What is 19\div 18+3\div 2\times 5\div 9-4\div 18 ?

The solution to 19\div 18+3\div 2\times 5\div 9-4\div 18 is 1 2/3

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19\div 18+3\div 2\times 5\div 9-4\div 18

Solution

19 \div 18 + 3 \div 2 \times 5 \div 9 - 4 \div 18

Solution

1 \frac{2}{3}

Solution steps

19 \div 18 + 3 \div 2 \times 5 \div 9 - 4 \div 18

Follow the PEMDAS order of operations

Multiply and divide (left to right)

19 \div 18 : \frac{19}{18}

19 \div 18

19 \div 18 = \frac{19}{18}

= \frac{19}{18}

= \frac{19}{18} + 3 \div 2 \times 5 \div 9 - 4 \div 18

Multiply and divide (left to right)

3 \div 2 \times 5 \div 9 : \frac{5}{6}

3 \div 2 \times 5 \div 9

3 \div 2 = \frac{3}{2}

= \frac{3}{2} \times 5 \div 9

\frac{3}{2} \times 5 = \frac{15}{2}

\frac{3}{2} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{3}{2} \cdot \frac{5}{1}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{3 \cdot 5}{2 \cdot 1}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{15}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{15}{2}

= \frac{15}{2} \div 9

\frac{15}{2} \div 9 = \frac{5}{6}

\frac{15}{2} \div 9

Convert element to fraction:

9 = \frac{9}{1}

= \frac{15}{2} \div \frac{9}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{15}{2} \cdot \frac{1}{9}

Cross-cancel common factor:

3

15, 9

Greatest Common Divisor (GCD)

Prime factorization of

15 : 3 \cdot 5

15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

The prime factors common to

15, 9

are

= 3

= \frac{5}{2} \cdot \frac{1}{3}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{5 \cdot 1}{2 \cdot 3}

Multiply the numbers:

5 \cdot 1 = 5

= \frac{5}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{5}{6}

= \frac{5}{6}

= \frac{19}{18} + \frac{5}{6} - 4 \div 18

Multiply and divide (left to right)

4 \div 18 : \frac{4}{18}

4 \div 18

4 \div 18 = \frac{4}{18}

= \frac{4}{18}

= \frac{19}{18} + \frac{5}{6} - \frac{4}{18}

Add and subtract (left to right)

\frac{19}{18} + \frac{5}{6} - \frac{4}{18} : \frac{5}{3}

\frac{19}{18} + \frac{5}{6} - \frac{4}{18}

\frac{19}{18} + \frac{5}{6} = \frac{17}{9}

\frac{19}{18} + \frac{5}{6}

Least Common Multiplier of

18, 6 : 18

18, 6

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

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

18

6

= 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{5}{6} :

multiply the denominator and numerator by

3

\frac{5}{6} = \frac{5 \cdot 3}{6 \cdot 3} = \frac{15}{18}

= \frac{19}{18} + \frac{15}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{19 + 15}{18}

Add the numbers:

19 + 15 = 34

= \frac{34}{18}

Cancel the common factor:

2

= \frac{17}{9}

= \frac{17}{9} - \frac{4}{18}

\frac{17}{9} - \frac{4}{18} = \frac{5}{3}

\frac{17}{9} - \frac{4}{18}

Cancel

\frac{4}{18} : \frac{2}{9}

\frac{4}{18}

Cancel the common factor:

2

= \frac{2}{9}

= \frac{17}{9} - \frac{2}{9}

Apply rule

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

= \frac{17 - 2}{9}

Subtract the numbers:

17 - 2 = 15

= \frac{15}{9}

Cancel the common factor:

3

= \frac{5}{3}

= \frac{5}{3}

= \frac{5}{3}

Convert improper fractions to mixed numbers:

\frac{5}{3} = 1 \frac{2}{3}

\frac{5}{3} = 1

Remainder

2

\frac{5}{3}

Write the problem in long division format

3 \overline{∣ 5}

Divide

5

3

to get

1

Divide

5

3

to get

1

1 3 \overline{∣ 5}

Multiply the quotient digit

(1)

by the divisor

3

1 3 \overline{∣ 5} \underline{3}

Subtract

3

from

5

1 3 \overline{∣ 5} \underline{3} 2

1 3 \overline{∣ 5} \underline{3} 2

The solution for Long Division of

\frac{5}{3}

1

with remainder of

2

1 Remainder 2

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{5}{3} = 1 \frac{2}{3}

= 1 \frac{2}{3}

= 1 \frac{2}{3}

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Frequently Asked Questions (FAQ)

What is 19\div 18+3\div 2\times 5\div 9-4\div 18 ?
The solution to 19\div 18+3\div 2\times 5\div 9-4\div 18 is 1 2/3