Pre-Algebra Examples

$19 \frac{8}{9} - 10 \frac{1}{8}$

Step 1

Convert $19 \frac{8}{9}$ to an improper fraction.

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Step 1.1

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

$19 + \frac{8}{9} - 10 \frac{1}{8}$

Step 1.2

Add $19$ and $\frac{8}{9}$ .

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Step 1.2.1

To write $19$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$19 \cdot \frac{9}{9} + \frac{8}{9} - 10 \frac{1}{8}$

Step 1.2.2

Combine $19$ and $\frac{9}{9}$ .

$\frac{19 \cdot 9}{9} + \frac{8}{9} - 10 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{19 \cdot 9 + 8}{9} - 10 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $19$ by $9$ .

$\frac{171 + 8}{9} - 10 \frac{1}{8}$

Step 1.2.4.2

Add $171$ and $8$ .

$\frac{179}{9} - 10 \frac{1}{8}$

Step 2

Convert $10 \frac{1}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{179}{9} - (10 + \frac{1}{8})$

Step 2.2

Add $10$ and $\frac{1}{8}$ .

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Step 2.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{179}{9} - (10 \cdot \frac{8}{8} + \frac{1}{8})$

Step 2.2.2

Combine $10$ and $\frac{8}{8}$ .

$\frac{179}{9} - (\frac{10 \cdot 8}{8} + \frac{1}{8})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{179}{9} - \frac{10 \cdot 8 + 1}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $10$ by $8$ .

$\frac{179}{9} - \frac{80 + 1}{8}$

Step 2.2.4.2

Add $80$ and $1$ .

$\frac{179}{9} - \frac{81}{8}$

Step 3

To write $\frac{179}{9}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{179}{9} \cdot \frac{8}{8} - \frac{81}{8}$

Step 4

To write $- \frac{81}{8}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{179}{9} \cdot \frac{8}{8} - \frac{81}{8} \cdot \frac{9}{9}$

Step 5

Write each expression with a common denominator of $72$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{179}{9}$ by $\frac{8}{8}$ .

$\frac{179 \cdot 8}{9 \cdot 8} - \frac{81}{8} \cdot \frac{9}{9}$

Step 5.2

Multiply $9$ by $8$ .

$\frac{179 \cdot 8}{72} - \frac{81}{8} \cdot \frac{9}{9}$

Step 5.3

Multiply $\frac{81}{8}$ by $\frac{9}{9}$ .

$\frac{179 \cdot 8}{72} - \frac{81 \cdot 9}{8 \cdot 9}$

Step 5.4

Multiply $8$ by $9$ .

$\frac{179 \cdot 8}{72} - \frac{81 \cdot 9}{72}$

Step 6

Combine the numerators over the common denominator.

$\frac{179 \cdot 8 - 81 \cdot 9}{72}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $179$ by $8$ .

$\frac{1432 - 81 \cdot 9}{72}$

Step 7.2

Multiply $- 81$ by $9$ .

$\frac{1432 - 729}{72}$

Step 7.3

Subtract $729$ from $1432$ .

$\frac{703}{72}$

Step 8

The approximate value of $19 \frac{8}{9} - 10 \frac{1}{8}$ found by front end estimation.

$19 \frac{8}{9} - 10 \frac{1}{8} \approx \frac{703}{72}$