operations on fractions
In this article, we will explore operations on fractions, specifically addition and subtraction of fractions with different denominators.
What are fractions?
Fractions are a way to represent partial amounts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 1/2, the numerator is 1 and the denominator is 2.
Operations on fractions
When we perform operations on fractions, we need to follow specific rules to get the correct answer.
Adding fractions with different denominators
To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.
Let's take the example of adding 5/6 and 1/4.
Step 1: Find the LCM of 6 and 4
The multiples of 6 are: 6, 12, 18, 24, ... The multiples of 4 are: 4, 8, 12, 16, ...
The first number that appears in both lists is 12, so the LCM of 6 and 4 is 12.
Step 2: Convert both fractions to have a denominator of 12
To do this, we need to multiply both the numerator and denominator of each fraction by the appropriate number.
5/6 = (5 x 2) / (6 x 2) = 10/12 1/4 = (1 x 3) / (4 x 3) = 3/12
Step 3: Add the fractions
Now that both fractions have the same denominator, we can add them:
10/12 + 3/12 = 13/12
So, 5/6 + 1/4 = 13/12.
Subtracting fractions with different denominators
Subtracting fractions with different denominators follows a similar process.
Let's take the example of subtracting 2/8 from 5/6.
Step 1: Find the LCM of 6 and 8
The multiples of 6 are: 6, 12, 18, 24, ... The multiples of 8 are: 8, 16, 24, ...
The first number that appears in both lists is 24, so the LCM of 6 and 8 is 24.
Step 2: Convert both fractions to have a denominator of 24
To do this, we need to multiply both the numerator and denominator of each fraction by the appropriate number.
5/6 = (5 x 4) / (6 x 4) = 20/24 2/8 = (2 x 3) / (8 x 3) = 6/24
Step 3: Subtract the fractions
Now that both fractions have the same denominator, we can subtract them:
20/24 - 6/24 = 14/24
So, 5/6 - 2/8 = 14/24.
Conclusion
In this article, we learned how to perform operations on fractions with different denominators. By finding the least common multiple of the denominators and converting both fractions to have the same denominator, we can add or subtract fractions with different denominators.
