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

The solution to (3/4)/((1/2+5/8-3/4))+5/3 is 11/3

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Popular >

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

Solution

simplify

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

Solution

\frac{11}{3}

Decimal Notation

3.66666 \dots

Solution steps

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

\frac{\frac{3}{4}}{\frac{1}{2} + \frac{5}{8} - \frac{3}{4}} = \frac{6}{3}

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

Apply the fraction rule:

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

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

Simplify

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

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

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

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

Least Common Multiplier of

2, 8, 4 : 8

2, 8, 4

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 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

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Compute a number comprised of factors that appear in at least one of the following:

2, 8, 4

= 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{1}{2} :

multiply the denominator and numerator by

4

\frac{1}{2} = \frac{1 \cdot 4}{2 \cdot 4} = \frac{4}{8}

For

\frac{3}{4} :

multiply the denominator and numerator by

2

\frac{3}{4} = \frac{3 \cdot 2}{4 \cdot 2} = \frac{6}{8}

= \frac{4}{8} + \frac{5}{8} - \frac{6}{8}

Apply the fraction rule:

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

= \frac{4 + 5 - 6}{8}

Add the numbers:

4 + 5 - 6 = 3

= \frac{3}{8}

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

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

4 \cdot \frac{3}{8}

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

4 \cdot \frac{3}{8}

Convert element to fraction:

4 = \frac{4}{1}

= \frac{4}{1} \cdot \frac{3}{8}

Apply the fraction rule:

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

= \frac{4 \cdot 3}{1 \cdot 8}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{12}{1 \cdot 8}

Multiply the numbers:

1 \cdot 8 = 8

= \frac{12}{8}

= \frac{12}{8}

Factor the number:

12 = 4 \cdot 3

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

Factor the number:

8 = 4 \cdot 2

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

Cancel the common factor:

4

= \frac{3}{2}

= \frac{3}{2}

= \frac{3}{\frac{3}{2}}

Apply the fraction rule:

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

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

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6}{3}

= \frac{6}{3} + \frac{5}{3}

\frac{6}{3} + \frac{5}{3} = \frac{11}{3}

\frac{6}{3} + \frac{5}{3}

Apply the fraction rule:

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

= \frac{6 + 5}{3}

Add the numbers:

6 + 5 = 11

= \frac{11}{3}

= \frac{11}{3}

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4^{2} + 9 \cdot 3

-3+(6-(7-2)+8)

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20 - 20 \div 2 + 5

Frequently Asked Questions (FAQ)

What is (3/4)/((1/2+5/8-3/4))+5/3 ?
The solution to (3/4)/((1/2+5/8-3/4))+5/3 is 11/3