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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

\frac{1}{2}

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{6} + \frac{2}{3}) : \frac{5}{6}

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

\frac{1}{6} + \frac{2}{3} = \frac{5}{6}

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

Least Common Multiplier of

6, 3 : 6

6, 3

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

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

6

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{2}{3} :

multiply the denominator and numerator by

2

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

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

Since the denominators are equal, combine the fractions:

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

= \frac{1 + 4}{6}

Add the numbers:

1 + 4 = 5

= \frac{5}{6}

= \frac{5}{6}

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

Calculate within parentheses

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

1 - \frac{2}{5}

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

1 - \frac{2}{5}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 5 - 2 = 3

1 \cdot 5 - 2

Multiply the numbers:

1 \cdot 5 = 5

= 5 - 2

Subtract the numbers:

5 - 2 = 3

= 3

= \frac{3}{5}

= \frac{3}{5}

= \frac{5}{6} \cdot \frac{3}{5}

Multiply and divide (left to right)

\frac{5}{6} \cdot \frac{3}{5} : \frac{1}{2}

\frac{5}{6} \cdot \frac{3}{5}

Cross-cancel common factor:

5

= \frac{3}{6}

Cancel the numbers:

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

= \frac{1}{2}

= \frac{1}{2}

Popular Examples

51^7-51^6

5 1^{7} - 5 1^{6}

(6-4)^2

(6 - 4)^{2}

-3/2 (2)^2

- \frac{3}{2} (2)^{2}

2+3^2

2 + 3^{2}

4(5)^3

4 (5)^{3}

Frequently Asked Questions (FAQ)

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