The solution to 4/52*4/52 is 1/169

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Simplify 4/52*4/52

Solution

4/52 \cdot 4/52

Solution

\frac{1}{169}

Solution steps

4/52 \cdot 4/52

Follow the PEMDAS order of operations

Multiply and divide (left to right)

4/52 = \frac{4}{52}

= \frac{4}{52} \cdot 4/52

\frac{4}{52} \cdot 4 = \frac{4}{13}

\frac{4}{52} \cdot 4

Cancel the numbers:

\frac{4}{52} = \frac{1}{13}

= \frac{1}{13} \cdot 4

\frac{1}{13} \cdot 4 = \frac{4}{13}

\frac{1}{13} \cdot 4

Convert element to fraction:

4 = \frac{4}{1}

= \frac{1}{13} \cdot \frac{4}{1}

Apply the fraction rule:

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

= \frac{1 \cdot 4}{13 \cdot 1}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{13 \cdot 1}

Multiply the numbers:

13 \cdot 1 = 13

= \frac{4}{13}

= \frac{4}{13}

= \frac{4}{13} /52

\frac{4}{13} /52 = \frac{1}{169}

\frac{4}{13} /52

Convert element to fraction:

52 = \frac{52}{1}

= \frac{4}{13} \div \frac{52}{1}

Apply the fraction rule:

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

= \frac{4}{13} \cdot \frac{1}{52}

Cross-cancel common factor:

4

4, 52

Greatest Common Divisor (GCD)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

52 : 2 \cdot 2 \cdot 13

52

52

divides by

252 = 26 \cdot 2

= 2 \cdot 26

26

divides by

226 = 13 \cdot 2

= 2 \cdot 2 \cdot 13

2, 13

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 13

The prime factors common to

4, 52

are

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

= \frac{1}{13} \cdot \frac{1}{13}

Multiply fractions:

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

= \frac{1 \cdot 1}{13 \cdot 13}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{13 \cdot 13}

Multiply the numbers:

13 \cdot 13 = 169

= \frac{1}{169}

= \frac{1}{169}

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Frequently Asked Questions (FAQ)

What is 4/52*4/52 ?
The solution to 4/52*4/52 is 1/169

Simplify 4/52*4/52

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 4/52*4/52 ?