What is 5/6 (2/3-1/6) ?

The solution to 5/6 (2/3-1/6) is 5/12

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Popular >

5/6 (2/3-1/6)

Solution

\frac{5}{6} (\frac{2}{3} - \frac{1}{6})

Solution

\frac{5}{12}

Solution steps

\frac{5}{6} (\frac{2}{3} - \frac{1}{6})

Follow the PEMDAS order of operations

Calculate within parentheses

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

\frac{2}{3} - \frac{1}{6}

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

\frac{2}{3} - \frac{1}{6}

Least Common Multiplier of

3, 6 : 6

3, 6

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

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

3

6

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 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{2}{3} :

multiply the denominator and numerator by

2

\frac{2}{3} = \frac{2 \cdot 2}{3 \cdot 2} = \frac{4}{6}

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

Since the denominators are equal, combine the fractions:

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

= \frac{4 - 1}{6}

Subtract the numbers:

4 - 1 = 3

= \frac{3}{6}

Cancel the common factor:

3

= \frac{1}{2}

= \frac{1}{2}

= \frac{5}{6} \cdot \frac{1}{2}

Multiply and divide (left to right)

\frac{5}{6} \cdot \frac{1}{2} : \frac{5}{12}

\frac{5}{6} \cdot \frac{1}{2}

Apply the fraction rule:

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

= \frac{5 \cdot 1}{6 \cdot 2}

Multiply the numbers:

5 \cdot 1 = 5

= \frac{5}{6 \cdot 2}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{5}{12}

= \frac{5}{12}

Popular Examples

3\times+2\times 3

3 \times + 2 \times 3

2*16/41+5*25/41

2 \cdot \frac{16}{41} + 5 \cdot \frac{25}{41}

4-6-9-7-2+8

4 - 6 - 9 - 7 - 2 + 8

(8-3/5)\div 3 1/2

(8 - \frac{3}{5}) \div 3 \frac{1}{2}

1^2+8^2

1^{2} + 8^{2}

Frequently Asked Questions (FAQ)

What is 5/6 (2/3-1/6) ?
The solution to 5/6 (2/3-1/6) is 5/12