Basic Math Examples

$4 \frac{1}{2} \div 1 \frac{1}{4} - 5 \frac{1}{2}$

Step 1

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

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Step 1.1

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

$(4 + \frac{1}{2}) \div 1 \frac{1}{4} - 5 \frac{1}{2}$

Step 1.2

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

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Step 1.2.1

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

$(4 \cdot \frac{2}{2} + \frac{1}{2}) \div 1 \frac{1}{4} - 5 \frac{1}{2}$

Step 1.2.2

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

$(\frac{4 \cdot 2}{2} + \frac{1}{2}) \div 1 \frac{1}{4} - 5 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 1}{2} \div 1 \frac{1}{4} - 5 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $2$ .

$\frac{8 + 1}{2} \div 1 \frac{1}{4} - 5 \frac{1}{2}$

Step 1.2.4.2

Add $8$ and $1$ .

$\frac{9}{2} \div 1 \frac{1}{4} - 5 \frac{1}{2}$

Step 2

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

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Step 2.1

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

$\frac{9}{2} \div (1 + \frac{1}{4}) - 5 \frac{1}{2}$

Step 2.2

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

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{9}{2} \div (\frac{4}{4} + \frac{1}{4}) - 5 \frac{1}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{9}{2} \div \frac{4 + 1}{4} - 5 \frac{1}{2}$

Step 2.2.3

Add $4$ and $1$ .

$\frac{9}{2} \div \frac{5}{4} - 5 \frac{1}{2}$

Step 3

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 3.1

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

$\frac{9}{2} \div \frac{5}{4} - (5 + \frac{1}{2})$

Step 3.2

Add $5$ and $\frac{1}{2}$ .

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Step 3.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{2} \div \frac{5}{4} - (5 \cdot \frac{2}{2} + \frac{1}{2})$

Step 3.2.2

Combine $5$ and $\frac{2}{2}$ .

$\frac{9}{2} \div \frac{5}{4} - (\frac{5 \cdot 2}{2} + \frac{1}{2})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} \div \frac{5}{4} - \frac{5 \cdot 2 + 1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $5$ by $2$ .

$\frac{9}{2} \div \frac{5}{4} - \frac{10 + 1}{2}$

Step 3.2.4.2

Add $10$ and $1$ .

$\frac{9}{2} \div \frac{5}{4} - \frac{11}{2}$

Step 4

Simplify each term.

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Step 4.1

To divide by a fraction, multiply by its reciprocal.

$\frac{9}{2} \cdot \frac{4}{5} - \frac{11}{2}$

Step 4.2

Cancel the common factor of $2$ .

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Step 4.2.1

Factor $2$ out of $4$ .

$\frac{9}{2} \cdot \frac{2 (2)}{5} - \frac{11}{2}$

Step 4.2.2

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 \cdot 2}{5} - \frac{11}{2}$

Step 4.2.3

Rewrite the expression.

$9 (\frac{2}{5}) - \frac{11}{2}$

Step 4.3

Combine $9$ and $\frac{2}{5}$ .

$\frac{9 \cdot 2}{5} - \frac{11}{2}$

Step 4.4

Multiply $9$ by $2$ .

$\frac{18}{5} - \frac{11}{2}$

Step 5

To write $\frac{18}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{18}{5} \cdot \frac{2}{2} - \frac{11}{2}$

Step 6

To write $- \frac{11}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{18}{5} \cdot \frac{2}{2} - \frac{11}{2} \cdot \frac{5}{5}$

Step 7

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{18}{5}$ by $\frac{2}{2}$ .

$\frac{18 \cdot 2}{5 \cdot 2} - \frac{11}{2} \cdot \frac{5}{5}$

Step 7.2

Multiply $5$ by $2$ .

$\frac{18 \cdot 2}{10} - \frac{11}{2} \cdot \frac{5}{5}$

Step 7.3

Multiply $\frac{11}{2}$ by $\frac{5}{5}$ .

$\frac{18 \cdot 2}{10} - \frac{11 \cdot 5}{2 \cdot 5}$

Step 7.4

Multiply $2$ by $5$ .

$\frac{18 \cdot 2}{10} - \frac{11 \cdot 5}{10}$

Step 8

Combine the numerators over the common denominator.

$\frac{18 \cdot 2 - 11 \cdot 5}{10}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $18$ by $2$ .

$\frac{36 - 11 \cdot 5}{10}$

Step 9.2

Multiply $- 11$ by $5$ .

$\frac{36 - 55}{10}$

Step 9.3

Subtract $55$ from $36$ .

$\frac{- 19}{10}$

Step 10

Move the negative in front of the fraction.

$- \frac{19}{10}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{19}{10}$

Decimal Form:

$- 1.9$

Mixed Number Form:

$- 1 \frac{9}{10}$