Basic Math Examples

$\frac{\frac{3}{4} - \frac{9}{8}}{\frac{1}{10} + \frac{12}{5}}$

Step 1

Multiply the numerator and denominator of the fraction by $40$ .

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Step 1.1

Multiply $\frac{\frac{3}{4} - \frac{9}{8}}{\frac{1}{10} + \frac{12}{5}}$ by $\frac{40}{40}$ .

$\frac{40}{40} \cdot \frac{\frac{3}{4} - \frac{9}{8}}{\frac{1}{10} + \frac{12}{5}}$

Step 1.2

Combine.

$\frac{40 (\frac{3}{4} - \frac{9}{8})}{40 (\frac{1}{10} + \frac{12}{5})}$

Step 2

Apply the distributive property.

$\frac{40 (\frac{3}{4}) + 40 (- \frac{9}{8})}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $40$ .

$\frac{4 (10) \frac{3}{4} + 40 (- \frac{9}{8})}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.1.2

Cancel the common factor.

$\frac{4 \cdot 10 \frac{3}{4} + 40 (- \frac{9}{8})}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.1.3

Rewrite the expression.

$\frac{10 \cdot 3 + 40 (- \frac{9}{8})}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.2

Multiply $10$ by $3$ .

$\frac{30 + 40 (- \frac{9}{8})}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.3

Cancel the common factor of $8$ .

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Step 3.3.1

Move the leading negative in $- \frac{9}{8}$ into the numerator.

$\frac{30 + 40 (\frac{- 9}{8})}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.3.2

Factor $8$ out of $40$ .

$\frac{30 + 8 (5) \frac{- 9}{8}}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.3.3

Cancel the common factor.

$\frac{30 + 8 \cdot 5 \frac{- 9}{8}}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.3.4

Rewrite the expression.

$\frac{30 + 5 \cdot - 9}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.4

Multiply $5$ by $- 9$ .

$\frac{30 - 45}{40 (\frac{1}{10}) + 40 (\frac{12}{5})}$

Step 3.5

Cancel the common factor of $10$ .

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Step 3.5.1

Factor $10$ out of $40$ .

$\frac{30 - 45}{10 (4) \frac{1}{10} + 40 (\frac{12}{5})}$

Step 3.5.2

Cancel the common factor.

$\frac{30 - 45}{10 \cdot 4 \frac{1}{10} + 40 (\frac{12}{5})}$

Step 3.5.3

Rewrite the expression.

$\frac{30 - 45}{4 + 40 (\frac{12}{5})}$

Step 3.6

Cancel the common factor of $5$ .

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Step 3.6.1

Factor $5$ out of $40$ .

$\frac{30 - 45}{4 + 5 (8) \frac{12}{5}}$

Step 3.6.2

Cancel the common factor.

$\frac{30 - 45}{4 + 5 \cdot 8 \frac{12}{5}}$

Step 3.6.3

Rewrite the expression.

$\frac{30 - 45}{4 + 8 \cdot 12}$

Step 3.7

Multiply $8$ by $12$ .

$\frac{30 - 45}{4 + 96}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $45$ from $30$ .

$\frac{- 15}{4 + 96}$

Step 4.2

Add $4$ and $96$ .

$\frac{- 15}{100}$

Step 4.3

Cancel the common factor of $- 15$ and $100$ .

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Step 4.3.1

Factor $5$ out of $- 15$ .

$\frac{5 (- 3)}{100}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $5$ out of $100$ .

$\frac{5 \cdot - 3}{5 \cdot 20}$

Step 4.3.2.2

Cancel the common factor.

$\frac{5 \cdot - 3}{5 \cdot 20}$

Step 4.3.2.3

Rewrite the expression.

$\frac{- 3}{20}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{3}{20}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{20}$

Decimal Form:

$- 0.15$