What is -2(1/2+7 1/3-2(4+6)-3)+6 ?

The solution to -2(1/2+7 1/3-2(4+6)-3)+6 is 36 1/3

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Popular Pre Algebra >

-2(1/2+7 1/3-2(4+6)-3)+6

Solution

- 2 (\frac{1}{2} + 7 \frac{1}{3} - 2 (4 + 6) - 3) + 6

Solution

36 \frac{1}{3}

Decimal

36.33333 \dots

Solution steps

- 2 (\frac{1}{2} + 7 \frac{1}{3} - 2 (4 + 6) - 3) + 6

Convert mixed numbers to improper fractions:

7 \frac{1}{3} = \frac{22}{3}

7 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

7 \frac{1}{3} = \frac{7 \cdot 3 + 1}{3}

= \frac{22}{3}

= - 2 (\frac{1}{2} + \frac{22}{3} - 2 (4 + 6) - 3) + 6

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{2} + \frac{22}{3} - 2 (4 + 6) - 3) : - \frac{91}{6}

\frac{1}{2} + \frac{22}{3} - 2 (4 + 6) - 3

Calculate within parentheses

(4 + 6) : 10

4 + 6

4 + 6 = 10

= 10

= \frac{1}{2} + \frac{22}{3} - 2 \cdot 10 - 3

Multiply and divide (left to right)

2 \cdot 10 : 20

2 \cdot 10

2 \cdot 10 = 20

= 20

= \frac{1}{2} + \frac{22}{3} - 20 - 3

Add and subtract (left to right)

\frac{1}{2} + \frac{22}{3} - 20 - 3 : - \frac{91}{6}

\frac{1}{2} + \frac{22}{3} - 20 - 3

\frac{1}{2} + \frac{22}{3} = \frac{47}{6}

\frac{1}{2} + \frac{22}{3}

Least Common Multiplier of

2, 3 : 6

2, 3

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

2

3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

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

6

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

For

\frac{22}{3} :

multiply the denominator and numerator by

2

\frac{22}{3} = \frac{22 \cdot 2}{3 \cdot 2} = \frac{44}{6}

= \frac{3}{6} + \frac{44}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{3 + 44}{6}

Add the numbers:

3 + 44 = 47

= \frac{47}{6}

= \frac{47}{6} - 20 - 3

\frac{47}{6} - 20 = - \frac{73}{6}

\frac{47}{6} - 20

Convert element to fraction:

20 = \frac{20 \cdot 6}{6}

= - \frac{20 \cdot 6}{6} + \frac{47}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- 20 \cdot 6 + 47}{6}

- 20 \cdot 6 + 47 = - 73

- 20 \cdot 6 + 47

Multiply the numbers:

20 \cdot 6 = 120

= - 120 + 47

Add/Subtract the numbers:

- 120 + 47 = - 73

= - 73

= \frac{- 73}{6}

Apply the fraction rule:

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

= - \frac{73}{6}

= - \frac{73}{6} - 3

- \frac{73}{6} - 3 = - \frac{91}{6}

- \frac{73}{6} - 3

Convert element to fraction:

3 = \frac{3 \cdot 6}{6}

= - \frac{3 \cdot 6}{6} - \frac{73}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- 3 \cdot 6 - 73}{6}

- 3 \cdot 6 - 73 = - 91

- 3 \cdot 6 - 73

Multiply the numbers:

3 \cdot 6 = 18

= - 18 - 73

Subtract the numbers:

- 18 - 73 = - 91

= - 91

= \frac{- 91}{6}

Apply the fraction rule:

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

= - \frac{91}{6}

= - \frac{91}{6}

= - \frac{91}{6}

= - 2 (- \frac{91}{6}) + 6

Multiply and divide (left to right)

- 2 (- \frac{91}{6}) : \frac{91}{3}

- 2 (- \frac{91}{6})

Apply rule

- a \cdot (- b) = a \cdot b

- 2 (- \frac{91}{6}) = 2 \cdot \frac{91}{6}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{91}{6}

Apply the fraction rule:

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

= \frac{2 \cdot 91}{1 \cdot 6}

\frac{2 \cdot 91}{1 \cdot 6} = \frac{91}{3}

\frac{2 \cdot 91}{1 \cdot 6}

Multiply the numbers:

1 \cdot 6 = 6

= \frac{2 \cdot 91}{6}

Factor the number:

6 = 2 \cdot 3

= \frac{2 \cdot 91}{2 \cdot 3}

Cancel the common factor:

2

= \frac{91}{3}

= \frac{91}{3}

= \frac{91}{3} + 6

Add and subtract (left to right)

\frac{91}{3} + 6 : \frac{109}{3}

\frac{91}{3} + 6

\frac{91}{3} + 6 = \frac{109}{3}

\frac{91}{3} + 6

Convert element to fraction:

6 = \frac{6 \cdot 3}{3}

= \frac{6 \cdot 3}{3} + \frac{91}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{6 \cdot 3 + 91}{3}

6 \cdot 3 + 91 = 109

6 \cdot 3 + 91

Multiply the numbers:

6 \cdot 3 = 18

= 18 + 91

Add the numbers:

18 + 91 = 109

= 109

= \frac{109}{3}

= \frac{109}{3}

= \frac{109}{3}

Convert improper fractions to mixed numbers:

\frac{109}{3} = 36 \frac{1}{3}

\frac{109}{3} = 36

Remainder

1

\frac{109}{3}

Write the problem in long division format

3 \overline{∣ 109}

Divide

10

3

to get

3

Divide

10

3

to get

3

3 3 \overline{∣ 109}

Multiply the quotient digit

(3)

by the divisor

3

3 3 \overline{∣ 109} \underline{9}

Subtract

9

from

10

3 3 \overline{∣ 109} \underline{9} 1

Bring down the next number of the dividend

3 3 \overline{∣ 109} \underline{9} 19

3 3 \overline{∣ 109} \underline{9} 19

Divide

19

3

to get

6

Divide

19

3

to get

6

36 3 \overline{∣ 109} \underline{9} 19

Multiply the quotient digit

(6)

by the divisor

3

36 3 \overline{∣ 109} \underline{9} 19 \underline{18}

Subtract

18

from

19

36 3 \overline{∣ 109} \underline{9} 19 \underline{18} 1

36 3 \overline{∣ 109} \underline{9} 19 \underline{18} 1

The solution for Long Division of

\frac{109}{3}

36

with remainder of

1

36 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{109}{3} = 36 \frac{1}{3}

= 36 \frac{1}{3}

= 36 \frac{1}{3}

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Frequently Asked Questions (FAQ)

What is -2(1/2+7 1/3-2(4+6)-3)+6 ?
The solution to -2(1/2+7 1/3-2(4+6)-3)+6 is 36 1/3

-2(1/2+7 1/3-2(4+6)-3)+6

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is -2(1/2+7 1/3-2(4+6)-3)+6 ?

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