What is 2-2/3+2/9-2/27 ?

The solution to 2-2/3+2/9-2/27 is 1 13/27

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Popular Pre Algebra >

2-2/3+2/9-2/27

Solution

2 - \frac{2}{3} + \frac{2}{9} - \frac{2}{27}

Solution

1 \frac{13}{27}

Decimal

1.48148 \dots

Solution steps

2 - \frac{2}{3} + \frac{2}{9} - \frac{2}{27}

Follow the PEMDAS order of operations

Add and subtract (left to right)

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

2 - \frac{2}{3}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 3 - 2 = 4

2 \cdot 3 - 2

Multiply the numbers:

2 \cdot 3 = 6

= 6 - 2

Subtract the numbers:

6 - 2 = 4

= 4

= \frac{4}{3}

= \frac{4}{3} + \frac{2}{9} - \frac{2}{27}

\frac{4}{3} + \frac{2}{9} = \frac{14}{9}

\frac{4}{3} + \frac{2}{9}

Least Common Multiplier of

3, 9 : 9

3, 9

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

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

3

9

= 3 \cdot 3

Multiply the numbers:

3 \cdot 3 = 9

= 9

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

9

For

\frac{4}{3} :

multiply the denominator and numerator by

3

\frac{4}{3} = \frac{4 \cdot 3}{3 \cdot 3} = \frac{12}{9}

= \frac{12}{9} + \frac{2}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{12 + 2}{9}

Add the numbers:

12 + 2 = 14

= \frac{14}{9}

= \frac{14}{9} - \frac{2}{27}

\frac{14}{9} - \frac{2}{27} = \frac{40}{27}

\frac{14}{9} - \frac{2}{27}

Least Common Multiplier of

9, 27 : 27

9, 27

Least Common Multiplier (LCM)

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

Prime factorization of

27 : 3 \cdot 3 \cdot 3

27

27

divides by

327 = 9 \cdot 3

= 3 \cdot 9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3 \cdot 3

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

9

27

= 3 \cdot 3 \cdot 3

Multiply the numbers:

3 \cdot 3 \cdot 3 = 27

= 27

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

27

For

\frac{14}{9} :

multiply the denominator and numerator by

3

\frac{14}{9} = \frac{14 \cdot 3}{9 \cdot 3} = \frac{42}{27}

= \frac{42}{27} - \frac{2}{27}

Since the denominators are equal, combine the fractions:

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

= \frac{42 - 2}{27}

Subtract the numbers:

42 - 2 = 40

= \frac{40}{27}

= \frac{40}{27}

Convert improper fractions to mixed numbers:

\frac{40}{27} = 1 \frac{13}{27}

\frac{40}{27} = 1

Remainder

13

\frac{40}{27}

Write the problem in long division format

27 \overline{∣ 40}

Divide

40

27

to get

1

Divide

40

27

to get

1

1 27 \overline{∣ 40}

Multiply the quotient digit

(1)

by the divisor

27

1 27 \overline{∣ 40} \underline{27}

Subtract

27

from

40

1 27 \overline{∣ 40} \underline{27} 13

1 27 \overline{∣ 40} \underline{27} 13

The solution for Long Division of

\frac{40}{27}

1

with remainder of

13

1 Remainder 13

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{40}{27} = 1 \frac{13}{27}

= 1 \frac{13}{27}

= 1 \frac{13}{27}

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Frequently Asked Questions (FAQ)

What is 2-2/3+2/9-2/27 ?
The solution to 2-2/3+2/9-2/27 is 1 13/27

2-2/3+2/9-2/27

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 2-2/3+2/9-2/27 ?

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