Basic Math Examples

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

Step 1

Find the common denominator.

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Step 1.1

Cancel the common factor of $25$ 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:

$3 \frac{25}{48}$