What is 5/(6+(1/3-1/5)/3) ?

The solution to 5/(6+(1/3-1/5)/3) is 225/272

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Popular >

5/(6+(1/3-1/5)/3)

Solution

5/ (6 + (1/3 - 1/5) /3)

Solution

\frac{225}{272}

Solution steps

5/ (6 + (1/3 - 1/5) /3)

Follow the PEMDAS order of operations

Calculate within parentheses

(6 + (1/3 - 1/5) /3) : \frac{272}{45}

6 + (1/3 - 1/5) /3

Calculate within parentheses

(1/3 - 1/5) : \frac{2}{15}

1/3 - 1/5

Multiply and divide (left to right)

1/3 : \frac{1}{3}

1/3

1/3 = \frac{1}{3}

= \frac{1}{3}

= \frac{1}{3} - 1/5

Multiply and divide (left to right)

1/5 : \frac{1}{5}

1/5

1/5 = \frac{1}{5}

= \frac{1}{5}

= \frac{1}{3} - \frac{1}{5}

Add and subtract (left to right)

\frac{1}{3} - \frac{1}{5} : \frac{2}{15}

\frac{1}{3} - \frac{1}{5}

\frac{1}{3} - \frac{1}{5} = \frac{2}{15}

\frac{1}{3} - \frac{1}{5}

Least Common Multiplier of

3, 5 : 15

3, 5

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

3

5

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15

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

15

For

\frac{1}{3} :

multiply the denominator and numerator by

5

\frac{1}{3} = \frac{1 \cdot 5}{3 \cdot 5} = \frac{5}{15}

For

\frac{1}{5} :

multiply the denominator and numerator by

3

\frac{1}{5} = \frac{1 \cdot 3}{5 \cdot 3} = \frac{3}{15}

= \frac{5}{15} - \frac{3}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{5 - 3}{15}

Subtract the numbers:

5 - 3 = 2

= \frac{2}{15}

= \frac{2}{15}

= \frac{2}{15}

= 6 + \frac{2}{15} /3

Multiply and divide (left to right)

\frac{2}{15} /3 : \frac{2}{45}

\frac{2}{15} /3

Convert element to fraction:

3 = \frac{3}{1}

= \frac{2}{15} \div \frac{3}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{2}{15} \cdot \frac{1}{3}

Multiply fractions:

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

= \frac{2 \cdot 1}{15 \cdot 3}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{2}{15 \cdot 3}

Multiply the numbers:

15 \cdot 3 = 45

= \frac{2}{45}

= 6 + \frac{2}{45}

Add and subtract (left to right)

6 + \frac{2}{45} : \frac{272}{45}

6 + \frac{2}{45}

6 + \frac{2}{45} = \frac{272}{45}

6 + \frac{2}{45}

Convert element to fraction:

6 = \frac{6 \cdot 45}{45}

= \frac{6 \cdot 45}{45} + \frac{2}{45}

Since the denominators are equal, combine the fractions:

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

= \frac{6 \cdot 45 + 2}{45}

6 \cdot 45 + 2 = 272

6 \cdot 45 + 2

Multiply the numbers:

6 \cdot 45 = 270

= 270 + 2

Add the numbers:

270 + 2 = 272

= 272

= \frac{272}{45}

= \frac{272}{45}

= \frac{272}{45}

= 5/ \frac{272}{45}

Multiply and divide (left to right)

5/ \frac{272}{45} : \frac{225}{272}

5/ \frac{272}{45}

Convert element to fraction:

5 = \frac{5}{1}

= \frac{5}{1} \div \frac{272}{45}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{5}{1} \cdot \frac{45}{272}

Multiply fractions:

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

= \frac{5 \cdot 45}{1 \cdot 272}

Multiply the numbers:

5 \cdot 45 = 225

= \frac{225}{1 \cdot 272}

Multiply the numbers:

1 \cdot 272 = 272

= \frac{225}{272}

= \frac{225}{272}

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Frequently Asked Questions (FAQ)

What is 5/(6+(1/3-1/5)/3) ?
The solution to 5/(6+(1/3-1/5)/3) is 225/272