Pre-Algebra Examples

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

Step 1

Convert $9 \frac{4}{9}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $9$ and $\frac{4}{9}$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $9$ by $9$ .

$\frac{81 + 4}{9} - 5 \frac{1}{4}$

Step 1.2.4.2

Add $81$ and $4$ .

$\frac{85}{9} - 5 \frac{1}{4}$

Step 2

Convert $5 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{85}{9} - (5 + \frac{1}{4})$

Step 2.2

Add $5$ and $\frac{1}{4}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{85}{9} - (5 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine $5$ and $\frac{4}{4}$ .

$\frac{85}{9} - (\frac{5 \cdot 4}{4} + \frac{1}{4})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{85}{9} - \frac{5 \cdot 4 + 1}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $4$ .

$\frac{85}{9} - \frac{20 + 1}{4}$

Step 2.2.4.2

Add $20$ and $1$ .

$\frac{85}{9} - \frac{21}{4}$

Step 3

To write $\frac{85}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{85}{9} \cdot \frac{4}{4} - \frac{21}{4}$

Step 4

To write $- \frac{21}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{85}{9} \cdot \frac{4}{4} - \frac{21}{4} \cdot \frac{9}{9}$

Step 5

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{85}{9}$ by $\frac{4}{4}$ .

$\frac{85 \cdot 4}{9 \cdot 4} - \frac{21}{4} \cdot \frac{9}{9}$

Step 5.2

Multiply $9$ by $4$ .

$\frac{85 \cdot 4}{36} - \frac{21}{4} \cdot \frac{9}{9}$

Step 5.3

Multiply $\frac{21}{4}$ by $\frac{9}{9}$ .

$\frac{85 \cdot 4}{36} - \frac{21 \cdot 9}{4 \cdot 9}$

Step 5.4

Multiply $4$ by $9$ .

$\frac{85 \cdot 4}{36} - \frac{21 \cdot 9}{36}$

Step 6

Combine the numerators over the common denominator.

$\frac{85 \cdot 4 - 21 \cdot 9}{36}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $85$ by $4$ .

$\frac{340 - 21 \cdot 9}{36}$

Step 7.2

Multiply $- 21$ by $9$ .

$\frac{340 - 189}{36}$

Step 7.3

Subtract $189$ from $340$ .

$\frac{151}{36}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{151}{36}$

Decimal Form:

$4.19\overline{4}$

Mixed Number Form:

$4 \frac{7}{36}$