in words explain how to simplify,ratios,and common denomerators.use each metod to comper 3/4 and 9/12.explain the proses in words. im desperet my homework is due fraiday november 16,2012.
To simplify the ratio and find the common denominator between 3/4 and 9/12, follow these steps:
1. Simplifying ratios:
- A ratio expresses a relationship between two numbers. To simplify a ratio, divide both numbers by their greatest common divisor (GCD).
2. Common denominators:
- A common denominator is the same number shared by two or more fractions.
- To find the common denominator, you need to identify the least common multiple (LCM) of the denominators.
3. Comparing 3/4 and 9/12:
- Start by simplifying the ratios:
- The GCD of 3 and 4 is 1. So the simplified ratio of 3/4 remains the same (i.e., 3/4).
- The GCD of 9 and 12 is 3. Dividing both numbers by 3 gives us a simplified ratio of 3/4 as well.
- Next, find the common denominator:
- The denominators are already factors of each other (4 and 12 share a common factor of 4), so we can skip this step.
- Finally, compare the fractions by ensuring they have the same denominator:
- Since 3/4 and 9/12 already have a common denominator of 4, we can directly compare the numerators.
- Because both fractions have the same numerator, 3, they are equivalent.
The process involved simplifying the ratios individually, finding the common denominator if needed, and then comparing the fractions by ensuring they have the same denominator. In this case, both 3/4 and 9/12 simplify to 3/4, meaning they represent the same ratio.