What is (1-1/5)\div (1+1/5) ?

The solution to (1-1/5)\div (1+1/5) is 2/3

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(1-1/5)\div (1+1/5)

(1 - \frac{1}{5}) \div (1 + \frac{1}{5})

\frac{2}{3}

Solution steps

(1 - \frac{1}{5}) \div (1 + \frac{1}{5})

Follow the PEMDAS order of operations

Calculate within parentheses

(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} \div (1 + \frac{1}{5})

Calculate within parentheses

(1 + \frac{1}{5}) : \frac{6}{5}

1 + \frac{1}{5}

1 + \frac{1}{5} = \frac{6}{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 = 6

1 \cdot 5 + 1

Multiply the numbers:

1 \cdot 5 = 5

= 5 + 1

Add the numbers:

5 + 1 = 6

= 6

= \frac{6}{5}

= \frac{6}{5}

= \frac{4}{5} \div \frac{6}{5}

Multiply and divide (left to right)

\frac{4}{5} \div \frac{6}{5} : \frac{2}{3}

\frac{4}{5} \div \frac{6}{5}

Apply the fraction rule:

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

= \frac{4}{5} \cdot \frac{5}{6}

Multiply fractions:

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

= \frac{4 \cdot 5}{5 \cdot 6}

Cancel the common factor:

5

= \frac{4}{6}

Cancel the common factor:

2

= \frac{2}{3}

= \frac{2}{3}

9^{2} + 4^{2}

9^{2} + 3^{2}

\frac{9}{4} - 2 + \frac{1}{2}

1 0^{2} + 6^{2}

3 - 3 \cdot 0 \cdot 3 + 3