What is (17/22+1)+(2-9/11) ?

The solution to (17/22+1)+(2-9/11) is 2 21/22

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(17/22+1)+(2-9/11)

Solution

(\frac{17}{22} + 1) + (2 - \frac{9}{11})

Solution

2 \frac{21}{22}

Solution steps

(\frac{17}{22} + 1) + (2 - \frac{9}{11})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{17}{22} + 1) : \frac{39}{22}

\frac{17}{22} + 1

\frac{17}{22} + 1 = \frac{39}{22}

\frac{17}{22} + 1

Convert element to fraction:

1 = \frac{1 \cdot 22}{22}

= \frac{1 \cdot 22}{22} + \frac{17}{22}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 22 + 17}{22}

1 \cdot 22 + 17 = 39

1 \cdot 22 + 17

Multiply the numbers:

1 \cdot 22 = 22

= 22 + 17

Add the numbers:

22 + 17 = 39

= 39

= \frac{39}{22}

= \frac{39}{22}

= \frac{39}{22} + (2 - \frac{9}{11})

Calculate within parentheses

(2 - \frac{9}{11}) : \frac{13}{11}

2 - \frac{9}{11}

2 - \frac{9}{11} = \frac{13}{11}

2 - \frac{9}{11}

Convert element to fraction:

2 = \frac{2 \cdot 11}{11}

= \frac{2 \cdot 11}{11} - \frac{9}{11}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 11 - 9}{11}

2 \cdot 11 - 9 = 13

2 \cdot 11 - 9

Multiply the numbers:

2 \cdot 11 = 22

= 22 - 9

Subtract the numbers:

22 - 9 = 13

= 13

= \frac{13}{11}

= \frac{13}{11}

= \frac{39}{22} + \frac{13}{11}

Add and subtract (left to right)

\frac{39}{22} + \frac{13}{11} : \frac{65}{22}

\frac{39}{22} + \frac{13}{11}

\frac{39}{22} + \frac{13}{11} = \frac{65}{22}

\frac{39}{22} + \frac{13}{11}

Least Common Multiplier of

22, 11 : 22

22, 11

Least Common Multiplier (LCM)

Prime factorization of

22 : 2 \cdot 11

22

22

divides by

222 = 11 \cdot 2

= 2 \cdot 11

2, 11

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 11

Prime factorization of

11 : 11

11

11

is a prime number, therefore no factorization is possible

= 11

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

22

11

= 2 \cdot 11

Multiply the numbers:

2 \cdot 11 = 22

= 22

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

22

For

\frac{13}{11} :

multiply the denominator and numerator by

2

\frac{13}{11} = \frac{13 \cdot 2}{11 \cdot 2} = \frac{26}{22}

= \frac{39}{22} + \frac{26}{22}

Since the denominators are equal, combine the fractions:

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

= \frac{39 + 26}{22}

Add the numbers:

39 + 26 = 65

= \frac{65}{22}

= \frac{65}{22}

= \frac{65}{22}

Convert improper fractions to mixed numbers:

\frac{65}{22} = 2 \frac{21}{22}

\frac{65}{22} = 2

Remainder

21

\frac{65}{22}

Write the problem in long division format

22 \overline{∣ 65}

Divide

65

22

to get

2

Divide

65

22

to get

2

2 22 \overline{∣ 65}

Multiply the quotient digit

(2)

by the divisor

22

2 22 \overline{∣ 65} \underline{44}

Subtract

44

from

65

2 22 \overline{∣ 65} \underline{44} 21

2 22 \overline{∣ 65} \underline{44} 21

The solution for Long Division of

\frac{65}{22}

2

with remainder of

21

2 Remainder 21

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{65}{22} = 2 \frac{21}{22}

= 2 \frac{21}{22}

= 2 \frac{21}{22}

Popular Examples

(-10+1)^2

(- 10 + 1)^{2}

-2(1)+5

- 2 (1) + 5

5*3^2

5 \cdot 3^{2}

7/9-3+2/3

\frac{7}{9} - 3 + \frac{2}{3}

72\div 9+7

72 \div 9 + 7

Frequently Asked Questions (FAQ)

What is (17/22+1)+(2-9/11) ?
The solution to (17/22+1)+(2-9/11) is 2 21/22