Basic Math Examples

$(\frac{3}{16} - \frac{1}{10}) \div (\frac{7}{12} + \frac{7}{10})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{3}{16} - \frac{1}{10}}{\frac{7}{12} + \frac{7}{10}}$

Step 2

Multiply the numerator and denominator of the fraction by $240$ .

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Step 2.1

Multiply $\frac{\frac{3}{16} - \frac{1}{10}}{\frac{7}{12} + \frac{7}{10}}$ by $\frac{240}{240}$ .

$\frac{240}{240} \cdot \frac{\frac{3}{16} - \frac{1}{10}}{\frac{7}{12} + \frac{7}{10}}$

Step 2.2

Combine.

$\frac{240 (\frac{3}{16} - \frac{1}{10})}{240 (\frac{7}{12} + \frac{7}{10})}$

Step 3

Apply the distributive property.

$\frac{240 (\frac{3}{16}) + 240 (- \frac{1}{10})}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $16$ .

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Step 4.1.1

Factor $16$ out of $240$ .

$\frac{16 (15) \frac{3}{16} + 240 (- \frac{1}{10})}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.1.2

Cancel the common factor.

$\frac{16 \cdot 15 \frac{3}{16} + 240 (- \frac{1}{10})}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.1.3

Rewrite the expression.

$\frac{15 \cdot 3 + 240 (- \frac{1}{10})}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.2

Multiply $15$ by $3$ .

$\frac{45 + 240 (- \frac{1}{10})}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.3

Cancel the common factor of $10$ .

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Step 4.3.1

Move the leading negative in $- \frac{1}{10}$ into the numerator.

$\frac{45 + 240 (\frac{- 1}{10})}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.3.2

Factor $10$ out of $240$ .

$\frac{45 + 10 (24) \frac{- 1}{10}}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.3.3

Cancel the common factor.

$\frac{45 + 10 \cdot 24 \frac{- 1}{10}}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.3.4

Rewrite the expression.

$\frac{45 + 24 \cdot - 1}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.4

Multiply $24$ by $- 1$ .

$\frac{45 - 24}{240 (\frac{7}{12}) + 240 (\frac{7}{10})}$

Step 4.5

Cancel the common factor of $12$ .

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Step 4.5.1

Factor $12$ out of $240$ .

$\frac{45 - 24}{12 (20) \frac{7}{12} + 240 (\frac{7}{10})}$

Step 4.5.2

Cancel the common factor.

$\frac{45 - 24}{12 \cdot 20 \frac{7}{12} + 240 (\frac{7}{10})}$

Step 4.5.3

Rewrite the expression.

$\frac{45 - 24}{20 \cdot 7 + 240 (\frac{7}{10})}$

Step 4.6

Multiply $20$ by $7$ .

$\frac{45 - 24}{140 + 240 (\frac{7}{10})}$

Step 4.7

Cancel the common factor of $10$ .

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Step 4.7.1

Factor $10$ out of $240$ .

$\frac{45 - 24}{140 + 10 (24) \frac{7}{10}}$

Step 4.7.2

Cancel the common factor.

$\frac{45 - 24}{140 + 10 \cdot 24 \frac{7}{10}}$

Step 4.7.3

Rewrite the expression.

$\frac{45 - 24}{140 + 24 \cdot 7}$

Step 4.8

Multiply $24$ by $7$ .

$\frac{45 - 24}{140 + 168}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Subtract $24$ from $45$ .

$\frac{21}{140 + 168}$

Step 5.2

Add $140$ and $168$ .

$\frac{21}{308}$

Step 5.3

Cancel the common factor of $21$ and $308$ .

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Step 5.3.1

Factor $7$ out of $21$ .

$\frac{7 (3)}{308}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $7$ out of $308$ .

$\frac{7 \cdot 3}{7 \cdot 44}$

Step 5.3.2.2

Cancel the common factor.

$\frac{7 \cdot 3}{7 \cdot 44}$

Step 5.3.2.3

Rewrite the expression.

$\frac{3}{44}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{44}$

Decimal Form:

$0.06\overline{81}$