4}}{\frac{4 \cdot 36}{4 (1)}}$

Step 10.2.2

Cancel the common factor.

$\frac{\frac{507}{4}}{\frac{4 \cdot 36}{4 \cdot 1}}$

Step 10.2.3

Rewrite the expression.

$\frac{\frac{507}{4}}{\frac{36}{1}}$

Step 10.2.4

Divide

$36$ by

$1$ .

$\frac{\frac{507}{4}}{36}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$\frac{507}{4} \cdot \frac{1}{36}$

Step 12

Cancel the common factor of

$3$ .

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Step 12.1

Factor

$3$ out of

$507$ .

$\frac{3 (169)}{4} \cdot \frac{1}{36}$

Step 12.2

Factor

$3$ out of

$36$ .

$\frac{3 \cdot 169}{4} \cdot \frac{1}{3 \cdot 12}$

Step 12.3

Cancel the common factor.

$\frac{3 \cdot 169}{4} \cdot \frac{1}{3 \cdot 12}$

Step 12.4

Rewrite the expression.

$\frac{169}{4} \cdot \frac{1}{12}$

Step 13

Multiply

$\frac{169}{4}$ by

$\frac{1}{12}$ .

$\frac{169}{4 \cdot 12}$

Step 14

Multiply

$4$ by

$12$ .

$\frac{169}{48}$

Step 15

The result can be shown in multiple forms.

Exact Form:

$\frac{169}{48}$

Decimal Form:

$3.5208\overline{3}$

Mixed Number Form:

$3 \frac{25}{48}$