What is 5-3\times 7\div 12+8\div 9\times 3+3-11 ?

The solution to 5-3\times 7\div 12+8\div 9\times 3+3-11 is -25/12

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Popular >

5-3\times 7\div 12+8\div 9\times 3+3-11

Solution

5 - 3 \times 7 \div 12 + 8 \div 9 \times 3 + 3 - 11

Solution

- \frac{25}{12}

Solution steps

5 - 3 \times 7 \div 12 + 8 \div 9 \times 3 + 3 - 11

Follow the PEMDAS order of operations

Multiply and divide (left to right)

3 \times 7 \div 12 : \frac{21}{12}

3 \times 7 \div 12

3 \times 7 = 21

= 21 \div 12

21 \div 12 = \frac{21}{12}

= \frac{21}{12}

= 5 - \frac{21}{12} + 8 \div 9 \times 3 + 3 - 11

Multiply and divide (left to right)

8 \div 9 \times 3 : \frac{8}{3}

8 \div 9 \times 3

8 \div 9 = \frac{8}{9}

= \frac{8}{9} \times 3

\frac{8}{9} \times 3 = \frac{8}{3}

\frac{8}{9} \cdot 3

Convert element to fraction:

3 = \frac{3}{1}

= \frac{8}{9} \cdot \frac{3}{1}

Apply the fraction rule:

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

= \frac{8 \cdot 3}{9 \cdot 1}

\frac{8 \cdot 3}{9 \cdot 1} = \frac{8}{3}

\frac{8 \cdot 3}{9 \cdot 1}

Multiply the numbers:

9 \cdot 1 = 9

= \frac{8 \cdot 3}{9}

Factor the number:

9 = 3 \cdot 3

= \frac{8 \cdot 3}{3 \cdot 3}

Cancel the common factor:

3

= \frac{8}{3}

= \frac{8}{3}

= \frac{8}{3}

= 5 - \frac{21}{12} + \frac{8}{3} + 3 - 11

Add and subtract (left to right)

5 - \frac{21}{12} + \frac{8}{3} + 3 - 11 : - \frac{25}{12}

5 - \frac{21}{12} + \frac{8}{3} + 3 - 11

5 - \frac{21}{12} = \frac{13}{4}

5 - \frac{21}{12}

Cancel

\frac{21}{12} : \frac{7}{4}

\frac{21}{12}

Cancel the common factor:

3

= \frac{7}{4}

= 5 - \frac{7}{4}

Convert element to fraction:

5 = \frac{5 \cdot 4}{4}

= \frac{5 \cdot 4}{4} - \frac{7}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 4 - 7}{4}

5 \cdot 4 - 7 = 13

5 \cdot 4 - 7

Multiply the numbers:

5 \cdot 4 = 20

= 20 - 7

Subtract the numbers:

20 - 7 = 13

= 13

= \frac{13}{4}

= \frac{13}{4} + \frac{8}{3} + 3 - 11

\frac{13}{4} + \frac{8}{3} = \frac{71}{12}

\frac{13}{4} + \frac{8}{3}

Least Common Multiplier of

4, 3 : 12

4, 3

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

4

3

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

For

\frac{13}{4} :

multiply the denominator and numerator by

3

\frac{13}{4} = \frac{13 \cdot 3}{4 \cdot 3} = \frac{39}{12}

For

\frac{8}{3} :

multiply the denominator and numerator by

4

\frac{8}{3} = \frac{8 \cdot 4}{3 \cdot 4} = \frac{32}{12}

= \frac{39}{12} + \frac{32}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{39 + 32}{12}

Add the numbers:

39 + 32 = 71

= \frac{71}{12}

= \frac{71}{12} + 3 - 11

\frac{71}{12} + 3 = \frac{107}{12}

\frac{71}{12} + 3

Convert element to fraction:

3 = \frac{3 \cdot 12}{12}

= \frac{3 \cdot 12}{12} + \frac{71}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{3 \cdot 12 + 71}{12}

3 \cdot 12 + 71 = 107

3 \cdot 12 + 71

Multiply the numbers:

3 \cdot 12 = 36

= 36 + 71

Add the numbers:

36 + 71 = 107

= 107

= \frac{107}{12}

= \frac{107}{12} - 11

\frac{107}{12} - 11 = - \frac{25}{12}

\frac{107}{12} - 11

Convert element to fraction:

11 = \frac{11 \cdot 12}{12}

= - \frac{11 \cdot 12}{12} + \frac{107}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{- 11 \cdot 12 + 107}{12}

- 11 \cdot 12 + 107 = - 25

- 11 \cdot 12 + 107

Multiply the numbers:

11 \cdot 12 = 132

= - 132 + 107

Add/Subtract the numbers:

- 132 + 107 = - 25

= - 25

= \frac{- 25}{12}

Apply the fraction rule:

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

= - \frac{25}{12}

= - \frac{25}{12}

= - \frac{25}{12}

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Frequently Asked Questions (FAQ)

What is 5-3\times 7\div 12+8\div 9\times 3+3-11 ?
The solution to 5-3\times 7\div 12+8\div 9\times 3+3-11 is -25/12