convert the ratio 28 : 42 in its simplest form
The correct answer and explanation is:
Correct Answer:
The ratio 28:42 in its simplest form is 2:3.
Explanation (300 words):
A ratio is a comparison of two quantities that shows how many times one value contains or is contained within the other. Simplifying a ratio is similar to simplifying a fraction: you divide both terms of the ratio by their greatest common divisor (GCD), also called the greatest common factor (GCF).
Let’s simplify the ratio 28:42 step-by-step:
Step 1: Find the GCF of 28 and 42
To do this, list the factors of each number:
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The greatest common factor they share is 14.
Step 2: Divide both terms of the ratio by the GCF
Now divide both 28 and 42 by 14:
- 28 ÷ 14 = 2
- 42 ÷ 14 = 3
So, the simplified form of 28:42 is 2:3.
Why Simplifying Ratios Matters
Simplifying ratios helps to better understand the relationship between two values in the simplest terms. For example, a ratio of 28:42 might be used to describe quantities like ingredients in a recipe, lengths in geometry, or numbers of people in groups. A simplified ratio, like 2:3, is easier to work with and interpret.
Think of it this way: if a classroom has 28 boys and 42 girls, simplifying the ratio of boys to girls gives us 2:3. That means for every 2 boys, there are 3 girls, which is easier to visualize and compare.
In summary, to simplify a ratio, divide both terms by the GCF. For 28:42, the GCF is 14, so the simplest form is 2:3.