What is ((\frac{75/200)/(25)}{800})-5/2 ?

The solution to ((\frac{75/200)/(25)}{800})-5/2 is -399997/160000

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Popular >

simplify ((\frac{75/200)/(25)}{800})-5/2

Solution

simplify

(\frac{\frac{\frac{75}{200}}{25}}{800}) - \frac{5}{2}

Solution

- \frac{399997}{160000}

Decimal Notation

- 2.49998125

Solution steps

(\frac{\frac{\frac{75}{200}}{25}}{800}) - \frac{5}{2}

Apply rule:

(a) = a

(\frac{\frac{\frac{75}{200}}{25}}{800}) = \frac{\frac{\frac{75}{200}}{25}}{800}

= \frac{\frac{\frac{75}{200}}{25}}{800} - \frac{5}{2}

\frac{\frac{\frac{75}{200}}{25}}{800} = \frac{75}{4000000}

\frac{\frac{\frac{75}{200}}{25}}{800}

\frac{\frac{\frac{75}{200}}{25}}{800} = \frac{75}{200 \cdot 25 \cdot 800}

\frac{\frac{\frac{75}{200}}{25}}{800}

Apply the fraction rule:

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

= \frac{\frac{75}{200}}{25 \cdot 800}

Apply the fraction rule:

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

= \frac{75}{200 \cdot 25 \cdot 800}

= \frac{75}{200 \cdot 25 \cdot 800}

Multiply the numbers:

200 \cdot 25 \cdot 800 = 4000000

= \frac{75}{4000000}

= \frac{75}{4000000} - \frac{5}{2}

\frac{75}{4000000} - \frac{5}{2} = - \frac{399997}{160000}

\frac{75}{4000000} - \frac{5}{2}

Cancel

\frac{75}{4000000} : \frac{3}{160000}

\frac{75}{4000000}

Factor the number:

75 = 25 \cdot 3

= \frac{25 \cdot 3}{4000000}

Factor the number:

4000000 = 25 \cdot 160000

= \frac{25 \cdot 3}{25 \cdot 160000}

Cancel the common factor:

25

= \frac{3}{160000}

= \frac{3}{160000} - \frac{5}{2}

\frac{3}{160000} - \frac{5}{2} = \frac{- 399997}{160000}

\frac{3}{160000} - \frac{5}{2}

Least Common Multiplier of

160000, 2 : 160000

160000, 2

Least Common Multiplier (LCM)

Prime factorization of

160000

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

160000

2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 \cdot 5 = 160000

= 160000

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

160000

For

\frac{5}{2} :

multiply the denominator and numerator by

80000

\frac{5}{2} = \frac{5 \cdot 80000}{2 \cdot 80000} = \frac{400000}{160000}

= \frac{3}{160000} - \frac{400000}{160000}

Apply the fraction rule:

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

= \frac{3 - 400000}{160000}

Subtract the numbers:

3 - 400000 = - 399997

= \frac{- 399997}{160000}

= \frac{- 399997}{160000}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{399997}{160000}

= - \frac{399997}{160000}

Popular Examples

8+3(2)

8 + 3 (2)

4+4\times 3/8

4 + 4 \times \frac{3}{8}

10(4)^2

10 (4)^{2}

-4+16-11

- 4 + 16 - 11

-2/7*7+2

- \frac{2}{7} \cdot 7 + 2

Frequently Asked Questions (FAQ)

What is ((\frac{75/200)/(25)}{800})-5/2 ?
The solution to ((\frac{75/200)/(25)}{800})-5/2 is -399997/160000