What is 4 2/9-(2 1/4+2/3) ?

The solution to 4 2/9-(2 1/4+2/3) is 1 11/36

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Popular >

4 2/9-(2 1/4+2/3)

Solution

4 \frac{2}{9} - (2 \frac{1}{4} + \frac{2}{3})

Solution

1 \frac{11}{36}

Solution steps

4 \frac{2}{9} - (2 \frac{1}{4} + \frac{2}{3})

Convert mixed numbers to improper fractions:

4 \frac{2}{9} = \frac{38}{9}

4 \frac{2}{9}

Convert mixed numbers to improper fraction:

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

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

= \frac{38}{9}

= \frac{38}{9} - (2 \frac{1}{4} + \frac{2}{3})

Convert mixed numbers to improper fractions:

2 \frac{1}{4} = \frac{9}{4}

2 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

2 \frac{1}{4} = \frac{2 \cdot 4 + 1}{4}

= \frac{9}{4}

= \frac{38}{9} - (\frac{9}{4} + \frac{2}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{9}{4} + \frac{2}{3}) : \frac{35}{12}

\frac{9}{4} + \frac{2}{3}

\frac{9}{4} + \frac{2}{3} = \frac{35}{12}

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

multiply the denominator and numerator by

3

\frac{9}{4} = \frac{9 \cdot 3}{4 \cdot 3} = \frac{27}{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{27}{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{27 + 8}{12}

Add the numbers:

27 + 8 = 35

= \frac{35}{12}

= \frac{35}{12}

= \frac{38}{9} - \frac{35}{12}

Add and subtract (left to right)

\frac{38}{9} - \frac{35}{12} : \frac{47}{36}

\frac{38}{9} - \frac{35}{12}

\frac{38}{9} - \frac{35}{12} = \frac{47}{36}

\frac{38}{9} - \frac{35}{12}

Least Common Multiplier of

9, 12 : 36

9, 12

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

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

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

9

12

= 3 \cdot 3 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 2 \cdot 2 = 36

= 36

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

36

For

\frac{38}{9} :

multiply the denominator and numerator by

4

\frac{38}{9} = \frac{38 \cdot 4}{9 \cdot 4} = \frac{152}{36}

For

\frac{35}{12} :

multiply the denominator and numerator by

3

\frac{35}{12} = \frac{35 \cdot 3}{12 \cdot 3} = \frac{105}{36}

= \frac{152}{36} - \frac{105}{36}

Since the denominators are equal, combine the fractions:

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

= \frac{152 - 105}{36}

Subtract the numbers:

152 - 105 = 47

= \frac{47}{36}

= \frac{47}{36}

= \frac{47}{36}

Convert improper fractions to mixed numbers:

\frac{47}{36} = 1 \frac{11}{36}

\frac{47}{36} = 1

Remainder

11

\frac{47}{36}

Write the problem in long division format

36 \overline{∣ 47}

Divide

47

36

to get

1

Divide

47

36

to get

1

1 36 \overline{∣ 47}

Multiply the quotient digit

(1)

by the divisor

36

1 36 \overline{∣ 47} \underline{36}

Subtract

36

from

47

1 36 \overline{∣ 47} \underline{36} 11

1 36 \overline{∣ 47} \underline{36} 11

The solution for Long Division of

\frac{47}{36}

1

with remainder of

11

1 Remainder 11

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{47}{36} = 1 \frac{11}{36}

= 1 \frac{11}{36}

= 1 \frac{11}{36}

Popular Examples

39\times (15\div 3)-16

39 \times (15 \div 3) - 16

((170-61)^2)/(61)

\frac{( 170 - 61 ) ^{2}}{61}

1/(3^2-9)

\frac{1}{3 ^{2} - 9}

10^0+5^0

1 0^{0} + 5^{0}

(12)/(2(-8)+16)

\frac{12}{2 ( - 8 ) + 16}

Frequently Asked Questions (FAQ)

What is 4 2/9-(2 1/4+2/3) ?
The solution to 4 2/9-(2 1/4+2/3) is 1 11/36