What is 2/15+(3/2-1/2)/5/3-1/3 ?

The solution to 2/15+(3/2-1/2)/5/3-1/3 is -2/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2/15+(3/2-1/2)/5/3-1/3

Solution

2/15 + (3/2 - 1/2) /5/3 - 1/3

Solution

- \frac{2}{15}

Solution steps

2/15 + (3/2 - 1/2) /5/3 - 1/3

Follow the PEMDAS order of operations

Calculate within parentheses

(3/2 - 1/2) : 1

3/2 - 1/2

Multiply and divide (left to right)

3/2 : \frac{3}{2}

3/2

3/2 = \frac{3}{2}

= \frac{3}{2}

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

Multiply and divide (left to right)

1/2 : \frac{1}{2}

1/2

1/2 = \frac{1}{2}

= \frac{1}{2}

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

Add and subtract (left to right)

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

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

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

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

Apply rule

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

= \frac{3 - 1}{2}

Subtract the numbers:

3 - 1 = 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

= 2/15 + 1/5/3 - 1/3

Multiply and divide (left to right)

2/15 : \frac{2}{15}

2/15

2/15 = \frac{2}{15}

= \frac{2}{15}

= \frac{2}{15} + 1/5/3 - 1/3

Multiply and divide (left to right)

1/5/3 : \frac{1}{15}

1/5/3

1/5 = \frac{1}{5}

= \frac{1}{5} /3

\frac{1}{5} /3 = \frac{1}{15}

\frac{1}{5} /3

Convert element to fraction:

3 = \frac{3}{1}

= \frac{1}{5} \div \frac{3}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{1}{5} \cdot \frac{1}{3}

Multiply fractions:

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

= \frac{1 \cdot 1}{5 \cdot 3}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= \frac{1}{15}

= \frac{1}{15}

= \frac{2}{15} + \frac{1}{15} - 1/3

Multiply and divide (left to right)

1/3 : \frac{1}{3}

1/3

1/3 = \frac{1}{3}

= \frac{1}{3}

= \frac{2}{15} + \frac{1}{15} - \frac{1}{3}

Add and subtract (left to right)

\frac{2}{15} + \frac{1}{15} - \frac{1}{3} : - \frac{2}{15}

\frac{2}{15} + \frac{1}{15} - \frac{1}{3}

\frac{2}{15} + \frac{1}{15} = \frac{1}{5}

\frac{2}{15} + \frac{1}{15}

Apply rule

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

= \frac{2 + 1}{15}

Add the numbers:

2 + 1 = 3

= \frac{3}{15}

Cancel the common factor:

3

= \frac{1}{5}

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

\frac{1}{5} - \frac{1}{3} = - \frac{2}{15}

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

Least Common Multiplier of

5, 3 : 15

5, 3

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

5

3

= 5 \cdot 3

Multiply the numbers:

5 \cdot 3 = 15

= 15

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

15

For

\frac{1}{5} :

multiply the denominator and numerator by

3

\frac{1}{5} = \frac{1 \cdot 3}{5 \cdot 3} = \frac{3}{15}

For

\frac{1}{3} :

multiply the denominator and numerator by

5

\frac{1}{3} = \frac{1 \cdot 5}{3 \cdot 5} = \frac{5}{15}

= \frac{3}{15} - \frac{5}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{3 - 5}{15}

Subtract the numbers:

3 - 5 = - 2

= \frac{- 2}{15}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{15}

= - \frac{2}{15}

= - \frac{2}{15}

Popular Examples

-9\times 9+7

- 9 \times 9 + 7

-8\div 2(3-3^2)

- 8 \div 2 (3 - 3^{2})

5\times+3\times+2

5 \times + 3 \times + 2

-2(-8)+7(0)

- 2 (- 8) + 7 (0)

(-12+2(2 1/2))/(1+2)

\frac{- 12 + 2 ( 2 \frac{1}{2} )}{1 + 2}

Frequently Asked Questions (FAQ)

What is 2/15+(3/2-1/2)/5/3-1/3 ?
The solution to 2/15+(3/2-1/2)/5/3-1/3 is -2/15