Write the ratio 24:20 in its simplest form.
The Correct Answer and Explanation is :
To simplify the ratio 24:20, we start by finding the greatest common divisor (GCD) of the two numbers, 24 and 20. The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: Find the GCD
- List the factors:
- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- The factors of 20 are: 1, 2, 4, 5, 10, 20
- Identify the common factors:
- The common factors of 24 and 20 are: 1, 2, 4
- Find the greatest common factor:
- The greatest of these is 4. Therefore, the GCD of 24 and 20 is 4.
Step 2: Simplify the Ratio
Now that we have the GCD, we can simplify the ratio by dividing both terms by this GCD.
- Divide both terms by 4:
- ( \frac{24}{4} = 6 )
- ( \frac{20}{4} = 5 )
Thus, the simplified ratio of 24:20 is 6:5.
Explanation of Ratios
Ratios are a way to compare quantities and express the relative size of two or more values. They can be used in various contexts, such as in cooking, financial analysis, or any scenario where proportional relationships are important.
Simplifying a ratio helps in understanding the relationship more clearly. In the case of 24:20, simplifying to 6:5 shows that for every 6 parts of one quantity, there are 5 parts of another. This makes it easier to visualize or apply in practical situations, like mixing ingredients in a recipe or determining resource allocation.
In summary, the ratio 24:20 simplifies to 6:5, making it more straightforward to understand the relationship between the two numbers.