Basic Math Examples

$4 \frac{1}{2} - 1 \frac{8}{9}$

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.

$4 + \frac{1}{2} - 1 \frac{8}{9}$

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 $\frac{2}{2}$ .

$4 \cdot \frac{2}{2} + \frac{1}{2} - 1 \frac{8}{9}$

Step 1.2.2

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

$\frac{4 \cdot 2}{2} + \frac{1}{2} - 1 \frac{8}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 1}{2} - 1 \frac{8}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $2$ .

$\frac{8 + 1}{2} - 1 \frac{8}{9}$

Step 1.2.4.2

Add $8$ and $1$ .

$\frac{9}{2} - 1 \frac{8}{9}$

Step 2

Convert $1 \frac{8}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{9}{2} - (1 + \frac{8}{9})$

Step 2.2

Add $1$ and $\frac{8}{9}$ .

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Step 2.2.1

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

$\frac{9}{2} - (\frac{9}{9} + \frac{8}{9})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{9 + 8}{9}$

Step 2.2.3

Add $9$ and $8$ .

$\frac{9}{2} - \frac{17}{9}$

Step 3

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{9}{2} \cdot \frac{9}{9} - \frac{17}{9}$

Step 4

To write $- \frac{17}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{2} \cdot \frac{9}{9} - \frac{17}{9} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{9}{2}$ by $\frac{9}{9}$ .

$\frac{9 \cdot 9}{2 \cdot 9} - \frac{17}{9} \cdot \frac{2}{2}$

Step 5.2

Multiply $2$ by $9$ .

$\frac{9 \cdot 9}{18} - \frac{17}{9} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{17}{9}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 9}{18} - \frac{17 \cdot 2}{9 \cdot 2}$

Step 5.4

Multiply $9$ by $2$ .

$\frac{9 \cdot 9}{18} - \frac{17 \cdot 2}{18}$

Step 6

Combine the numerators over the common denominator.

$\frac{9 \cdot 9 - 17 \cdot 2}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $9$ by $9$ .

$\frac{81 - 17 \cdot 2}{18}$

Step 7.2

Multiply $- 17$ by $2$ .

$\frac{81 - 34}{18}$

Step 7.3

Subtract $34$ from $81$ .

$\frac{47}{18}$