The ratio 8:2 in its simplest form is
The Correct Answer and Explanation is:
The ratio 8:2 in its simplest form is 4:1.
Explanation:
A ratio is a way to compare two or more quantities. In this case, we are given the ratio 8:2. To simplify a ratio, we need to divide both numbers in the ratio by their greatest common divisor (GCD), also known as the greatest common factor (GCF). The GCD of two numbers is the largest number that divides both of them exactly.
Steps to Simplify the Ratio 8:2:
- Find the Greatest Common Divisor (GCD):
To find the GCD of 8 and 2, we list their factors:
- The factors of 8 are 1, 2, 4, and 8.
- The factors of 2 are 1 and 2. The greatest common divisor between 8 and 2 is 2, as it is the largest number that divides both 8 and 2 without leaving a remainder.
- Divide Both Parts of the Ratio by the GCD:
Now, we divide both numbers in the ratio 8:2 by their GCD, which is 2:
- Divide the first number (8) by 2:
[
\frac{8}{2} = 4
] - Divide the second number (2) by 2:
[
\frac{2}{2} = 1
]
- Write the Simplified Ratio:
After dividing both numbers by 2, we get the simplified ratio:
[
4:1
]
Thus, the ratio 8:2 simplifies to 4:1.
Why Simplifying Ratios is Important:
Simplifying ratios makes them easier to understand and work with. It also ensures that you are working with the most efficient form of the ratio, which is particularly useful when comparing quantities, scaling recipes, or solving mathematical problems involving proportions. Simplification reduces the ratio to its smallest, most meaningful form, making the comparison between the two quantities clearer and more straightforward.