What is 5/36-(7/16+((1/4)/3)/(5)) ?

The solution to 5/36-(7/16+((1/4)/3)/(5)) is -227/720

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Popular >

simplify 5/36-(7/16+((1/4)/3)/(5))

Solution

simplify

\frac{5}{36} - (\frac{7}{16} + \frac{\frac{\frac{1}{4}}{3}}{5})

Solution

- \frac{227}{720}

Decimal Notation

- 0.31527 \dots

Solution steps

\frac{5}{36} - (\frac{7}{16} + \frac{\frac{\frac{1}{4}}{3}}{5})

\frac{7}{16} + \frac{\frac{\frac{1}{4}}{3}}{5} = \frac{109}{240}

\frac{7}{16} + \frac{\frac{\frac{1}{4}}{3}}{5}

\frac{\frac{\frac{1}{4}}{3}}{5} = \frac{1}{60}

\frac{\frac{\frac{1}{4}}{3}}{5}

\frac{\frac{\frac{1}{4}}{3}}{5} = \frac{1}{4 \cdot 3 \cdot 5}

\frac{\frac{\frac{1}{4}}{3}}{5}

Apply the fraction rule:

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

= \frac{\frac{1}{4}}{3 \cdot 5}

Apply the fraction rule:

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

= \frac{1}{4 \cdot 3 \cdot 5}

= \frac{1}{4 \cdot 3 \cdot 5}

Multiply the numbers:

4 \cdot 3 \cdot 5 = 60

= \frac{1}{60}

= \frac{7}{16} + \frac{1}{60}

\frac{7}{16} + \frac{1}{60} = \frac{109}{240}

\frac{7}{16} + \frac{1}{60}

Least Common Multiplier of

16, 60 : 240

16, 60

Least Common Multiplier (LCM)

Prime factorization of

16 : 2 \cdot 2 \cdot 2 \cdot 2

16

16

divides by

216 = 8 \cdot 2

= 2 \cdot 8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2

Prime factorization of

60 : 2 \cdot 2 \cdot 3 \cdot 5

60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 5

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

16

60

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5 = 240

= 240

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

240

For

\frac{7}{16} :

multiply the denominator and numerator by

15

\frac{7}{16} = \frac{7 \cdot 15}{16 \cdot 15} = \frac{105}{240}

For

\frac{1}{60} :

multiply the denominator and numerator by

4

\frac{1}{60} = \frac{1 \cdot 4}{60 \cdot 4} = \frac{4}{240}

= \frac{105}{240} + \frac{4}{240}

Apply the fraction rule:

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

= \frac{105 + 4}{240}

Add the numbers:

105 + 4 = 109

= \frac{109}{240}

= \frac{109}{240}

= \frac{5}{36} - \frac{109}{240}

\frac{5}{36} - \frac{109}{240} = - \frac{227}{720}

\frac{5}{36} - \frac{109}{240}

Least Common Multiplier of

36, 240 : 720

36, 240

Least Common Multiplier (LCM)

Prime factorization of

36 : 2 \cdot 2 \cdot 3 \cdot 3

36

36

divides by

236 = 18 \cdot 2

= 2 \cdot 18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3 \cdot 3

Prime factorization of

240 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5

240

240

divides by

2240 = 120 \cdot 2

= 2 \cdot 120

120

divides by

2120 = 60 \cdot 2

= 2 \cdot 2 \cdot 60

60

divides by

260 = 30 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 5

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

36

240

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 = 720

= 720

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

720

For

\frac{5}{36} :

multiply the denominator and numerator by

20

\frac{5}{36} = \frac{5 \cdot 20}{36 \cdot 20} = \frac{100}{720}

For

\frac{109}{240} :

multiply the denominator and numerator by

3

\frac{109}{240} = \frac{109 \cdot 3}{240 \cdot 3} = \frac{327}{720}

= \frac{100}{720} - \frac{327}{720}

Apply the fraction rule:

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

= \frac{100 - 327}{720}

Subtract the numbers:

100 - 327 = - 227

= \frac{- 227}{720}

Apply the fraction rule:

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

= - \frac{227}{720}

= - \frac{227}{720}

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Frequently Asked Questions (FAQ)

What is 5/36-(7/16+((1/4)/3)/(5)) ?
The solution to 5/36-(7/16+((1/4)/3)/(5)) is -227/720