Basic Math Examples

$- 2 \frac{1}{4} \div 3 \frac{1}{2} \div (- \frac{9}{224})$

Step 1

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$- (2 + \frac{1}{4}) \div 3 \frac{1}{2} \div (- \frac{9}{224})$

Step 1.2

Add $2$ and $\frac{1}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- (2 \cdot \frac{4}{4} + \frac{1}{4}) \div 3 \frac{1}{2} \div (- \frac{9}{224})$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$- (\frac{2 \cdot 4}{4} + \frac{1}{4}) \div 3 \frac{1}{2} \div (- \frac{9}{224})$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 4 + 1}{4} \div 3 \frac{1}{2} \div (- \frac{9}{224})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$- \frac{8 + 1}{4} \div 3 \frac{1}{2} \div (- \frac{9}{224})$

Step 1.2.4.2

Add $8$ and $1$ .

$- \frac{9}{4} \div 3 \frac{1}{2} \div (- \frac{9}{224})$

Step 2

Convert $3 \frac{1}{2}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{9}{4} \div (3 + \frac{1}{2}) \div (- \frac{9}{224})$

Step 2.2

Add $3$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{9}{4} \div (3 \cdot \frac{2}{2} + \frac{1}{2}) \div (- \frac{9}{224})$

Step 2.2.2

Combine $3$ and $\frac{2}{2}$ .

$- \frac{9}{4} \div (\frac{3 \cdot 2}{2} + \frac{1}{2}) \div (- \frac{9}{224})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{9}{4} \div \frac{3 \cdot 2 + 1}{2} \div (- \frac{9}{224})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $2$ .

$- \frac{9}{4} \div \frac{6 + 1}{2} \div (- \frac{9}{224})$

Step 2.2.4.2

Add $6$ and $1$ .

$- \frac{9}{4} \div \frac{7}{2} \div (- \frac{9}{224})$

Step 3

To divide by a fraction, multiply by its reciprocal.

$- \frac{9}{4} \div \frac{7}{2} (- \frac{224}{9})$

Step 4

To divide by a fraction, multiply by its reciprocal.

$- \frac{9}{4} \cdot \frac{2}{7} (- \frac{224}{9})$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Move the leading negative in $- \frac{9}{4}$ into the numerator.

$\frac{- 9}{4} \cdot \frac{2}{7} (- \frac{224}{9})$

Step 5.2

Factor $2$ out of $4$ .

$\frac{- 9}{2 (2)} \cdot \frac{2}{7} (- \frac{224}{9})$

Step 5.3

Cancel the common factor.

$\frac{- 9}{2 \cdot 2} \cdot \frac{2}{7} (- \frac{224}{9})$

Step 5.4

Rewrite the expression.

$\frac{- 9}{2} \cdot \frac{1}{7} (- \frac{224}{9})$

Step 6

Multiply $\frac{- 9}{2}$ by $\frac{1}{7}$ .

$\frac{- 9}{2 \cdot 7} (- \frac{224}{9})$

Step 7

Multiply $2$ by $7$ .

$\frac{- 9}{14} (- \frac{224}{9})$

Step 8

Cancel the common factor of $9$ .

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Step 8.1

Move the leading negative in $- \frac{224}{9}$ into the numerator.

$\frac{- 9}{14} \cdot \frac{- 224}{9}$

Step 8.2

Factor $9$ out of $- 9$ .

$\frac{9 (- 1)}{14} \cdot \frac{- 224}{9}$

Step 8.3

Cancel the common factor.

$\frac{9 \cdot - 1}{14} \cdot \frac{- 224}{9}$

Step 8.4

Rewrite the expression.

$\frac{- 1}{14} \cdot - 224$

Step 9

Cancel the common factor of $14$ .

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Step 9.1

Factor $14$ out of $- 224$ .

$\frac{- 1}{14} \cdot (14 (- 16))$

Step 9.2

Cancel the common factor.

$\frac{- 1}{14} \cdot (14 \cdot - 16)$

Step 9.3

Rewrite the expression.

$- - 16$

Step 10

Multiply $- 1$ by $- 16$ .

$16$