What is 18-(1/2+1/3+1/4) ?

The solution to 18-(1/2+1/3+1/4) is 16 11/12

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18-(1/2+1/3+1/4)

Solution

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

Solution

16 \frac{11}{12}

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{2} + \frac{1}{3} + \frac{1}{4}) : \frac{13}{12}

\frac{1}{2} + \frac{1}{3} + \frac{1}{4}

\frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{13}{12}

\frac{1}{2} + \frac{1}{3} + \frac{1}{4}

Least Common Multiplier of

2, 3, 4 : 12

2, 3, 4

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Compute a number comprised of factors that appear in at least one of the following:

2, 3, 4

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

12

For

\frac{1}{2} :

multiply the denominator and numerator by

6

\frac{1}{2} = \frac{1 \cdot 6}{2 \cdot 6} = \frac{6}{12}

For

\frac{1}{3} :

multiply the denominator and numerator by

4

\frac{1}{3} = \frac{1 \cdot 4}{3 \cdot 4} = \frac{4}{12}

For

\frac{1}{4} :

multiply the denominator and numerator by

3

\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}

= \frac{6}{12} + \frac{4}{12} + \frac{3}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{6 + 4 + 3}{12}

Add the numbers:

6 + 4 + 3 = 13

= \frac{13}{12}

= \frac{13}{12}

= 18 - \frac{13}{12}

Add and subtract (left to right)

18 - \frac{13}{12} : \frac{203}{12}

18 - \frac{13}{12}

18 - \frac{13}{12} = \frac{203}{12}

18 - \frac{13}{12}

Convert element to fraction:

18 = \frac{18 \cdot 12}{12}

= \frac{18 \cdot 12}{12} - \frac{13}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{18 \cdot 12 - 13}{12}

18 \cdot 12 - 13 = 203

18 \cdot 12 - 13

Multiply the numbers:

18 \cdot 12 = 216

= 216 - 13

Subtract the numbers:

216 - 13 = 203

= 203

= \frac{203}{12}

= \frac{203}{12}

= \frac{203}{12}

Convert improper fractions to mixed numbers:

\frac{203}{12} = 16 \frac{11}{12}

\frac{203}{12} = 16

Remainder

11

\frac{203}{12}

Write the problem in long division format

12 \overline{∣ 203}

Divide

20

12

to get

1

Divide

20

12

to get

1

1 12 \overline{∣ 203}

Multiply the quotient digit

(1)

by the divisor

12

1 12 \overline{∣ 203} \underline{12}

Subtract

12

from

20

1 12 \overline{∣ 203} \underline{12} 8

Bring down the next number of the dividend

1 12 \overline{∣ 203} \underline{12} 83

1 12 \overline{∣ 203} \underline{12} 83

Divide

83

12

to get

6

Divide

83

12

to get

6

16 12 \overline{∣ 203} \underline{12} 83

Multiply the quotient digit

(6)

by the divisor

12

16 12 \overline{∣ 203} \underline{12} 83 \underline{72}

Subtract

72

from

83

16 12 \overline{∣ 203} \underline{12} 83 \underline{72} 11

16 12 \overline{∣ 203} \underline{12} 83 \underline{72} 11

The solution for Long Division of

\frac{203}{12}

16

with remainder of

11

16 Remainder 11

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{203}{12} = 16 \frac{11}{12}

= 16 \frac{11}{12}

= 16 \frac{11}{12}

Popular Examples

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\frac{6 ( 17 - 8 ) - 4}{6 ^{2} - 26}

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(4) (3) - 10 (- 8)

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5 (4 + 2 (2))

simplify-((25/6)/(-31))/6 simplify

- \frac{\frac{\frac{25}{6}}{- 31}}{6}

Frequently Asked Questions (FAQ)

What is 18-(1/2+1/3+1/4) ?
The solution to 18-(1/2+1/3+1/4) is 16 11/12