Basic Math Examples

$- 10 \div (- 3 \frac{2}{3} - 2 \frac{6}{7}) \cdot 5.6$

Step 1

Convert $3 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$- 10 \div (- (3 + \frac{2}{3}) - 2 \frac{6}{7}) \cdot 5.6$

Step 1.2

Add $3$ and $\frac{2}{3}$ .

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Step 1.2.1

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

$- 10 \div (- (3 \cdot \frac{3}{3} + \frac{2}{3}) - 2 \frac{6}{7}) \cdot 5.6$

Step 1.2.2

Combine $3$ and $\frac{3}{3}$ .

$- 10 \div (- (\frac{3 \cdot 3}{3} + \frac{2}{3}) - 2 \frac{6}{7}) \cdot 5.6$

Step 1.2.3

Combine the numerators over the common denominator.

$- 10 \div (- \frac{3 \cdot 3 + 2}{3} - 2 \frac{6}{7}) \cdot 5.6$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $3$ .

$- 10 \div (- \frac{9 + 2}{3} - 2 \frac{6}{7}) \cdot 5.6$

Step 1.2.4.2

Add $9$ and $2$ .

$- 10 \div (- \frac{11}{3} - 2 \frac{6}{7}) \cdot 5.6$

Step 2

Convert $2 \frac{6}{7}$ to an improper fraction.

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Step 2.1

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

$- 10 \div (- \frac{11}{3} - (2 + \frac{6}{7})) \cdot 5.6$

Step 2.2

Add $2$ and $\frac{6}{7}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 10 \div (- \frac{11}{3} - (2 \cdot \frac{7}{7} + \frac{6}{7})) \cdot 5.6$

Step 2.2.2

Combine $2$ and $\frac{7}{7}$ .

$- 10 \div (- \frac{11}{3} - (\frac{2 \cdot 7}{7} + \frac{6}{7})) \cdot 5.6$

Step 2.2.3

Combine the numerators over the common denominator.

$- 10 \div (- \frac{11}{3} - \frac{2 \cdot 7 + 6}{7}) \cdot 5.6$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $7$ .

$- 10 \div (- \frac{11}{3} - \frac{14 + 6}{7}) \cdot 5.6$

Step 2.2.4.2

Add $14$ and $6$ .

$- 10 \div (- \frac{11}{3} - \frac{20}{7}) \cdot 5.6$

Step 3

Simplify the denominator.

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Step 3.1

To write $- \frac{11}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 10 \div (- \frac{11}{3} \cdot \frac{7}{7} - \frac{20}{7}) \cdot 5.6$

Step 3.2

To write $- \frac{20}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 10 \div (- \frac{11}{3} \cdot \frac{7}{7} - \frac{20}{7} \cdot \frac{3}{3}) \cdot 5.6$

Step 3.3

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

$- 10 \div (- \frac{11 \cdot 7}{3 \cdot 7} - \frac{20}{7} \cdot \frac{3}{3}) \cdot 5.6$

Step 3.3.2

Multiply $3$ by $7$ .

$- 10 \div (- \frac{11 \cdot 7}{21} - \frac{20}{7} \cdot \frac{3}{3}) \cdot 5.6$

Step 3.3.3

Multiply $\frac{20}{7}$ by $\frac{3}{3}$ .

$- 10 \div (- \frac{11 \cdot 7}{21} - \frac{20 \cdot 3}{7 \cdot 3}) \cdot 5.6$

Step 3.3.4

Multiply $7$ by $3$ .

$- 10 \div (- \frac{11 \cdot 7}{21} - \frac{20 \cdot 3}{21}) \cdot 5.6$

Step 3.4

Combine the numerators over the common denominator.

$- 10 \div \frac{- 11 \cdot 7 - 20 \cdot 3}{21} \cdot 5.6$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 11$ by $7$ .

$- 10 \div \frac{- 77 - 20 \cdot 3}{21} \cdot 5.6$

Step 3.5.2

Multiply $- 20$ by $3$ .

$- 10 \div \frac{- 77 - 60}{21} \cdot 5.6$

Step 3.5.3

Subtract $60$ from $- 77$ .

$- 10 \div \frac{- 137}{21} \cdot 5.6$

Step 3.6

Move the negative in front of the fraction.

$- 10 \div (- \frac{137}{21}) \cdot 5.6$

Step 4

To divide by a fraction, multiply by its reciprocal.

$- 10 (- \frac{21}{137}) \cdot 5.6$

Step 5

Multiply $- 10 (- \frac{21}{137})$ .

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Step 5.1

Multiply $- 1$ by $- 10$ .

$10 (\frac{21}{137}) \cdot 5.6$

Step 5.2

Combine $10$ and $\frac{21}{137}$ .

$\frac{10 \cdot 21}{137} \cdot 5.6$

Step 5.3

Multiply $10$ by $21$ .

$\frac{210}{137} \cdot 5.6$

Step 6

Multiply $\frac{210}{137} \cdot 5.6$ .

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Step 6.1

Combine $\frac{210}{137}$ and $5.6$ .

$\frac{210 \cdot 5.6}{137}$

Step 6.2

Multiply $210$ by $5.6$ .

$\frac{1176}{137}$

Step 7

Cancel the common factor of $1176$ and $137$ .

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Step 7.1

Rewrite $1176$ as $1 (1176)$ .

$\frac{1 (1176)}{137}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Rewrite $137$ as $1 (137)$ .

$\frac{1 \cdot 1176}{1 \cdot 137}$

Step 7.2.2

Cancel the common factor.

$\frac{1 \cdot 1176}{1 \cdot 137}$

Step 7.2.3

Rewrite the expression.

$\frac{1176}{137}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1176}{137}$

Decimal Form:

$8.58394160 \dots$

Mixed Number Form:

$8 \frac{80}{137}$