What is 8\div (1-1\div 5) ?

The solution to 8\div (1-1\div 5) is 10

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8\div (1-1\div 5)

8 \div (1 - 1 \div 5)

10

Solution steps

8 \div (1 - 1 \div 5)

Follow the PEMDAS order of operations

Calculate within parentheses

(1 - 1 \div 5) : \frac{4}{5}

1 - 1 \div 5

Multiply and divide (left to right)

1 \div 5 : \frac{1}{5}

1 \div 5

1 \div 5 = \frac{1}{5}

= \frac{1}{5}

= 1 - \frac{1}{5}

Add and subtract (left to right)

1 - \frac{1}{5} : \frac{4}{5}

1 - \frac{1}{5}

1 - \frac{1}{5} = \frac{4}{5}

1 - \frac{1}{5}

Convert element to fraction:

1 = \frac{1 \cdot 5}{5}

= \frac{1 \cdot 5}{5} - \frac{1}{5}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 5 - 1}{5}

1 \cdot 5 - 1 = 4

1 \cdot 5 - 1

Multiply the numbers:

1 \cdot 5 = 5

= 5 - 1

Subtract the numbers:

5 - 1 = 4

= 4

= \frac{4}{5}

= \frac{4}{5}

= \frac{4}{5}

= 8 \div \frac{4}{5}

Multiply and divide (left to right)

8 \div \frac{4}{5} : 10

8 \div \frac{4}{5}

Convert element to fraction:

8 = \frac{8}{1}

= \frac{8}{1} \div \frac{4}{5}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{8}{1} \cdot \frac{5}{4}

Cross-cancel common factor:

4

= \frac{2}{1} \cdot \frac{5}{1}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 \cdot 5}{1 \cdot 1}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{10}{1 \cdot 1}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{10}{1}

Apply rule

\frac{a}{1} = a

= 10

= 10

\frac{5}{4} (- 8) + 1

2^{2} - 2 + 1

3^{2} + (12 \div 2 + 3^{2})

(3)^{2} - 3 (3) + 2

- 2 - (- 3)^{2} + (7 - 5)^{2}