What is 1/2+1\div 3-4/5 ?

The solution to 1/2+1\div 3-4/5 is 1/30

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Popular >

1/2+1\div 3-4/5

Solution

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

Solution

\frac{1}{30}

Solution steps

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

Follow the PEMDAS order of operations

Multiply and divide (left to right)

1 \div 3 : \frac{1}{3}

1 \div 3

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

= \frac{1}{3}

= \frac{1}{2} + \frac{1}{3} - \frac{4}{5}

Add and subtract (left to right)

\frac{1}{2} + \frac{1}{3} - \frac{4}{5} : \frac{1}{30}

\frac{1}{2} + \frac{1}{3} - \frac{4}{5}

\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{4}{5}

\frac{5}{6} - \frac{4}{5} = \frac{1}{30}

\frac{5}{6} - \frac{4}{5}

Least Common Multiplier of

6, 5 : 30

6, 5

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

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

6

5

= 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 30

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

30

For

\frac{5}{6} :

multiply the denominator and numerator by

5

\frac{5}{6} = \frac{5 \cdot 5}{6 \cdot 5} = \frac{25}{30}

For

\frac{4}{5} :

multiply the denominator and numerator by

6

\frac{4}{5} = \frac{4 \cdot 6}{5 \cdot 6} = \frac{24}{30}

= \frac{25}{30} - \frac{24}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{25 - 24}{30}

Subtract the numbers:

25 - 24 = 1

= \frac{1}{30}

= \frac{1}{30}

= \frac{1}{30}

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Frequently Asked Questions (FAQ)

What is 1/2+1\div 3-4/5 ?
The solution to 1/2+1\div 3-4/5 is 1/30