What is 3/8+(2/9-1/9) ?

The solution to 3/8+(2/9-1/9) is 35/72

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Popular >

3/8+(2/9-1/9)

Solution

\frac{3}{8} + (\frac{2}{9} - \frac{1}{9})

Solution

\frac{35}{72}

Solution steps

\frac{3}{8} + (\frac{2}{9} - \frac{1}{9})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{2}{9} - \frac{1}{9}) : \frac{1}{9}

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

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

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

Apply rule

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

= \frac{2 - 1}{9}

Subtract the numbers:

2 - 1 = 1

= \frac{1}{9}

= \frac{1}{9}

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

Add and subtract (left to right)

\frac{3}{8} + \frac{1}{9} : \frac{35}{72}

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

\frac{3}{8} + \frac{1}{9} = \frac{35}{72}

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

Least Common Multiplier of

8, 9 : 72

8, 9

Least Common Multiplier (LCM)

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

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

8

9

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

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = 72

= 72

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

72

For

\frac{3}{8} :

multiply the denominator and numerator by

9

\frac{3}{8} = \frac{3 \cdot 9}{8 \cdot 9} = \frac{27}{72}

For

\frac{1}{9} :

multiply the denominator and numerator by

8

\frac{1}{9} = \frac{1 \cdot 8}{9 \cdot 8} = \frac{8}{72}

= \frac{27}{72} + \frac{8}{72}

Since the denominators are equal, combine the fractions:

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

= \frac{27 + 8}{72}

Add the numbers:

27 + 8 = 35

= \frac{35}{72}

= \frac{35}{72}

= \frac{35}{72}

Popular Examples

15^2*5

1 5^{2} \cdot 5

78\times 16+39

78 \times 16 + 39

(2-(3\times (3-6+7)^2-2\times 3)+5)\div 2

(2 - (3 \times (3 - 6 + 7)^{2} - 2 \times 3) + 5) \div 2

3/8+4/8 \div 5+1/3

\frac{3}{8} + \frac{4}{8} \div 5 + \frac{1}{3}

60-1/2 (8)^2

60 - \frac{1}{2} (8)^{2}

Frequently Asked Questions (FAQ)

What is 3/8+(2/9-1/9) ?
The solution to 3/8+(2/9-1/9) is 35/72