What is 4-11/3 \div 4-2/3 ?

The solution to 4-11/3 \div 4-2/3 is 2 5/12

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4-11/3 \div 4-2/3

Solution

4 - \frac{11}{3} \div 4 - \frac{2}{3}

Solution

2 \frac{5}{12}

Solution steps

4 - \frac{11}{3} \div 4 - \frac{2}{3}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{11}{3} \div 4 : \frac{11}{12}

\frac{11}{3} \div 4

Convert element to fraction:

4 = \frac{4}{1}

= \frac{11}{3} \div \frac{4}{1}

Apply the fraction rule:

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

= \frac{11}{3} \cdot \frac{1}{4}

Multiply fractions:

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

= \frac{11 \cdot 1}{3 \cdot 4}

Multiply the numbers:

11 \cdot 1 = 11

= \frac{11}{3 \cdot 4}

Multiply the numbers:

3 \cdot 4 = 12

= \frac{11}{12}

= 4 - \frac{11}{12} - \frac{2}{3}

Add and subtract (left to right)

4 - \frac{11}{12} - \frac{2}{3} : \frac{29}{12}

4 - \frac{11}{12} - \frac{2}{3}

4 - \frac{11}{12} = \frac{37}{12}

4 - \frac{11}{12}

Convert element to fraction:

4 = \frac{4 \cdot 12}{12}

= \frac{4 \cdot 12}{12} - \frac{11}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{4 \cdot 12 - 11}{12}

4 \cdot 12 - 11 = 37

4 \cdot 12 - 11

Multiply the numbers:

4 \cdot 12 = 48

= 48 - 11

Subtract the numbers:

48 - 11 = 37

= 37

= \frac{37}{12}

= \frac{37}{12} - \frac{2}{3}

\frac{37}{12} - \frac{2}{3} = \frac{29}{12}

\frac{37}{12} - \frac{2}{3}

Least Common Multiplier of

12, 3 : 12

12, 3

Least Common Multiplier (LCM)

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

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

12

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{2}{3} :

multiply the denominator and numerator by

4

\frac{2}{3} = \frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{12}

= \frac{37}{12} - \frac{8}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{37 - 8}{12}

Subtract the numbers:

37 - 8 = 29

= \frac{29}{12}

= \frac{29}{12}

= \frac{29}{12}

Convert improper fractions to mixed numbers:

\frac{29}{12} = 2 \frac{5}{12}

\frac{29}{12} = 2

Remainder

5

\frac{29}{12}

Write the problem in long division format

12 \overline{∣ 29}

Divide

29

12

to get

2

Divide

29

12

to get

2

2 12 \overline{∣ 29}

Multiply the quotient digit

(2)

by the divisor

12

2 12 \overline{∣ 29} \underline{24}

Subtract

24

from

29

2 12 \overline{∣ 29} \underline{24} 5

2 12 \overline{∣ 29} \underline{24} 5

The solution for Long Division of

\frac{29}{12}

2

with remainder of

5

2 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{29}{12} = 2 \frac{5}{12}

= 2 \frac{5}{12}

= 2 \frac{5}{12}

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Frequently Asked Questions (FAQ)

What is 4-11/3 \div 4-2/3 ?
The solution to 4-11/3 \div 4-2/3 is 2 5/12