Pre-Algebra Examples

$23 \frac{8}{15} - 8 \frac{3}{5}$

Step 1

Convert $23 \frac{8}{15}$ to an improper fraction.

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Step 1.1

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

$23 + \frac{8}{15} - 8 \frac{3}{5}$

Step 1.2

Add $23$ and $\frac{8}{15}$ .

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Step 1.2.1

To write $23$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$23 \cdot \frac{15}{15} + \frac{8}{15} - 8 \frac{3}{5}$

Step 1.2.2

Combine $23$ and $\frac{15}{15}$ .

$\frac{23 \cdot 15}{15} + \frac{8}{15} - 8 \frac{3}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{23 \cdot 15 + 8}{15} - 8 \frac{3}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $23$ by $15$ .

$\frac{345 + 8}{15} - 8 \frac{3}{5}$

Step 1.2.4.2

Add $345$ and $8$ .

$\frac{353}{15} - 8 \frac{3}{5}$

Step 2

Convert $8 \frac{3}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{353}{15} - (8 + \frac{3}{5})$

Step 2.2

Add $8$ and $\frac{3}{5}$ .

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Step 2.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{353}{15} - (8 \cdot \frac{5}{5} + \frac{3}{5})$

Step 2.2.2

Combine $8$ and $\frac{5}{5}$ .

$\frac{353}{15} - (\frac{8 \cdot 5}{5} + \frac{3}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{353}{15} - \frac{8 \cdot 5 + 3}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $8$ by $5$ .

$\frac{353}{15} - \frac{40 + 3}{5}$

Step 2.2.4.2

Add $40$ and $3$ .

$\frac{353}{15} - \frac{43}{5}$

Step 3

To write $- \frac{43}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{353}{15} - \frac{43}{5} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{43}{5}$ by $\frac{3}{3}$ .

$\frac{353}{15} - \frac{43 \cdot 3}{5 \cdot 3}$

Step 4.2

Multiply $5$ by $3$ .

$\frac{353}{15} - \frac{43 \cdot 3}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{353 - 43 \cdot 3}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 43$ by $3$ .

$\frac{353 - 129}{15}$

Step 6.2

Subtract $129$ from $353$ .

$\frac{224}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{224}{15}$

Decimal Form:

$14.9\overline{3}$

Mixed Number Form:

$14 \frac{14}{15}$