Determine if 12:16 and 72:96 :are equivalent ratios
The Correct answer and Explanation is:
To determine whether the ratios 12:16 and 72:96 are equivalent, we need to simplify each ratio and check if they are equal.
Simplifying the Ratios
1. Simplifying 12:16:
- To simplify the ratio 12:16, we find the greatest common divisor (GCD) of 12 and 16. The GCD is 4.
- Now, we divide both numbers by their GCD:
- (12 ÷ 4 = 3)
- (16 ÷ 4 = 4)
- Thus, the simplified form of the ratio 12:16 is 3:4.
2. Simplifying 72:96:
- Next, we simplify the ratio 72:96 by finding the GCD of 72 and 96. The GCD is 24.
- We divide both numbers by their GCD:
- (72 ÷ 24 = 3)
- (96 ÷ 24 = 4)
- Therefore, the simplified form of the ratio 72:96 is also 3:4.
Comparing the Simplified Ratios
Now that we have simplified both ratios, we can compare them:
- The simplified form of 12:16 is 3:4.
- The simplified form of 72:96 is also 3:4.
Since both ratios reduce to the same value (3:4), we can conclude that 12:16 and 72:96 are indeed equivalent ratios.
Conclusion
In conclusion, equivalent ratios express the same relationship between two quantities, even if the numbers used differ. In this case, both 12:16 and 72:96 simplify to the same ratio of 3:4, confirming their equivalence. This property is essential in various fields, including mathematics and real-life applications like cooking, scaling recipes, and comparing proportions in data analysis. Understanding how to simplify and compare ratios is a crucial skill that can aid in problem-solving across many disciplines.