What is -4/5-(-3)-2/3 ?

The solution to -4/5-(-3)-2/3 is 1 8/15

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Popular >

-4/5-(-3)-2/3

Solution

- \frac{4}{5} - (- 3) - \frac{2}{3}

Solution

1 \frac{8}{15}

Solution steps

- \frac{4}{5} - (- 3) - \frac{2}{3}

Follow the PEMDAS order of operations

Add and subtract (left to right)

Apply rule

- (- a) = + a

- (- 3) = + 3

= - \frac{4}{5} + 3 - \frac{2}{3}

- \frac{4}{5} + 3 = \frac{11}{5}

- \frac{4}{5} + 3

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

3 \cdot 5 - 4 = 11

3 \cdot 5 - 4

Multiply the numbers:

3 \cdot 5 = 15

= 15 - 4

Subtract the numbers:

15 - 4 = 11

= 11

= \frac{11}{5}

= \frac{11}{5} - \frac{2}{3}

\frac{11}{5} - \frac{2}{3} = \frac{23}{15}

\frac{11}{5} - \frac{2}{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{11}{5} :

multiply the denominator and numerator by

3

\frac{11}{5} = \frac{11 \cdot 3}{5 \cdot 3} = \frac{33}{15}

For

\frac{2}{3} :

multiply the denominator and numerator by

5

\frac{2}{3} = \frac{2 \cdot 5}{3 \cdot 5} = \frac{10}{15}

= \frac{33}{15} - \frac{10}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{33 - 10}{15}

Subtract the numbers:

33 - 10 = 23

= \frac{23}{15}

= \frac{23}{15}

Convert improper fractions to mixed numbers:

\frac{23}{15} = 1 \frac{8}{15}

\frac{23}{15} = 1

Remainder

8

\frac{23}{15}

Write the problem in long division format

15 \overline{∣ 23}

Divide

23

15

to get

1

Divide

23

15

to get

1

1 15 \overline{∣ 23}

Multiply the quotient digit

(1)

by the divisor

15

1 15 \overline{∣ 23} \underline{15}

Subtract

15

from

23

1 15 \overline{∣ 23} \underline{15} 8

1 15 \overline{∣ 23} \underline{15} 8

The solution for Long Division of

\frac{23}{15}

1

with remainder of

8

1 Remainder 8

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{23}{15} = 1 \frac{8}{15}

= 1 \frac{8}{15}

= 1 \frac{8}{15}

Popular Examples

-2(2)^2

- 2 (2)^{2}

6/(2(2+1))

\frac{6}{2 ( 2 + 1 )}

2-(3/8+1/4)

2 - (\frac{3}{8} + \frac{1}{4})

-3(1)^2

- 3 (1)^{2}

(3+1/4)(1-4/5)

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

Frequently Asked Questions (FAQ)

What is -4/5-(-3)-2/3 ?
The solution to -4/5-(-3)-2/3 is 1 8/15