Write the ratio 32 : 24 in its simplest form

Write the ratio 32 : 24 in its simplest form

The correct answer and explanation is:

To simplify the ratio 32:24, follow these steps:

1. Find the greatest common divisor (GCD) of 32 and 24. The GCD is the largest number that divides both 32 and 24 exactly.
   • Factors of 32: 1, 2, 4, 8, 16, 32
   • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
   The largest number common to both sets of factors is 8. Therefore, the GCD of 32 and 24 is 8.
2. Divide both terms of the ratio by the GCD.
   • Divide 32 by 8: 328=4\frac{32}{8} = 4
   • Divide 24 by 8: 248=3\frac{24}{8} = 3
   The simplified ratio is 4:3.
3. Final Answer: The ratio 32:24 simplifies to 4:3.

Explanation:

Simplifying a ratio is similar to reducing fractions. By finding the GCD, you reduce the two numbers to their smallest possible form. This is important in various applications, such as scaling, simplifying measurements, or comparing quantities. Ratios represent the relationship between two quantities, and simplifying them makes comparisons clearer and easier to work with.

In this case, the ratio 32:24 means that for every 32 parts of one quantity, there are 24 parts of another. By simplifying it to 4:3, you still maintain the same proportion between the two quantities but in a more manageable form. Simplified ratios are often used in recipes, finance, and other areas where clear comparisons are needed.