What is 5+2/(1+(1/2)/(2-1/4)) ?

The solution to 5+2/(1+(1/2)/(2-1/4)) is 6 5/9

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5+2/(1+(1/2)/(2-1/4))

Solution

5 + 2/ (1 + (1/2) / (2 - 1/4))

Solution

6 \frac{5}{9}

Solution steps

5 + 2/ (1 + (1/2) / (2 - 1/4))

Follow the PEMDAS order of operations

Calculate within parentheses

(1 + (1/2) / (2 - 1/4)) : \frac{9}{7}

1 + (1/2) / (2 - 1/4)

Calculate within parentheses

(1/2) : \frac{1}{2}

1/2

1/2 = \frac{1}{2}

= \frac{1}{2}

= 1 + \frac{1}{2} / (2 - 1/4)

Calculate within parentheses

(2 - 1/4) : \frac{7}{4}

2 - 1/4

Multiply and divide (left to right)

1/4 : \frac{1}{4}

1/4

1/4 = \frac{1}{4}

= \frac{1}{4}

= 2 - \frac{1}{4}

Add and subtract (left to right)

2 - \frac{1}{4} : \frac{7}{4}

2 - \frac{1}{4}

2 - \frac{1}{4} = \frac{7}{4}

2 - \frac{1}{4}

Convert element to fraction:

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

= \frac{2 \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{2 \cdot 4 - 1}{4}

2 \cdot 4 - 1 = 7

2 \cdot 4 - 1

Multiply the numbers:

2 \cdot 4 = 8

= 8 - 1

Subtract the numbers:

8 - 1 = 7

= 7

= \frac{7}{4}

= \frac{7}{4}

= \frac{7}{4}

= 1 + \frac{1}{2} / \frac{7}{4}

Multiply and divide (left to right)

\frac{1}{2} / \frac{7}{4} : \frac{2}{7}

\frac{1}{2} / \frac{7}{4}

Apply the fraction rule:

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

= \frac{1}{2} \cdot \frac{4}{7}

Cross-cancel common factor:

2

= \frac{2}{7}

= 1 + \frac{2}{7}

Add and subtract (left to right)

1 + \frac{2}{7} : \frac{9}{7}

1 + \frac{2}{7}

1 + \frac{2}{7} = \frac{9}{7}

1 + \frac{2}{7}

Convert element to fraction:

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

= \frac{1 \cdot 7}{7} + \frac{2}{7}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 7 + 2}{7}

1 \cdot 7 + 2 = 9

1 \cdot 7 + 2

Multiply the numbers:

1 \cdot 7 = 7

= 7 + 2

Add the numbers:

7 + 2 = 9

= 9

= \frac{9}{7}

= \frac{9}{7}

= \frac{9}{7}

= 5 + 2/ \frac{9}{7}

Multiply and divide (left to right)

2/ \frac{9}{7} : \frac{14}{9}

2/ \frac{9}{7}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \div \frac{9}{7}

Apply the fraction rule:

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

= \frac{2}{1} \cdot \frac{7}{9}

Multiply fractions:

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

= \frac{2 \cdot 7}{1 \cdot 9}

Multiply the numbers:

2 \cdot 7 = 14

= \frac{14}{1 \cdot 9}

Multiply the numbers:

1 \cdot 9 = 9

= \frac{14}{9}

= 5 + \frac{14}{9}

Add and subtract (left to right)

5 + \frac{14}{9} : \frac{59}{9}

5 + \frac{14}{9}

5 + \frac{14}{9} = \frac{59}{9}

5 + \frac{14}{9}

Convert element to fraction:

5 = \frac{5 \cdot 9}{9}

= \frac{5 \cdot 9}{9} + \frac{14}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 9 + 14}{9}

5 \cdot 9 + 14 = 59

5 \cdot 9 + 14

Multiply the numbers:

5 \cdot 9 = 45

= 45 + 14

Add the numbers:

45 + 14 = 59

= 59

= \frac{59}{9}

= \frac{59}{9}

= \frac{59}{9}

Convert improper fractions to mixed numbers:

\frac{59}{9} = 6 \frac{5}{9}

\frac{59}{9} = 6

Remainder

5

\frac{59}{9}

Write the problem in long division format

9 \overline{∣ 59}

Divide

59

9

to get

6

Divide

59

9

to get

6

6 9 \overline{∣ 59}

Multiply the quotient digit

(6)

by the divisor

9

6 9 \overline{∣ 59} \underline{54}

Subtract

54

from

59

6 9 \overline{∣ 59} \underline{54} 5

6 9 \overline{∣ 59} \underline{54} 5

The solution for Long Division of

\frac{59}{9}

6

with remainder of

5

6 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{59}{9} = 6 \frac{5}{9}

= 6 \frac{5}{9}

= 6 \frac{5}{9}

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Frequently Asked Questions (FAQ)

What is 5+2/(1+(1/2)/(2-1/4)) ?
The solution to 5+2/(1+(1/2)/(2-1/4)) is 6 5/9