What is (-12+2(2 1/2))/(1+2) ?

The solution to (-12+2(2 1/2))/(1+2) is -2 1/3

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

Solution

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

Solution

- 2 \frac{1}{3}

Solution steps

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

Convert mixed numbers to improper fractions:

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

2 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

2 \frac{1}{2} = \frac{2 \cdot 2 + 1}{2}

= \frac{5}{2}

= \frac{- 12 + 2 ( \frac{5}{2} )}{1 + 2}

Solve

- 12 + 2 (\frac{5}{2}) : - 7

Follow the PEMDAS order of operations

Multiply and divide (left to right)

2 (\frac{5}{2}) : 5

2 (\frac{5}{2})

Remove parentheses:

(a) = a

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

Multiply fractions:

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

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

Cancel the common factor:

2

= 5

= - 12 + 5

Add and subtract (left to right)

- 12 + 5 : - 7

- 12 + 5

- 12 + 5 = - 7

= - 7

= - 7

Solve

1 + 2 : 3

1 + 2 = 3

= 3

= \frac{- 7}{3}

Simplify

\frac{- 7}{3} : - 2 \frac{1}{3}

Apply the fraction rule:

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

= - \frac{7}{3}

Convert improper fractions to mixed numbers:

\frac{7}{3} = 2 \frac{1}{3}

\frac{7}{3} = 2

Remainder

1

\frac{7}{3}

Write the problem in long division format

3 \overline{∣ 7}

Divide

7

3

to get

2

Divide

7

3

to get

2

2 3 \overline{∣ 7}

Multiply the quotient digit

(2)

by the divisor

3

2 3 \overline{∣ 7} \underline{6}

Subtract

6

from

7

2 3 \overline{∣ 7} \underline{6} 1

2 3 \overline{∣ 7} \underline{6} 1

The solution for Long Division of

\frac{7}{3}

2

with remainder of

1

2 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{7}{3} = 2 \frac{1}{3}

= 2 \frac{1}{3}

= - 2 \frac{1}{3}

= - 2 \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is (-12+2(2 1/2))/(1+2) ?
The solution to (-12+2(2 1/2))/(1+2) is -2 1/3