Simplifying the Sum of Fractions: 3/10 + 1/3
Introduction
When dealing with fractions, it's essential to understand how to add and simplify them. In this article, we'll explore the step-by-step process of simplifying the sum of two fractions: 3/10 + 1/3.
Step 1: Find the Least Common Multiple (LCM)
To add fractions, we need to find the least common multiple (LCM) of their denominators. In this case, the denominators are 10 and 3.
The multiples of 10 are: 10, 20, 30, 40, ... The multiples of 3 are: 3, 6, 9, 12, ...
The first number that appears in both lists is 30, which is the LCM of 10 and 3.
Step 2: Convert Fractions to Have the LCM as the Denominator
Now that we have the LCM, we need to convert both fractions to have 30 as their denominator.
3/10 = ?/30 To do this, we'll multiply both the numerator and denominator of 3/10 by 3, since 10 × 3 = 30.
3/10 = 9/30
1/3 = ?/30 To convert 1/3, we'll multiply both the numerator and denominator by 10, since 3 × 10 = 30.
1/3 = 10/30
Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them.
9/30 + 10/30 = ?/30
Add the numerators (9 + 10 = 19) and keep the denominator the same.
9/30 + 10/30 = 19/30
Simplified Result
The simplified result of the sum of fractions 3/10 + 1/3 is:
19/30
This is the final answer, and it's in its simplest form.
