Pre-Algebra Examples

$- 8 \frac{2}{7} \cdot 9 \frac{4}{5}$

Step 1

Convert $8 \frac{2}{7}$ to an improper fraction.

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Step 1.1

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

$- (8 + \frac{2}{7}) \cdot 9 \frac{4}{5}$

Step 1.2

Add $8$ and $\frac{2}{7}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- (8 \cdot \frac{7}{7} + \frac{2}{7}) \cdot 9 \frac{4}{5}$

Step 1.2.2

Combine $8$ and $\frac{7}{7}$ .

$- (\frac{8 \cdot 7}{7} + \frac{2}{7}) \cdot 9 \frac{4}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{8 \cdot 7 + 2}{7} \cdot 9 \frac{4}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $7$ .

$- \frac{56 + 2}{7} \cdot 9 \frac{4}{5}$

Step 1.2.4.2

Add $56$ and $2$ .

$- \frac{58}{7} \cdot 9 \frac{4}{5}$

Step 2

Convert $9 \frac{4}{5}$ to an improper fraction.

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Step 2.1

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

$- \frac{58}{7} \cdot (9 + \frac{4}{5})$

Step 2.2

Add $9$ and $\frac{4}{5}$ .

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Step 2.2.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{58}{7} \cdot (9 \cdot \frac{5}{5} + \frac{4}{5})$

Step 2.2.2

Combine $9$ and $\frac{5}{5}$ .

$- \frac{58}{7} \cdot (\frac{9 \cdot 5}{5} + \frac{4}{5})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{58}{7} \cdot \frac{9 \cdot 5 + 4}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $9$ by $5$ .

$- \frac{58}{7} \cdot \frac{45 + 4}{5}$

Step 2.2.4.2

Add $45$ and $4$ .

$- \frac{58}{7} \cdot \frac{49}{5}$

Step 3

Cancel the common factor of $7$ .

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Step 3.1

Move the leading negative in $- \frac{58}{7}$ into the numerator.

$\frac{- 58}{7} \cdot \frac{49}{5}$

Step 3.2

Factor $7$ out of $49$ .

$\frac{- 58}{7} \cdot \frac{7 (7)}{5}$

Step 3.3

Cancel the common factor.

$\frac{- 58}{7} \cdot \frac{7 \cdot 7}{5}$

Step 3.4

Rewrite the expression.

$- 58 \cdot \frac{7}{5}$

Step 4

Combine $- 58$ and $\frac{7}{5}$ .

$\frac{- 58 \cdot 7}{5}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $- 58$ by $7$ .

$\frac{- 406}{5}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{406}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{406}{5}$

Decimal Form:

$- 81.2$

Mixed Number Form:

$- 81 \frac{1}{5}$