Basic Math Examples

$- 8 \frac{4}{7} \cdot 8 \frac{1}{6}$

Step 1

Convert $8 \frac{4}{7}$ to an improper fraction.

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Step 1.1

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

$- (8 + \frac{4}{7}) \cdot 8 \frac{1}{6}$

Step 1.2

Add $8$ and $\frac{4}{7}$ .

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Step 1.2.1

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

$- (8 \cdot \frac{7}{7} + \frac{4}{7}) \cdot 8 \frac{1}{6}$

Step 1.2.2

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

$- (\frac{8 \cdot 7}{7} + \frac{4}{7}) \cdot 8 \frac{1}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{8 \cdot 7 + 4}{7} \cdot 8 \frac{1}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $7$ .

$- \frac{56 + 4}{7} \cdot 8 \frac{1}{6}$

Step 1.2.4.2

Add $56$ and $4$ .

$- \frac{60}{7} \cdot 8 \frac{1}{6}$

Step 2

Convert $8 \frac{1}{6}$ to an improper fraction.

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Step 2.1

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

$- \frac{60}{7} \cdot (8 + \frac{1}{6})$

Step 2.2

Add $8$ and $\frac{1}{6}$ .

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Step 2.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{60}{7} \cdot (8 \cdot \frac{6}{6} + \frac{1}{6})$

Step 2.2.2

Combine $8$ and $\frac{6}{6}$ .

$- \frac{60}{7} \cdot (\frac{8 \cdot 6}{6} + \frac{1}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{60}{7} \cdot \frac{8 \cdot 6 + 1}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $8$ by $6$ .

$- \frac{60}{7} \cdot \frac{48 + 1}{6}$

Step 2.2.4.2

Add $48$ and $1$ .

$- \frac{60}{7} \cdot \frac{49}{6}$

Step 3

Cancel the common factor of $6$ .

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Step 3.1

Move the leading negative in $- \frac{60}{7}$ into the numerator.

$\frac{- 60}{7} \cdot \frac{49}{6}$

Step 3.2

Factor $6$ out of $- 60$ .

$\frac{6 (- 10)}{7} \cdot \frac{49}{6}$

Step 3.3

Cancel the common factor.

$\frac{6 \cdot - 10}{7} \cdot \frac{49}{6}$

Step 3.4

Rewrite the expression.

$\frac{- 10}{7} \cdot 49$

Step 4

Cancel the common factor of $7$ .

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Step 4.1

Factor $7$ out of $49$ .

$\frac{- 10}{7} \cdot (7 (7))$

Step 4.2

Cancel the common factor.

$\frac{- 10}{7} \cdot (7 \cdot 7)$

Step 4.3

Rewrite the expression.

$- 10 \cdot 7$

Step 5

Multiply $- 10$ by $7$ .

$- 70$