Understanding the Problem
To simplify the ratio 6 2/3 : 7 1/2, we first need to convert the mixed numbers into improper fractions.
Convert Mixed Numbers to Improper Fractions
- 6 2/3 can be converted as follows:
- 6 x 3 + 2 = 18 + 2 = 20
- Therefore, 6 2/3 = 20/3
- 7 1/2 can be converted as follows:
- 7 x 2 + 1 = 14 + 1 = 15
- Therefore, 7 1/2 = 15/2
Forming the Ratio
Now we can express the ratio as:
- 20/3 : 15/2
Eliminate the Fractions
To simplify this ratio, we can multiply both sides by the least common multiple (LCM) of the denominators (3 and 2), which is 6:
- (20/3) * 6 : (15/2) * 6
This gives us:
- 40 : 45
Simplify the Ratio
Now, we can simplify 40 : 45 by finding the greatest common divisor (GCD), which is 5:
- 40 ÷ 5 = 8
- 45 ÷ 5 = 9
Therefore, the simplified ratio is:
- 8 : 9
Final Result
The simplified ratio of 6 2/3 : 7 1/2 is 8 : 9. This method ensures that both mixed numbers are accurately converted and the resulting ratio is presented in its simplest form.