What is 5-1/9+2/3-7/6 ?

The solution to 5-1/9+2/3-7/6 is 4 7/18

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5-1/9+2/3-7/6

Solution

5 - \frac{1}{9} + \frac{2}{3} - \frac{7}{6}

Solution

4 \frac{7}{18}

Solution steps

5 - \frac{1}{9} + \frac{2}{3} - \frac{7}{6}

Follow the PEMDAS order of operations

Add and subtract (left to right)

5 - \frac{1}{9} = \frac{44}{9}

5 - \frac{1}{9}

Convert element to fraction:

5 = \frac{5 \cdot 9}{9}

= \frac{5 \cdot 9}{9} - \frac{1}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 9 - 1}{9}

5 \cdot 9 - 1 = 44

5 \cdot 9 - 1

Multiply the numbers:

5 \cdot 9 = 45

= 45 - 1

Subtract the numbers:

45 - 1 = 44

= 44

= \frac{44}{9}

= \frac{44}{9} + \frac{2}{3} - \frac{7}{6}

\frac{44}{9} + \frac{2}{3} = \frac{50}{9}

\frac{44}{9} + \frac{2}{3}

Least Common Multiplier of

9, 3 : 9

9, 3

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

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

9

3

= 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{2}{3} :

multiply the denominator and numerator by

3

\frac{2}{3} = \frac{2 \cdot 3}{3 \cdot 3} = \frac{6}{9}

= \frac{44}{9} + \frac{6}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{44 + 6}{9}

Add the numbers:

44 + 6 = 50

= \frac{50}{9}

= \frac{50}{9} - \frac{7}{6}

\frac{50}{9} - \frac{7}{6} = \frac{79}{18}

\frac{50}{9} - \frac{7}{6}

Least Common Multiplier of

9, 6 : 18

9, 6

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

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

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

9

6

= 3 \cdot 3 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 2 = 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{50}{9} :

multiply the denominator and numerator by

2

\frac{50}{9} = \frac{50 \cdot 2}{9 \cdot 2} = \frac{100}{18}

For

\frac{7}{6} :

multiply the denominator and numerator by

3

\frac{7}{6} = \frac{7 \cdot 3}{6 \cdot 3} = \frac{21}{18}

= \frac{100}{18} - \frac{21}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{100 - 21}{18}

Subtract the numbers:

100 - 21 = 79

= \frac{79}{18}

= \frac{79}{18}

Convert improper fractions to mixed numbers:

\frac{79}{18} = 4 \frac{7}{18}

\frac{79}{18} = 4

Remainder

7

\frac{79}{18}

Write the problem in long division format

18 \overline{∣ 79}

Divide

79

18

to get

4

Divide

79

18

to get

4

4 18 \overline{∣ 79}

Multiply the quotient digit

(4)

by the divisor

18

4 18 \overline{∣ 79} \underline{72}

Subtract

72

from

79

4 18 \overline{∣ 79} \underline{72} 7

4 18 \overline{∣ 79} \underline{72} 7

The solution for Long Division of

\frac{79}{18}

4

with remainder of

7

4 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{79}{18} = 4 \frac{7}{18}

= 4 \frac{7}{18}

= 4 \frac{7}{18}

Popular Examples

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

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

20+(3\times 4-(17-3\times 2^2))\times 2

20 + (3 \times 4 - (17 - 3 \times 2^{2})) \times 2

-2-(-2+6)+5

- 2 - (- 2 + 6) + 5

20^2-17^2

2 0^{2} - 1 7^{2}

8\div 2^2+6*3

8 \div 2^{2} + 6 \cdot 3

Frequently Asked Questions (FAQ)

What is 5-1/9+2/3-7/6 ?
The solution to 5-1/9+2/3-7/6 is 4 7/18