What is 2\div 9+22\div 4+(-15\div 2) ?

The solution to 2\div 9+22\div 4+(-15\div 2) is -16/9

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Popular Pre Algebra >

2\div 9+22\div 4+(-15\div 2)

Solution

2 \div 9 + 22 \div 4 + (- 15 \div 2)

Solution

- \frac{16}{9}

Decimal

- 1.77777 \dots

Solution steps

2 \div 9 + 22 \div 4 + (- 15 \div 2)

Follow the PEMDAS order of operations

Calculate within parentheses

(- 15 \div 2) : \frac{- 15}{2}

- 15 \div 2

- 15 \div 2 = \frac{- 15}{2}

= \frac{- 15}{2}

= 2 \div 9 + 22 \div 4 + \frac{- 15}{2}

Multiply and divide (left to right)

2 \div 9 : \frac{2}{9}

2 \div 9

2 \div 9 = \frac{2}{9}

= \frac{2}{9}

= \frac{2}{9} + 22 \div 4 + \frac{- 15}{2}

Multiply and divide (left to right)

22 \div 4 : \frac{22}{4}

22 \div 4

22 \div 4 = \frac{22}{4}

= \frac{22}{4}

= \frac{2}{9} + \frac{22}{4} + \frac{- 15}{2}

Add and subtract (left to right)

\frac{2}{9} + \frac{22}{4} + \frac{- 15}{2} : - \frac{16}{9}

\frac{2}{9} + \frac{22}{4} + \frac{- 15}{2}

\frac{2}{9} + \frac{22}{4} = \frac{103}{18}

\frac{2}{9} + \frac{22}{4}

Cancel

\frac{22}{4} : \frac{11}{2}

\frac{22}{4}

Cancel the common factor:

2

= \frac{11}{2}

= \frac{2}{9} + \frac{11}{2}

Least Common Multiplier of

9, 2 : 18

9, 2

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

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

9

2

= 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{2}{9} :

multiply the denominator and numerator by

2

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

For

\frac{11}{2} :

multiply the denominator and numerator by

9

\frac{11}{2} = \frac{11 \cdot 9}{2 \cdot 9} = \frac{99}{18}

= \frac{4}{18} + \frac{99}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{4 + 99}{18}

Add the numbers:

4 + 99 = 103

= \frac{103}{18}

= \frac{103}{18} + \frac{- 15}{2}

\frac{103}{18} + \frac{- 15}{2} = - \frac{16}{9}

\frac{103}{18} + \frac{- 15}{2}

Apply the fraction rule:

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

= \frac{103}{18} - \frac{15}{2}

Least Common Multiplier of

18, 2 : 18

18, 2

Least Common Multiplier (LCM)

Prime factorization of

18 : 2 \cdot 3 \cdot 3

18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

18

2

= 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{15}{2} :

multiply the denominator and numerator by

9

\frac{15}{2} = \frac{15 \cdot 9}{2 \cdot 9} = \frac{135}{18}

= \frac{103}{18} - \frac{135}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{103 - 135}{18}

Subtract the numbers:

103 - 135 = - 32

= \frac{- 32}{18}

Apply the fraction rule:

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

= - \frac{32}{18}

Cancel the common factor:

2

= - \frac{16}{9}

= - \frac{16}{9}

= - \frac{16}{9}

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Frequently Asked Questions (FAQ)

What is 2\div 9+22\div 4+(-15\div 2) ?
The solution to 2\div 9+22\div 4+(-15\div 2) is -16/9

2\div 9+22\div 4+(-15\div 2)

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 2\div 9+22\div 4+(-15\div 2) ?

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