what is a common denominator for 1/6 and 3/5
The Correct Answer and Explanation is:
Correct Answer:
The common denominator for 1/6 and 3/5 is 30.
Explanation
When you work with fractions that have different denominators, it’s often necessary to find a common denominator before adding, subtracting, or comparing them. A common denominator is a shared multiple of the denominators of two or more fractions. The goal is to rewrite the fractions so they have the same bottom number (denominator), making them easier to work with.
To find a common denominator for the fractions 1/6 and 3/5, you need to look for the least common multiple (LCM) of the numbers 6 and 5. The LCM is the smallest number that both denominators divide evenly into.
Here are the steps:
- List multiples of 6:
6, 12, 18, 24, 30, 36, 42… - List multiples of 5:
5, 10, 15, 20, 25, 30, 35… - The smallest number that appears in both lists is 30.
So, 30 is the least common denominator of 1/6 and 3/5.
Now convert each fraction:
- 1/6 becomes 5/30 because 6 × 5 = 30, so multiply both numerator and denominator by 5:
(1 × 5)/(6 × 5) = 5/30 - 3/5 becomes 18/30 because 5 × 6 = 30, so multiply both numerator and denominator by 6:
(3 × 6)/(5 × 6) = 18/30
Now that both fractions share a denominator of 30, they can be easily added, subtracted, or compared.
In conclusion, the common denominator for 1/6 and 3/5 is 30, and using it allows us to perform further operations with these fractions smoothly and accurately.
