need to know how to reduce this fraction

need to know how to reduce this fraction

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Kevin S. |

Look for a common factor. Since both numbers are even, 2 is a common factor:

7272/10000 = (2)(3636)/(2)(5000) = 3636/5000

These are still even, so we can try 2 again... BUT... we could be awhile...

Let's look at the divisibility rules:

A number is divisible by:

- 2 if the number is even

- 3 if the sum of the digits of the number is divisible by 3

- 4 if the last two digits of the number is divisible by 4

- 5 if the number ends in 5 or 0

- 6 if the number is even AND divisible by 3

- 8 if the last three digits of the number is divisible by 8

- 9 if the sum of the digits of the number is divisible by 9

(what about 7? There is a rule, but it's so obscure that it's just as easy to test it via division)

So...

272 is divisible by 8 (8 * 34 = 272), so 7272 is divisible by 8. 1000 is divisible by 8, s0 10000 is divisible by 8 as well.

7272/10000 = 909/1250.

Now, let's reexamine the divisibility rules for both top and bottom:

909 - odd, divisible by 3 and 9, but not by 2, 4, 5, 6, or 8

1250 - even, divisible by 2, 5, but not by 3, 4, 6, 7, 8, or 9

Since we have no other common factors, our answer is 909/1250

To reduce this fraction, you need to factor both numerator and denominator into a product of prime numbers. Once you've done that, you can cancel out like factors in both numerator and denominator.

Let's start with 7272. It's an even number, so we know 2 is a factor. We can keep dividing by 2 until the remainder is odd.

7272 / 2 = 3636

3636 / 2 = 1818

1818 / 2 = 909

Now the number is odd. Since the sum of the numbers in 909 = 18, a factor of 3, we know that this number is evenly divisible by 3:

909 / 3 = 303

303 / 3 = 101

You may not recognize it at first, but turns out 101 is a prime number, so we can stop factoring there. Let's go back and gather up all our factors for 7272: 2, 2, 2, 3, 3 and 101.

Let's repeat for 10000. Again, it's an even number, so we can divide by 2 until the remainder is odd:

10000 / 2 = 5000

5000 / 2 = 2500

2500 / 2 = 1250

1250 / 2 = 625

Now, since this number ends in 5, we know it is divisible by 5.

625 / 5 = 125

125 / 5 = 25

25 / 5 = 5

And now we're down to a prime number, so we can stop.

The factors of 10000 are 2, 2, 2, 2, 5, 5, 5, 5.

Let's see what we can cancel out now:

7272 = 2 * 2 * 2 * 3 * 3 * 101

10000 = 2 * 2 * 2 * 2 * 5 * 5 * 5 *5

There are three 2s that can be canceled out, as they appear in both numerator and denominator.

We are left with 3 * 3 * 101 in the numerator, and 2* 5 * 5 * 5 * 5 in the denominator.

Multiplying these out, the reduced fraction is 909 / 1250.

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