What is 8\div 3+1\div 2+6\div 4 ?

The solution to 8\div 3+1\div 2+6\div 4 is 4 2/3

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8\div 3+1\div 2+6\div 4

Solution

8 \div 3 + 1 \div 2 + 6 \div 4

Solution

4 \frac{2}{3}

Solution steps

8 \div 3 + 1 \div 2 + 6 \div 4

Follow the PEMDAS order of operations

Multiply and divide (left to right)

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

8 \div 3

8 \div 3 = \frac{8}{3}

= \frac{8}{3}

= \frac{8}{3} + 1 \div 2 + 6 \div 4

Multiply and divide (left to right)

1 \div 2 : \frac{1}{2}

1 \div 2

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

= \frac{1}{2}

= \frac{8}{3} + \frac{1}{2} + 6 \div 4

Multiply and divide (left to right)

6 \div 4 : \frac{6}{4}

6 \div 4

6 \div 4 = \frac{6}{4}

= \frac{6}{4}

= \frac{8}{3} + \frac{1}{2} + \frac{6}{4}

Add and subtract (left to right)

\frac{8}{3} + \frac{1}{2} + \frac{6}{4} : \frac{14}{3}

\frac{8}{3} + \frac{1}{2} + \frac{6}{4}

\frac{8}{3} + \frac{1}{2} = \frac{19}{6}

\frac{8}{3} + \frac{1}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 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

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

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

6

For

\frac{8}{3} :

multiply the denominator and numerator by

2

\frac{8}{3} = \frac{8 \cdot 2}{3 \cdot 2} = \frac{16}{6}

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

= \frac{16}{6} + \frac{3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{16 + 3}{6}

Add the numbers:

16 + 3 = 19

= \frac{19}{6}

= \frac{19}{6} + \frac{6}{4}

\frac{19}{6} + \frac{6}{4} = \frac{14}{3}

\frac{19}{6} + \frac{6}{4}

Cancel

\frac{6}{4} : \frac{3}{2}

\frac{6}{4}

Cancel the common factor:

2

= \frac{3}{2}

= \frac{19}{6} + \frac{3}{2}

Least Common Multiplier of

6, 2 : 6

6, 2

Least Common Multiplier (LCM)

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

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

6

2

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

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

6

For

\frac{3}{2} :

multiply the denominator and numerator by

3

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

= \frac{19}{6} + \frac{9}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{19 + 9}{6}

Add the numbers:

19 + 9 = 28

= \frac{28}{6}

Cancel the common factor:

2

= \frac{14}{3}

= \frac{14}{3}

= \frac{14}{3}

Convert improper fractions to mixed numbers:

\frac{14}{3} = 4 \frac{2}{3}

\frac{14}{3} = 4

Remainder

2

\frac{14}{3}

Write the problem in long division format

3 \overline{∣ 14}

Divide

14

3

to get

4

Divide

14

3

to get

4

4 3 \overline{∣ 14}

Multiply the quotient digit

(4)

by the divisor

3

4 3 \overline{∣ 14} \underline{12}

Subtract

12

from

14

4 3 \overline{∣ 14} \underline{12} 2

4 3 \overline{∣ 14} \underline{12} 2

The solution for Long Division of

\frac{14}{3}

4

with remainder of

2

4 Remainder 2

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{14}{3} = 4 \frac{2}{3}

= 4 \frac{2}{3}

= 4 \frac{2}{3}

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Frequently Asked Questions (FAQ)

What is 8\div 3+1\div 2+6\div 4 ?
The solution to 8\div 3+1\div 2+6\div 4 is 4 2/3