What is (-2/5+4)-(-1/3+1) ?

The solution to (-2/5+4)-(-1/3+1) is 2 14/15

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Popular >

(-2/5+4)-(-1/3+1)

Solution

(- \frac{2}{5} + 4) - (- \frac{1}{3} + 1)

Solution

2 \frac{14}{15}

Solution steps

(- \frac{2}{5} + 4) - (- \frac{1}{3} + 1)

Follow the PEMDAS order of operations

Calculate within parentheses

(- \frac{2}{5} + 4) : \frac{18}{5}

- \frac{2}{5} + 4

- \frac{2}{5} + 4 = \frac{18}{5}

- \frac{2}{5} + 4

Convert element to fraction:

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

= \frac{4 \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{4 \cdot 5 - 2}{5}

4 \cdot 5 - 2 = 18

4 \cdot 5 - 2

Multiply the numbers:

4 \cdot 5 = 20

= 20 - 2

Subtract the numbers:

20 - 2 = 18

= 18

= \frac{18}{5}

= \frac{18}{5}

= \frac{18}{5} - (- \frac{1}{3} + 1)

Calculate within parentheses

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

- \frac{1}{3} + 1

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

- \frac{1}{3} + 1

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 3 - 1 = 2

1 \cdot 3 - 1

Multiply the numbers:

1 \cdot 3 = 3

= 3 - 1

Subtract the numbers:

3 - 1 = 2

= 2

= \frac{2}{3}

= \frac{2}{3}

= \frac{18}{5} - \frac{2}{3}

Add and subtract (left to right)

\frac{18}{5} - \frac{2}{3} : \frac{44}{15}

\frac{18}{5} - \frac{2}{3}

\frac{18}{5} - \frac{2}{3} = \frac{44}{15}

\frac{18}{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{18}{5} :

multiply the denominator and numerator by

3

\frac{18}{5} = \frac{18 \cdot 3}{5 \cdot 3} = \frac{54}{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{54}{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{54 - 10}{15}

Subtract the numbers:

54 - 10 = 44

= \frac{44}{15}

= \frac{44}{15}

= \frac{44}{15}

Convert improper fractions to mixed numbers:

\frac{44}{15} = 2 \frac{14}{15}

\frac{44}{15} = 2

Remainder

14

\frac{44}{15}

Write the problem in long division format

15 \overline{∣ 44}

Divide

44

15

to get

2

Divide

44

15

to get

2

2 15 \overline{∣ 44}

Multiply the quotient digit

(2)

by the divisor

15

2 15 \overline{∣ 44} \underline{30}

Subtract

30

from

44

2 15 \overline{∣ 44} \underline{30} 14

2 15 \overline{∣ 44} \underline{30} 14

The solution for Long Division of

\frac{44}{15}

2

with remainder of

14

2 Remainder 14

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{44}{15} = 2 \frac{14}{15}

= 2 \frac{14}{15}

= 2 \frac{14}{15}

Popular Examples

(-6)+(-18)+(-3)

(- 6) + (- 18) + (- 3)

-4\times (-6)\times (-1)

- 4 \times (- 6) \times (- 1)

5\times 4+30\div 6-35-7

5 \times 4 + 30 \div 6 - 35 - 7

3\times (2+5)-6\times 5+2\times (3-4)-(6-8)

3 \times (2 + 5) - 6 \times 5 + 2 \times (3 - 4) - (6 - 8)

1^3+2^3+3^3

1^{3} + 2^{3} + 3^{3}

Frequently Asked Questions (FAQ)

What is (-2/5+4)-(-1/3+1) ?
The solution to (-2/5+4)-(-1/3+1) is 2 14/15