What is the ratio 48:24 as a simplified fraction
The Correct Answer and Explanation is:
The ratio 48:24 simplifies to 2:1. Here’s the step-by-step process for simplifying this ratio into its simplest form:
Step 1: Understand the concept of ratios
A ratio is a way of comparing two quantities. The ratio 48:24 compares the number 48 with the number 24. To simplify this ratio, we need to divide both numbers by their greatest common divisor (GCD), also called the greatest common factor (GCF). The GCD is the largest number that divides both 48 and 24 without leaving a remainder.
Step 2: Find the greatest common divisor (GCD) of 48 and 24
To find the GCD of two numbers, one method is to list the factors of each number and identify the largest common factor.
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The common factors of 48 and 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest of these common factors is 24.
Step 3: Divide both terms of the ratio by the GCD
Now that we know the GCD is 24, we divide both terms of the ratio by 24:
[
\frac{48}{24} = 2 \quad \text{and} \quad \frac{24}{24} = 1
]
So, the simplified ratio is 2:1.
Step 4: Interpretation of the simplified ratio
A ratio of 2:1 means that for every 2 parts of one quantity, there is 1 part of the other. This simplified ratio shows the relationship between the two numbers in its most reduced form. Simplifying ratios is an important concept in mathematics, as it allows for a clearer understanding and comparison of quantities.
Conclusion
The simplified form of the ratio 48:24 is 2:1. This process of finding the GCD and dividing both terms of the ratio ensures that we are expressing the relationship between the two quantities in its simplest and most straightforward form.