What is 1-1/3 (1-1/2 (1 1/6)) ?

The solution to 1-1/3 (1-1/2 (1 1/6)) is 31/36

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Popular >

1-1/3 (1-1/2 (1 1/6))

Solution

1 - \frac{1}{3} (1 - \frac{1}{2} (1 \frac{1}{6}))

Solution

\frac{31}{36}

Solution steps

1 - \frac{1}{3} (1 - \frac{1}{2} (1 \frac{1}{6}))

Convert mixed numbers to improper fractions:

1 \frac{1}{6} = \frac{7}{6}

1 \frac{1}{6}

Convert mixed numbers to improper fraction:

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

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

= \frac{7}{6}

= 1 - \frac{1}{3} (1 - \frac{1}{2} (\frac{7}{6}))

Follow the PEMDAS order of operations

Calculate within parentheses

(1 - \frac{1}{2} (\frac{7}{6})) : \frac{5}{12}

1 - \frac{1}{2} (\frac{7}{6})

Multiply and divide (left to right)

\frac{1}{2} (\frac{7}{6}) : \frac{7}{12}

\frac{1}{2} (\frac{7}{6})

Remove parentheses:

(a) = a

= \frac{1}{2} \cdot \frac{7}{6}

Multiply fractions:

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

= \frac{1 \cdot 7}{2 \cdot 6}

Multiply the numbers:

1 \cdot 7 = 7

= \frac{7}{2 \cdot 6}

Multiply the numbers:

2 \cdot 6 = 12

= \frac{7}{12}

= 1 - \frac{7}{12}

Add and subtract (left to right)

1 - \frac{7}{12} : \frac{5}{12}

1 - \frac{7}{12}

1 - \frac{7}{12} = \frac{5}{12}

1 - \frac{7}{12}

Convert element to fraction:

1 = \frac{1 \cdot 12}{12}

= \frac{1 \cdot 12}{12} - \frac{7}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 12 - 7}{12}

1 \cdot 12 - 7 = 5

1 \cdot 12 - 7

Multiply the numbers:

1 \cdot 12 = 12

= 12 - 7

Subtract the numbers:

12 - 7 = 5

= 5

= \frac{5}{12}

= \frac{5}{12}

= \frac{5}{12}

= 1 - \frac{1}{3} \cdot \frac{5}{12}

Multiply and divide (left to right)

\frac{1}{3} \cdot \frac{5}{12} : \frac{5}{36}

\frac{1}{3} \cdot \frac{5}{12}

Apply the fraction rule:

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

= \frac{1 \cdot 5}{3 \cdot 12}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{3 \cdot 12}

Multiply the numbers:

3 \cdot 12 = 36

= \frac{5}{36}

= 1 - \frac{5}{36}

Add and subtract (left to right)

1 - \frac{5}{36} : \frac{31}{36}

1 - \frac{5}{36}

1 - \frac{5}{36} = \frac{31}{36}

1 - \frac{5}{36}

Convert element to fraction:

1 = \frac{1 \cdot 36}{36}

= \frac{1 \cdot 36}{36} - \frac{5}{36}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 36 - 5}{36}

1 \cdot 36 - 5 = 31

1 \cdot 36 - 5

Multiply the numbers:

1 \cdot 36 = 36

= 36 - 5

Subtract the numbers:

36 - 5 = 31

= 31

= \frac{31}{36}

= \frac{31}{36}

= \frac{31}{36}

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4 (16) + 3

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(3^{2} \div 9) + 9

-3^3-3^2

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245\times (7/10)

245 \times (7/10)

Frequently Asked Questions (FAQ)

What is 1-1/3 (1-1/2 (1 1/6)) ?
The solution to 1-1/3 (1-1/2 (1 1/6)) is 31/36