What is 3 5/8-(2 3/4+1/8) ?

The solution to 3 5/8-(2 3/4+1/8) is 3/4

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3 5/8-(2 3/4+1/8)

Solution

3 \frac{5}{8} - (2 \frac{3}{4} + \frac{1}{8})

Solution

\frac{3}{4}

Solution steps

3 \frac{5}{8} - (2 \frac{3}{4} + \frac{1}{8})

Convert mixed numbers to improper fractions:

3 \frac{5}{8} = \frac{29}{8}

3 \frac{5}{8}

Convert mixed numbers to improper fraction:

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

3 \frac{5}{8} = \frac{3 \cdot 8 + 5}{8}

= \frac{29}{8}

= \frac{29}{8} - (2 \frac{3}{4} + \frac{1}{8})

Convert mixed numbers to improper fractions:

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

2 \frac{3}{4}

Convert mixed numbers to improper fraction:

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

2 \frac{3}{4} = \frac{2 \cdot 4 + 3}{4}

= \frac{11}{4}

= \frac{29}{8} - (\frac{11}{4} + \frac{1}{8})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{11}{4} + \frac{1}{8}) : \frac{23}{8}

\frac{11}{4} + \frac{1}{8}

\frac{11}{4} + \frac{1}{8} = \frac{23}{8}

\frac{11}{4} + \frac{1}{8}

Least Common Multiplier of

4, 8 : 8

4, 8

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

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

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

4

8

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{11}{4} :

multiply the denominator and numerator by

2

\frac{11}{4} = \frac{11 \cdot 2}{4 \cdot 2} = \frac{22}{8}

= \frac{22}{8} + \frac{1}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{22 + 1}{8}

Add the numbers:

22 + 1 = 23

= \frac{23}{8}

= \frac{23}{8}

= \frac{29}{8} - \frac{23}{8}

Add and subtract (left to right)

\frac{29}{8} - \frac{23}{8} : \frac{3}{4}

\frac{29}{8} - \frac{23}{8}

\frac{29}{8} - \frac{23}{8} = \frac{3}{4}

\frac{29}{8} - \frac{23}{8}

Apply rule

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

= \frac{29 - 23}{8}

Subtract the numbers:

29 - 23 = 6

= \frac{6}{8}

Cancel the common factor:

2

= \frac{3}{4}

= \frac{3}{4}

= \frac{3}{4}

Popular Examples

4\times 2\times 18-(12)^2

4 \times 2 \times 18 - (12)^{2}

3^4+1

3^{4} + 1

3^4-5

3^{4} - 5

5+3\times (7-3)

5 + 3 \times (7 - 3)

(4)^2-9(4)+8

(4)^{2} - 9 (4) + 8

Frequently Asked Questions (FAQ)

What is 3 5/8-(2 3/4+1/8) ?
The solution to 3 5/8-(2 3/4+1/8) is 3/4