What is [ 1/2-1/3 ]\times 5 ?

The solution to [ 1/2-1/3 ]\times 5 is 5/6

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Popular >

[ 1/2-1/3 ]\times 5

Solution

[\frac{1}{2} - \frac{1}{3}] \cdot 5

Solution

\frac{5}{6}

Solution steps

[\frac{1}{2} - \frac{1}{3}] \cdot 5

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 5

Multiply and divide (left to right)

\frac{1}{6} \cdot 5 : \frac{5}{6}

\frac{1}{6} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{1}{6} \cdot \frac{5}{1}

Apply the fraction rule:

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

= \frac{1 \cdot 5}{6 \cdot 1}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{6 \cdot 1}

Multiply the numbers:

6 \cdot 1 = 6

= \frac{5}{6}

= \frac{5}{6}

Popular Examples

(-2)^2+2(-2)+2

(- 2)^{2} + 2 (- 2) + 2

10(4)+4(1)\times 5(5)

10 (4) + 4 (1) \times 5 (5)

11^2+8^2

1 1^{2} + 8^{2}

3-[-2+1-(4-5-7)]-2+[-3-(5-6-1)+2]

3 - [- 2 + 1 - (4 - 5 - 7)] - 2 + [- 3 - (5 - 6 - 1) + 2]

1^3+1

1^{3} + 1

Frequently Asked Questions (FAQ)

What is [ 1/2-1/3 ]\times 5 ?
The solution to [ 1/2-1/3 ]\times 5 is 5/6