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how do you reduce 7272/10000 a nath problem

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3 Answers

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.

To reduce 7272/10000 to the simplest fractional value simply factor the numerator and factor the denominator and cancel the common factors above and below the line which equal one. 7272 is factored as 2x2x2x3x3x101. 10000 is factored as 2x2x2x2x5x5x5x5. The common factors are 2x2x2, so the simplest fractional value is 909/1250.