The solution to 2+1/6-4/9 is 1 13/18

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2+1/6-4/9

Solution

2 + \frac{1}{6} - \frac{4}{9}

Solution

1 \frac{13}{18}

Solution steps

2 + \frac{1}{6} - \frac{4}{9}

Follow the PEMDAS order of operations

Add and subtract (left to right)

2 + \frac{1}{6} = \frac{13}{6}

2 + \frac{1}{6}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 6 + 1 = 13

2 \cdot 6 + 1

Multiply the numbers:

2 \cdot 6 = 12

= 12 + 1

Add the numbers:

12 + 1 = 13

= 13

= \frac{13}{6}

= \frac{13}{6} - \frac{4}{9}

\frac{13}{6} - \frac{4}{9} = \frac{31}{18}

\frac{13}{6} - \frac{4}{9}

Least Common Multiplier of

6, 9 : 18

6, 9

Least Common Multiplier (LCM)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 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

6

9

= 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 3 \cdot 3 = 18

= 18

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

18

For

\frac{13}{6} :

multiply the denominator and numerator by

3

\frac{13}{6} = \frac{13 \cdot 3}{6 \cdot 3} = \frac{39}{18}

For

\frac{4}{9} :

multiply the denominator and numerator by

2

\frac{4}{9} = \frac{4 \cdot 2}{9 \cdot 2} = \frac{8}{18}

= \frac{39}{18} - \frac{8}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{39 - 8}{18}

Subtract the numbers:

39 - 8 = 31

= \frac{31}{18}

= \frac{31}{18}

Convert improper fractions to mixed numbers:

\frac{31}{18} = 1 \frac{13}{18}

\frac{31}{18} = 1

Remainder

13

\frac{31}{18}

Write the problem in long division format

18 \overline{∣ 31}

Divide

31

18

to get

1

Divide

31

18

to get

1

1 18 \overline{∣ 31}

Multiply the quotient digit

(1)

by the divisor

18

1 18 \overline{∣ 31} \underline{18}

Subtract

18

from

31

1 18 \overline{∣ 31} \underline{18} 13

1 18 \overline{∣ 31} \underline{18} 13

The solution for Long Division of

\frac{31}{18}

1

with remainder of

13

1 Remainder 13

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{31}{18} = 1 \frac{13}{18}

= 1 \frac{13}{18}

= 1 \frac{13}{18}

Popular Examples

7+2+3+1+(-1)

7 + 2 + 3 + 1 + (- 1)

1^4+641

1^{4} + 641

-1^2+2(-1)+3

- 1^{2} + 2 (- 1) + 3

7^2+71

7^{2} + 71

(1-4(4))/(15)

\frac{1 - 4 ( 4 )}{15}

Frequently Asked Questions (FAQ)

What is 2+1/6-4/9 ?
The solution to 2+1/6-4/9 is 1 13/18

2+1/6-4/9

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 2+1/6-4/9 ?