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

The solution to (-1 1/3)+(1-1/5) is -8/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

- \frac{8}{15}

Solution steps

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

Convert mixed numbers to improper fractions:

1 \frac{1}{3} = \frac{4}{3}

1 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{4}{3}

= (- \frac{4}{3}) + (1 - \frac{1}{5})

Follow the PEMDAS order of operations

Calculate within parentheses

(1 - \frac{1}{5}) : \frac{4}{5}

1 - \frac{1}{5}

1 - \frac{1}{5} = \frac{4}{5}

1 - \frac{1}{5}

Convert element to fraction:

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

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

1 \cdot 5 - 1 = 4

1 \cdot 5 - 1

Multiply the numbers:

1 \cdot 5 = 5

= 5 - 1

Subtract the numbers:

5 - 1 = 4

= 4

= \frac{4}{5}

= \frac{4}{5}

= (- \frac{4}{3}) + \frac{4}{5}

Add and subtract (left to right)

(- \frac{4}{3}) + \frac{4}{5} : - \frac{8}{15}

(- \frac{4}{3}) + \frac{4}{5}

(- \frac{4}{3}) + \frac{4}{5} = - \frac{8}{15}

(- \frac{4}{3}) + \frac{4}{5}

Remove parentheses:

(- a) = - a

= - \frac{4}{3} + \frac{4}{5}

Least Common Multiplier of

3, 5 : 15

3, 5

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

3

5

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 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{4}{3} :

multiply the denominator and numerator by

5

\frac{4}{3} = \frac{4 \cdot 5}{3 \cdot 5} = \frac{20}{15}

For

\frac{4}{5} :

multiply the denominator and numerator by

3

\frac{4}{5} = \frac{4 \cdot 3}{5 \cdot 3} = \frac{12}{15}

= - \frac{20}{15} + \frac{12}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{- 20 + 12}{15}

Add/Subtract the numbers:

- 20 + 12 = - 8

= \frac{- 8}{15}

Apply the fraction rule:

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

= - \frac{8}{15}

= - \frac{8}{15}

= - \frac{8}{15}

Popular Examples

12-4\times (5+3)

12 - 4 \times (5 + 3)

(-2)^3\times (-2)

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

12-24-36-48

12 - 24 - 36 - 48

3(5)-4

3 (5) - 4

3(5)-1

3 (5) - 1

Frequently Asked Questions (FAQ)

What is (-1 1/3)+(1-1/5) ?
The solution to (-1 1/3)+(1-1/5) is -8/15