Basic Math Examples

$- 10 \frac{2}{7} \div (- 4 \frac{4}{11})$

Step 1

Convert $10 \frac{2}{7}$ to an improper fraction.

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Step 1.1

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

$- (10 + \frac{2}{7}) \div (- 4 \frac{4}{11})$

Step 1.2

Add $10$ and $\frac{2}{7}$ .

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Step 1.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- (10 \cdot \frac{7}{7} + \frac{2}{7}) \div (- 4 \frac{4}{11})$

Step 1.2.2

Combine $10$ and $\frac{7}{7}$ .

$- (\frac{10 \cdot 7}{7} + \frac{2}{7}) \div (- 4 \frac{4}{11})$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{10 \cdot 7 + 2}{7} \div (- 4 \frac{4}{11})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $10$ by $7$ .

$- \frac{70 + 2}{7} \div (- 4 \frac{4}{11})$

Step 1.2.4.2

Add $70$ and $2$ .

$- \frac{72}{7} \div (- 4 \frac{4}{11})$

Step 2

Convert $4 \frac{4}{11}$ to an improper fraction.

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Step 2.1

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

$- \frac{72}{7} \div (- (4 + \frac{4}{11}))$

Step 2.2

Add $4$ and $\frac{4}{11}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$- \frac{72}{7} \div (- (4 \cdot \frac{11}{11} + \frac{4}{11}))$

Step 2.2.2

Combine $4$ and $\frac{11}{11}$ .

$- \frac{72}{7} \div (- (\frac{4 \cdot 11}{11} + \frac{4}{11}))$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{72}{7} \div (- \frac{4 \cdot 11 + 4}{11})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $11$ .

$- \frac{72}{7} \div (- \frac{44 + 4}{11})$

Step 2.2.4.2

Add $44$ and $4$ .

$- \frac{72}{7} \div (- \frac{48}{11})$

Step 3

To divide by a fraction, multiply by its reciprocal.

$- \frac{72}{7} (- \frac{11}{48})$

Step 4

Cancel the common factor of $24$ .

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Step 4.1

Move the leading negative in $- \frac{72}{7}$ into the numerator.

$\frac{- 72}{7} (- \frac{11}{48})$

Step 4.2

Move the leading negative in $- \frac{11}{48}$ into the numerator.

$\frac{- 72}{7} \cdot \frac{- 11}{48}$

Step 4.3

Factor $24$ out of $- 72$ .

$\frac{24 (- 3)}{7} \cdot \frac{- 11}{48}$

Step 4.4

Factor $24$ out of $48$ .

$\frac{24 \cdot - 3}{7} \cdot \frac{- 11}{24 \cdot 2}$

Step 4.5

Cancel the common factor.

$\frac{24 \cdot - 3}{7} \cdot \frac{- 11}{24 \cdot 2}$

Step 4.6

Rewrite the expression.

$\frac{- 3}{7} \cdot \frac{- 11}{2}$

Step 5

Multiply $\frac{- 3}{7}$ by $\frac{- 11}{2}$ .

$\frac{- 3 \cdot - 11}{7 \cdot 2}$

Step 6

Multiply.

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Step 6.1

Multiply $- 3$ by $- 11$ .

$\frac{33}{7 \cdot 2}$

Step 6.2

Multiply $7$ by $2$ .

$\frac{33}{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{14}$

Decimal Form:

$2.35714285 \dots$

Mixed Number Form:

$2 \frac{5}{14}$