Add 2/5 and 1/5
Question
Find the sum: 2/5 + 1/5
Solution — Step by Step
These two fractions have the same denominator (both have 5 at the bottom). Fractions with the same denominator are called like fractions. Adding like fractions is the simplest kind of fraction addition.
Step 1: Check the denominators.
2/5 and 1/5 — both have 5 as the denominator. They are like fractions.
Step 2: Add only the numerators. Keep the denominator the same.
2/5 + 1/5 = (2 + 1)/5
Step 3: Simplify the numerator.
(2 + 1)/5 = 3/5
Step 4: Check if the result can be simplified.
3/5 — can we simplify this? HCF of 3 and 5 is 1. So 3/5 is already in its simplest form.
a/c + b/c = (a + b)/c
Here: 2/5 + 1/5 = (2 + 1)/5 = 3/5
Answer: 2/5 + 1/5 = 3/5
Why This Works
Think of the denominator as the “name” of the equal parts. When both fractions have the same denominator, they are talking about the same size of piece — so we just count how many pieces we have altogether.
Imagine a chocolate bar cut into 5 equal pieces. Riya takes 2 pieces (2/5) and her friend Kavya takes 1 piece (1/5). Together they have 2 + 1 = 3 pieces, which is 3/5 of the bar. We never add the “number of pieces the bar is cut into” — that would be like saying the bar is suddenly cut into 10 pieces, which makes no sense.
This is exactly why the rule says: add the numerators, keep the denominator the same.
Always check the denominators first before adding fractions. If both denominators are the same, just add the numerators. That’s all there is to it!
Common Mistake
Wrong: 2/5 + 1/5 = 3/10
This is the most common error — students add the denominators (5 + 5 = 10) along with the numerators. This is incorrect. The denominator stays the same because the size of each piece has not changed. The answer is 3/5, not 3/10.
Think about it this way: if you have 2 apples and someone gives you 1 more apple, you have 3 apples — not 3 “two-apples.” The type of object (apples, or fifths) does not change when you add more of them.
Let’s Check
We can verify our answer makes sense:
- 2/5 is less than 1 (a proper fraction)
- 1/5 is less than 1 (a proper fraction)
- Their sum 3/5 is also less than 1 (still a proper fraction)
This makes sense — adding two parts of the same whole should give us fewer parts than the whole, and 3 out of 5 is indeed less than the full 5 out of 5.