Basic Math Examples

$(42 + \frac{8}{15}) - (22 + \frac{13}{15})$

Step 1

Find the common denominator.

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Step 1.1

Write $42$ as a fraction with denominator $1$ .

$\frac{42}{1} + \frac{8}{15} - (22 + \frac{13}{15})$

Step 1.2

Multiply $\frac{42}{1}$ by $\frac{15}{15}$ .

$\frac{42}{1} \cdot \frac{15}{15} + \frac{8}{15} - (22 + \frac{13}{15})$

Step 1.3

Multiply $\frac{42}{1}$ by $\frac{15}{15}$ .

$\frac{42 \cdot 15}{15} + \frac{8}{15} - (22 + \frac{13}{15})$

Step 1.4

Write $- (22 + \frac{13}{15})$ as a fraction with denominator $1$ .

$\frac{42 \cdot 15}{15} + \frac{8}{15} + \frac{- (22 + \frac{13}{15})}{1}$

Step 1.5

Multiply $\frac{- (22 + \frac{13}{15})}{1}$ by $\frac{15}{15}$ .

$\frac{42 \cdot 15}{15} + \frac{8}{15} + \frac{- (22 + \frac{13}{15})}{1} \cdot \frac{15}{15}$

Step 1.6

Multiply $\frac{- (22 + \frac{13}{15})}{1}$ by $\frac{15}{15}$ .

$\frac{42 \cdot 15}{15} + \frac{8}{15} + \frac{- (22 + \frac{13}{15}) \cdot 15}{15}$

Step 2

Combine the numerators over the common denominator.

$\frac{42 \cdot 15 + 8 - (22 + \frac{13}{15}) \cdot 15}{15}$

Step 3

Simplify each term.

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Step 3.1

Multiply $42$ by $15$ .

$\frac{630 + 8 - (22 + \frac{13}{15}) \cdot 15}{15}$

Step 3.2

To write $22$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{630 + 8 - (22 \cdot \frac{15}{15} + \frac{13}{15}) \cdot 15}{15}$

Step 3.3

Combine $22$ and $\frac{15}{15}$ .

$\frac{630 + 8 - (\frac{22 \cdot 15}{15} + \frac{13}{15}) \cdot 15}{15}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{630 + 8 - \frac{22 \cdot 15 + 13}{15} \cdot 15}{15}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $22$ by $15$ .

$\frac{630 + 8 - \frac{330 + 13}{15} \cdot 15}{15}$

Step 3.5.2

Add $330$ and $13$ .

$\frac{630 + 8 - \frac{343}{15} \cdot 15}{15}$

Step 3.6

Cancel the common factor of $15$ .

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Step 3.6.1

Move the leading negative in $- \frac{343}{15}$ into the numerator.

$\frac{630 + 8 + \frac{- 343}{15} \cdot 15}{15}$

Step 3.6.2

Cancel the common factor.

$\frac{630 + 8 + \frac{- 343}{15} \cdot 15}{15}$

Step 3.6.3

Rewrite the expression.

$\frac{630 + 8 - 343}{15}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add $630$ and $8$ .

$\frac{638 - 343}{15}$

Step 4.2

Subtract $343$ from $638$ .

$\frac{295}{15}$

Step 4.3

Cancel the common factor of $295$ and $15$ .

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Step 4.3.1

Factor $5$ out of $295$ .

$\frac{5 (59)}{15}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $5$ out of $15$ .

$\frac{5 \cdot 59}{5 \cdot 3}$

Step 4.3.2.2

Cancel the common factor.

$\frac{5 \cdot 59}{5 \cdot 3}$

Step 4.3.2.3

Rewrite the expression.

$\frac{59}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{3}$

Decimal Form:

$19.\overline{6}$

Mixed Number Form:

$19 \frac{2}{3}$