Simplifying the Ratio 88:72
The ratio 88:72 can be simplified by finding the greatest common divisor (GCD) of 88 and 72 and then dividing both numbers by the GCD. Let's break down the process:
1. Finding the Greatest Common Divisor (GCD)
There are several ways to find the GCD. One common method is to use prime factorization:
- Prime factorization of 88: 2 x 2 x 2 x 11 (or 2³ x 11)
- Prime factorization of 72: 2 x 2 x 2 x 3 x 3 (or 2³ x 3²)
The common prime factors are 2 x 2 x 2 = 8. Therefore, the GCD of 88 and 72 is 8.
2. Simplifying the Ratio
Now, divide both parts of the ratio (88 and 72) by the GCD (8):
- 88 ÷ 8 = 11
- 72 ÷ 8 = 9
3. The Simplest Form
The simplified ratio is 11:9. This means that for every 11 units of one quantity, there are 9 units of another. The ratio cannot be further simplified because 11 and 9 have no common divisors other than 1.
In summary: The ratio 88:72, in its simplest form, is 11:9.
