What is 1\div [2-3\div (4+1/5)] ?

The solution to 1\div [2-3\div (4+1/5)] is 7/9

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Popular >

1\div [2-3\div (4+1/5)]

Solution

1 \div [2 - 3 \div (4 + \frac{1}{5})]

Solution

\frac{7}{9}

Solution steps

1 \div [2 - 3 \div (4 + \frac{1}{5})]

Follow the PEMDAS order of operations

Calculate within parentheses

[2 - 3 \div (4 + \frac{1}{5})] : \frac{9}{7}

2 - 3 \div (4 + \frac{1}{5})

Calculate within parentheses

(4 + \frac{1}{5}) : \frac{21}{5}

4 + \frac{1}{5}

4 + \frac{1}{5} = \frac{21}{5}

4 + \frac{1}{5}

Convert element to fraction:

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

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

4 \cdot 5 + 1 = 21

4 \cdot 5 + 1

Multiply the numbers:

4 \cdot 5 = 20

= 20 + 1

Add the numbers:

20 + 1 = 21

= 21

= \frac{21}{5}

= \frac{21}{5}

= 2 - 3 \div \frac{21}{5}

Multiply and divide (left to right)

3 \div \frac{21}{5} : \frac{5}{7}

3 \div \frac{21}{5}

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \div \frac{21}{5}

Apply the fraction rule:

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

= \frac{3}{1} \cdot \frac{5}{21}

Cross-cancel common factor:

3

3, 21

Greatest Common Divisor (GCD)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

21 : 3 \cdot 7

21

21

divides by

321 = 7 \cdot 3

= 3 \cdot 7

3, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 7

The prime factors common to

3, 21

are

= 3

= \frac{5}{7}

= 2 - \frac{5}{7}

Add and subtract (left to right)

2 - \frac{5}{7} : \frac{9}{7}

2 - \frac{5}{7}

2 - \frac{5}{7} = \frac{9}{7}

2 - \frac{5}{7}

Convert element to fraction:

2 = \frac{2 \cdot 7}{7}

= \frac{2 \cdot 7}{7} - \frac{5}{7}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 7 - 5}{7}

2 \cdot 7 - 5 = 9

2 \cdot 7 - 5

Multiply the numbers:

2 \cdot 7 = 14

= 14 - 5

Subtract the numbers:

14 - 5 = 9

= 9

= \frac{9}{7}

= \frac{9}{7}

= \frac{9}{7}

= 1 \div \frac{9}{7}

Multiply and divide (left to right)

1 \div \frac{9}{7} : \frac{7}{9}

1 \div \frac{9}{7}

Convert element to fraction:

1 = \frac{1}{1}

= \frac{1}{1} \div \frac{9}{7}

Apply the fraction rule:

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

= \frac{1}{1} \cdot \frac{7}{9}

Apply rule

\frac{a}{a} = 1

\frac{1}{1} = 1

= 1 \cdot \frac{7}{9}

Multiply:

1 \cdot \frac{7}{9} = \frac{7}{9}

= \frac{7}{9}

= \frac{7}{9}

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Frequently Asked Questions (FAQ)

What is 1\div [2-3\div (4+1/5)] ?
The solution to 1\div [2-3\div (4+1/5)] is 7/9