How can you simplify 24 to 96
The Correct Answer and Explanation is:
To simplify the ratio 24:96, we follow a process similar to simplifying fractions. The goal is to express the ratio in its simplest form, which means reducing it to the smallest whole numbers that still maintain the same relationship between the two values.
Steps to Simplify 24:96:
- Find the Greatest Common Divisor (GCD):
To begin, we need to determine the greatest common divisor (GCD) of 24 and 96. The GCD is the largest number that divides both 24 and 96 without leaving a remainder.
- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
- The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. The greatest common divisor is 24, as it is the largest number that appears in both lists.
- Divide Both Numbers by the GCD:
Now, we divide both terms of the ratio by 24, the GCD of 24 and 96: [
\frac{24}{24} = 1
]
[
\frac{96}{24} = 4
] After dividing, the simplified ratio is 1:4.
Why This Works:
Simplifying ratios is essentially reducing fractions to their lowest terms. By dividing both terms by their greatest common divisor, we ensure that the ratio remains equivalent but is expressed in its simplest form. This process helps make comparisons or interpretations easier because the numbers are smaller and more manageable.
In this case, simplifying 24:96 to 1:4 means that for every 1 unit of the first quantity, there are 4 units of the second quantity, while maintaining the same proportional relationship between the two.