What is (1-1/3)\div (1-1/5) ?

The solution to (1-1/3)\div (1-1/5) is 5/6

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(1-1/3)\div (1-1/5)

Solution

(1 - \frac{1}{3}) \div (1 - \frac{1}{5})

Solution

\frac{5}{6}

Solution steps

(1 - \frac{1}{3}) \div (1 - \frac{1}{5})

Follow the PEMDAS order of operations

Calculate within parentheses

(1 - \frac{1}{3}) : \frac{2}{3}

1 - \frac{1}{3}

1 - \frac{1}{3} = \frac{2}{3}

1 - \frac{1}{3}

Convert element to fraction:

1 = \frac{1 \cdot 3}{3}

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 3 - 1 = 2

1 \cdot 3 - 1

Multiply the numbers:

1 \cdot 3 = 3

= 3 - 1

Subtract the numbers:

3 - 1 = 2

= 2

= \frac{2}{3}

= \frac{2}{3}

= \frac{2}{3} \div (1 - \frac{1}{5})

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

Multiply and divide (left to right)

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

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

Apply the fraction rule:

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

= \frac{2}{3} \cdot \frac{5}{4}

Cross-cancel common factor:

2

2, 4

Greatest Common Divisor (GCD)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

2, 4

are

= 2

= \frac{1}{3} \cdot \frac{5}{2}

Multiply fractions:

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

= \frac{1 \cdot 5}{3 \cdot 2}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{5}{6}

= \frac{5}{6}

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7 5^{2} - 8 5^{2}

2(-3)^2-3(-3)+5

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

-101+40-57+113+87

- 101 + 40 - 57 + 113 + 87

(2\times 5)\times 5

(2 \times 5) \times 5

3+7(2^3-6)^2

3 + 7 (2^{3} - 6)^{2}

Frequently Asked Questions (FAQ)

What is (1-1/3)\div (1-1/5) ?
The solution to (1-1/3)\div (1-1/5) is 5/6