What is 3/5\times 4/15\times 25/24 ?

The solution to 3/5\times 4/15\times 25/24 is 1/6

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Popular >

3/5\times 4/15\times 25/24

Solution

3/5 \times 4/15 \times 25/24

Solution

\frac{1}{6}

Solution steps

3/5 \times 4/15 \times 25/24

Follow the PEMDAS order of operations

Multiply and divide (left to right)

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

= \frac{3}{5} \times 4/15 \times 25/24

\frac{3}{5} \times 4 = \frac{12}{5}

\frac{3}{5} \cdot 4

Convert element to fraction:

4 = \frac{4}{1}

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

Apply the fraction rule:

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

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

Multiply the numbers:

3 \cdot 4 = 12

= \frac{12}{5 \cdot 1}

Multiply the numbers:

5 \cdot 1 = 5

= \frac{12}{5}

= \frac{12}{5} /15 \times 25/24

\frac{12}{5} /15 = \frac{4}{25}

\frac{12}{5} /15

Convert element to fraction:

15 = \frac{15}{1}

= \frac{12}{5} \div \frac{15}{1}

Apply the fraction rule:

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

= \frac{12}{5} \cdot \frac{1}{15}

Cross-cancel common factor:

3

12, 15

Greatest Common Divisor (GCD)

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

Prime factorization of

15 : 3 \cdot 5

15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5

The prime factors common to

12, 15

are

= 3

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

Multiply fractions:

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

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

Multiply the numbers:

4 \cdot 1 = 4

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

Multiply the numbers:

5 \cdot 5 = 25

= \frac{4}{25}

= \frac{4}{25} \times 25/24

\frac{4}{25} \times 25 = 4

\frac{4}{25} \cdot 25

Convert element to fraction:

25 = \frac{25}{1}

= \frac{4}{25} \cdot \frac{25}{1}

Cross-cancel common factor:

25

= \frac{4}{1}

Divide the numbers:

\frac{4}{1} = 4

= 4

= 4/24

4/24 = \frac{4}{24}

= \frac{4}{24}

Cancel the common factor:

4

= \frac{1}{6}

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Frequently Asked Questions (FAQ)

What is 3/5\times 4/15\times 25/24 ?
The solution to 3/5\times 4/15\times 25/24 is 1/6