need to know how to reduce this fraction
need to know how to reduce this fraction
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.