Pre-Algebra Examples

$- 4 \frac{7}{10} - 9 \frac{7}{15}$

Step 1

Convert $4 \frac{7}{10}$ to an improper fraction.

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Step 1.1

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

$- (4 + \frac{7}{10}) - 9 \frac{7}{15}$

Step 1.2

Add $4$ and $\frac{7}{10}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- (4 \cdot \frac{10}{10} + \frac{7}{10}) - 9 \frac{7}{15}$

Step 1.2.2

Combine $4$ and $\frac{10}{10}$ .

$- (\frac{4 \cdot 10}{10} + \frac{7}{10}) - 9 \frac{7}{15}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{4 \cdot 10 + 7}{10} - 9 \frac{7}{15}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $10$ .

$- \frac{40 + 7}{10} - 9 \frac{7}{15}$

Step 1.2.4.2

Add $40$ and $7$ .

$- \frac{47}{10} - 9 \frac{7}{15}$

Step 2

Convert $9 \frac{7}{15}$ to an improper fraction.

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Step 2.1

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

$- \frac{47}{10} - (9 + \frac{7}{15})$

Step 2.2

Add $9$ and $\frac{7}{15}$ .

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Step 2.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$- \frac{47}{10} - (9 \cdot \frac{15}{15} + \frac{7}{15})$

Step 2.2.2

Combine $9$ and $\frac{15}{15}$ .

$- \frac{47}{10} - (\frac{9 \cdot 15}{15} + \frac{7}{15})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{47}{10} - \frac{9 \cdot 15 + 7}{15}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $9$ by $15$ .

$- \frac{47}{10} - \frac{135 + 7}{15}$

Step 2.2.4.2

Add $135$ and $7$ .

$- \frac{47}{10} - \frac{142}{15}$

Step 3

To write $- \frac{47}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{47}{10} \cdot \frac{3}{3} - \frac{142}{15}$

Step 4

To write $- \frac{142}{15}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{47}{10} \cdot \frac{3}{3} - \frac{142}{15} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{47}{10}$ by $\frac{3}{3}$ .

$- \frac{47 \cdot 3}{10 \cdot 3} - \frac{142}{15} \cdot \frac{2}{2}$

Step 5.2

Multiply $10$ by $3$ .

$- \frac{47 \cdot 3}{30} - \frac{142}{15} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{142}{15}$ by $\frac{2}{2}$ .

$- \frac{47 \cdot 3}{30} - \frac{142 \cdot 2}{15 \cdot 2}$

Step 5.4

Multiply $15$ by $2$ .

$- \frac{47 \cdot 3}{30} - \frac{142 \cdot 2}{30}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 47 \cdot 3 - 142 \cdot 2}{30}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 47$ by $3$ .

$\frac{- 141 - 142 \cdot 2}{30}$

Step 7.2

Multiply $- 142$ by $2$ .

$\frac{- 141 - 284}{30}$

Step 7.3

Subtract $284$ from $- 141$ .

$\frac{- 425}{30}$

Step 8

Cancel the common factor of $- 425$ and $30$ .

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Step 8.1

Factor $5$ out of $- 425$ .

$\frac{5 (- 85)}{30}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $5$ out of $30$ .

$\frac{5 \cdot - 85}{5 \cdot 6}$

Step 8.2.2

Cancel the common factor.

$\frac{5 \cdot - 85}{5 \cdot 6}$

Step 8.2.3

Rewrite the expression.

$\frac{- 85}{6}$

Step 9

Move the negative in front of the fraction.

$- \frac{85}{6}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{85}{6}$

Decimal Form:

$- 14.1\overline{6}$

Mixed Number Form:

$- 14 \frac{1}{6}$