Pre-Algebra Examples

$0.8 + 0.2 \div (\frac{7}{15} - 1 \frac{1}{6} + \frac{9}{20})$

Step 1

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

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Step 1.1

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

$0.8 + 0.2 \div (\frac{7}{15} - (1 + \frac{1}{6}) + \frac{9}{20})$

Step 1.2

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

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$0.8 + 0.2 \div (\frac{7}{15} - (\frac{6}{6} + \frac{1}{6}) + \frac{9}{20})$

Step 1.2.2

Combine the numerators over the common denominator.

$0.8 + 0.2 \div (\frac{7}{15} - \frac{6 + 1}{6} + \frac{9}{20})$

Step 1.2.3

Add $6$ and $1$ .

$0.8 + 0.2 \div (\frac{7}{15} - \frac{7}{6} + \frac{9}{20})$

Step 2

Simplify each term.

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Step 2.1

Rewrite the division as a fraction.

$0.8 + \frac{0.2}{\frac{7}{15} - \frac{7}{6} + \frac{9}{20}}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

To write $\frac{7}{15}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$0.8 + \frac{0.2}{\frac{7}{15} \cdot \frac{2}{2} - \frac{7}{6} + \frac{9}{20}}$

Step 2.2.2

To write $- \frac{7}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$0.8 + \frac{0.2}{\frac{7}{15} \cdot \frac{2}{2} - \frac{7}{6} \cdot \frac{5}{5} + \frac{9}{20}}$

Step 2.2.3

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

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Step 2.2.3.1

Multiply $\frac{7}{15}$ by $\frac{2}{2}$ .

$0.8 + \frac{0.2}{\frac{7 \cdot 2}{15 \cdot 2} - \frac{7}{6} \cdot \frac{5}{5} + \frac{9}{20}}$

Step 2.2.3.2

Multiply $15$ by $2$ .

$0.8 + \frac{0.2}{\frac{7 \cdot 2}{30} - \frac{7}{6} \cdot \frac{5}{5} + \frac{9}{20}}$

Step 2.2.3.3

Multiply $\frac{7}{6}$ by $\frac{5}{5}$ .

$0.8 + \frac{0.2}{\frac{7 \cdot 2}{30} - \frac{7 \cdot 5}{6 \cdot 5} + \frac{9}{20}}$

Step 2.2.3.4

Multiply $6$ by $5$ .

$0.8 + \frac{0.2}{\frac{7 \cdot 2}{30} - \frac{7 \cdot 5}{30} + \frac{9}{20}}$

Step 2.2.4

Combine the numerators over the common denominator.

$0.8 + \frac{0.2}{\frac{7 \cdot 2 - 7 \cdot 5}{30} + \frac{9}{20}}$

Step 2.2.5

Simplify the numerator.

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Step 2.2.5.1

Multiply $7$ by $2$ .

$0.8 + \frac{0.2}{\frac{14 - 7 \cdot 5}{30} + \frac{9}{20}}$

Step 2.2.5.2

Multiply $- 7$ by $5$ .

$0.8 + \frac{0.2}{\frac{14 - 35}{30} + \frac{9}{20}}$

Step 2.2.5.3

Subtract $35$ from $14$ .

$0.8 + \frac{0.2}{\frac{- 21}{30} + \frac{9}{20}}$

Step 2.2.6

To write $\frac{- 21}{30}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$0.8 + \frac{0.2}{\frac{- 21}{30} \cdot \frac{2}{2} + \frac{9}{20}}$

Step 2.2.7

To write $\frac{9}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$0.8 + \frac{0.2}{\frac{- 21}{30} \cdot \frac{2}{2} + \frac{9}{20} \cdot \frac{3}{3}}$

Step 2.2.8

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.8.1

Multiply $\frac{- 21}{30}$ by $\frac{2}{2}$ .

$0.8 + \frac{0.2}{\frac{- 21 \cdot 2}{30 \cdot 2} + \frac{9}{20} \cdot \frac{3}{3}}$

Step 2.2.8.2

Multiply $30$ by $2$ .

$0.8 + \frac{0.2}{\frac{- 21 \cdot 2}{60} + \frac{9}{20} \cdot \frac{3}{3}}$

Step 2.2.8.3

Multiply $\frac{9}{20}$ by $\frac{3}{3}$ .

$0.8 + \frac{0.2}{\frac{- 21 \cdot 2}{60} + \frac{9 \cdot 3}{20 \cdot 3}}$

Step 2.2.8.4

Multiply $20$ by $3$ .

$0.8 + \frac{0.2}{\frac{- 21 \cdot 2}{60} + \frac{9 \cdot 3}{60}}$

Step 2.2.9

Combine the numerators over the common denominator.

$0.8 + \frac{0.2}{\frac{- 21 \cdot 2 + 9 \cdot 3}{60}}$

Step 2.2.10

Simplify the numerator.

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Step 2.2.10.1

Multiply $- 21$ by $2$ .

$0.8 + \frac{0.2}{\frac{- 42 + 9 \cdot 3}{60}}$

Step 2.2.10.2

Multiply $9$ by $3$ .

$0.8 + \frac{0.2}{\frac{- 42 + 27}{60}}$

Step 2.2.10.3

Add $- 42$ and $27$ .

$0.8 + \frac{0.2}{\frac{- 15}{60}}$

Step 2.2.11

Reduce the expression by cancelling the common factors.

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Step 2.2.11.1

Cancel the common factor of $- 15$ and $60$ .

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Step 2.2.11.1.1

Factor $15$ out of $- 15$ .

$0.8 + \frac{0.2}{\frac{15 (- 1)}{60}}$

Step 2.2.11.1.2

Cancel the common factors.

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Step 2.2.11.1.2.1

Factor $15$ out of $60$ .

$0.8 + \frac{0.2}{\frac{15 \cdot - 1}{15 \cdot 4}}$

Step 2.2.11.1.2.2

Cancel the common factor.

$0.8 + \frac{0.2}{\frac{15 \cdot - 1}{15 \cdot 4}}$

Step 2.2.11.1.2.3

Rewrite the expression.

$0.8 + \frac{0.2}{\frac{- 1}{4}}$

Step 2.2.11.2

Move the negative in front of the fraction.

$0.8 + \frac{0.2}{- \frac{1}{4}}$

Step 2.3

Multiply the numerator by the reciprocal of the denominator.

$0.8 + 0.2 (- 1 \cdot 4)$

Step 2.4

Multiply $0.2 (- 1 \cdot 4)$ .

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Step 2.4.1

Multiply $- 1$ by $4$ .

$0.8 + 0.2 \cdot - 4$

Step 2.4.2

Multiply $0.2$ by $- 4$ .

$0.8 - 0.8$

Step 3

Subtract $0.8$ from $0.8$ .

$0$