What is 1/2+1/3+1/4 ?

The solution to 1/2+1/3+1/4 is 1 1/12

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Popular >

Simplify 1/2+1/3+1/4

Solution

1/2 + 1/3 + 1/4

Solution

1 \frac{1}{12}

Solution steps

1/2 + 1/3 + 1/4

Follow the PEMDAS order of operations

Multiply and divide (left to right)

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

1/2

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

= \frac{1}{2}

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

Multiply and divide (left to right)

1/3 : \frac{1}{3}

1/3

1/3 = \frac{1}{3}

= \frac{1}{3}

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

Multiply and divide (left to right)

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

1/4

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

= \frac{1}{4}

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

Add and subtract (left to right)

\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{5}{6}

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

Least Common Multiplier of

2, 3 : 6

2, 3

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

Multiply each factor the greatest number of times it occurs in either

2

3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

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

6

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

For

\frac{1}{3} :

multiply the denominator and numerator by

2

\frac{1}{3} = \frac{1 \cdot 2}{3 \cdot 2} = \frac{2}{6}

= \frac{3}{6} + \frac{2}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{3 + 2}{6}

Add the numbers:

3 + 2 = 5

= \frac{5}{6}

= \frac{5}{6} + \frac{1}{4}

\frac{5}{6} + \frac{1}{4} = \frac{13}{12}

\frac{5}{6} + \frac{1}{4}

Least Common Multiplier of

6, 4 : 12

6, 4

Least Common Multiplier (LCM)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Multiply each factor the greatest number of times it occurs in either

6

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{5}{6} :

multiply the denominator and numerator by

2

\frac{5}{6} = \frac{5 \cdot 2}{6 \cdot 2} = \frac{10}{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{10}{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{10 + 3}{12}

Add the numbers:

10 + 3 = 13

= \frac{13}{12}

= \frac{13}{12}

= \frac{13}{12}

Convert improper fractions to mixed numbers:

\frac{13}{12} = 1 \frac{1}{12}

\frac{13}{12} = 1

Remainder

1

\frac{13}{12}

Write the problem in long division format

12 \overline{∣ 13}

Divide

13

12

to get

1

Divide

13

12

to get

1

1 12 \overline{∣ 13}

Multiply the quotient digit

(1)

by the divisor

12

1 12 \overline{∣ 13} \underline{12}

Subtract

12

from

13

1 12 \overline{∣ 13} \underline{12} 1

1 12 \overline{∣ 13} \underline{12} 1

The solution for Long Division of

\frac{13}{12}

1

with remainder of

1

1 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{13}{12} = 1 \frac{1}{12}

= 1 \frac{1}{12}

= 1 \frac{1}{12}

Popular Examples

Find the Possible Factors 80 positive factors of

80

Convert to a Decimal 7/6 convert to decimal

\frac{7}{6}

Convert to a Mixed Number 43/6 mixed number

\frac{43}{6}

Convert to a Simplified Fraction 1.14 convert to fraction

1.14

Reduce the Fraction 35/24 reduce fraction

t h e \frac{35}{24}

Frequently Asked Questions (FAQ)

What is 1/2+1/3+1/4 ?
The solution to 1/2+1/3+1/4 is 1 1/12