What is (1-1/4)\div (1+1/8) ?

The solution to (1-1/4)\div (1+1/8) is 2/3

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(1-1/4)\div (1+1/8)

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

\frac{2}{3}

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(1 - \frac{1}{4}) : \frac{3}{4}

1 - \frac{1}{4}

1 - \frac{1}{4} = \frac{3}{4}

1 - \frac{1}{4}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

Multiply the numbers:

1 \cdot 4 = 4

= 4 - 1

Subtract the numbers:

4 - 1 = 3

= 3

= \frac{3}{4}

= \frac{3}{4}

= \frac{3}{4} \div (1 + \frac{1}{8})

Calculate within parentheses

(1 + \frac{1}{8}) : \frac{9}{8}

1 + \frac{1}{8}

1 + \frac{1}{8} = \frac{9}{8}

1 + \frac{1}{8}

Convert element to fraction:

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

= \frac{1 \cdot 8}{8} + \frac{1}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 8 + 1}{8}

1 \cdot 8 + 1 = 9

1 \cdot 8 + 1

Multiply the numbers:

1 \cdot 8 = 8

= 8 + 1

Add the numbers:

8 + 1 = 9

= 9

= \frac{9}{8}

= \frac{9}{8}

= \frac{3}{4} \div \frac{9}{8}

Multiply and divide (left to right)

\frac{3}{4} \div \frac{9}{8} : \frac{2}{3}

\frac{3}{4} \div \frac{9}{8}

Apply the fraction rule:

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

= \frac{3}{4} \cdot \frac{8}{9}

Multiply fractions:

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

= \frac{3 \cdot 8}{4 \cdot 9}

Multiply the numbers:

3 \cdot 8 = 24

= \frac{24}{4 \cdot 9}

Multiply the numbers:

4 \cdot 9 = 36

= \frac{24}{36}

Cancel the common factor:

12

= \frac{2}{3}

= \frac{2}{3}

- 1 \cdot (- 1) + 5

4 (5)^{2} - 3

5^{4} + 4^{3} - 2^{3}

35 - 2 - 2 - 2 - 2 - 1

3^{2} + 5 (3) + 6