Understanding the Given Ratio
To simplify the ratio 6 3/2 : 7 2/1, we first convert the mixed numbers into improper fractions for easier calculations.
Step 1: Convert Mixed Numbers to Improper Fractions
- 6 3/2 can be converted as follows:
- 6 = 12/2
- 3/2 is already a fraction.
- Therefore, 6 3/2 = 12/2 + 3/2 = 15/2.
- 7 2/1 can be treated as:
- 7 = 7/1.
- 2/1 is also a whole number.
- Thus, 7 2/1 = 7 + 2 = 9.
Step 2: Rewrite the Ratio
Now, our ratio becomes:
15/2 : 9.
Step 3: Simplify the Ratio
To simplify the ratio, we can write it as a fraction:
(15/2) / 9.
This is equivalent to:
15/2 * 1/9 = 15/18.
Step 4: Further Simplification
Now we can simplify 15/18:
- Both 15 and 18 can be divided by 3:
- 15 ÷ 3 = 5
- 18 ÷ 3 = 6.
Thus, the simplified ratio is:
5 : 6.
Final Result
The simplified ratio of 6 3/2 : 7 2/1 is 5 : 6.
This methodical approach allows for clear understanding and simplification of ratios!