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

The solution to (1/2-1/3)\times 6 is 1

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Popular >

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

Solution

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

Solution

1

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

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

\frac{1}{2} - \frac{1}{3}

\frac{1}{2} - \frac{1}{3} = \frac{1}{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}

Subtract the numbers:

3 - 2 = 1

= \frac{1}{6}

= \frac{1}{6}

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

Multiply and divide (left to right)

\frac{1}{6} \cdot 6 : 1

\frac{1}{6} \cdot 6

Convert element to fraction:

6 = \frac{6}{1}

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

Cross-cancel common factor:

6

= 1

= 1

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13+42\div 3-2\times 3^2

13 + 42 \div 3 - 2 \times 3^{2}

9-(0)^2

9 - (0)^{2}

Frequently Asked Questions (FAQ)

What is (1/2-1/3)\times 6 ?
The solution to (1/2-1/3)\times 6 is 1