Addition of Fifth Fractions: Finding the Sum of 1/5 and 2/5

Fraction Addition with Same Denominators

Solve the following exercise:

15+25=? \frac{1}{5}+\frac{2}{5}=\text{?}

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Step-by-step video solution

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00:00 Solve
00:03 Let's add the fractions under a common denominator
00:11 Let's calculate the numerator
00:16 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Solve the following exercise:

15+25=? \frac{1}{5}+\frac{2}{5}=\text{?}

2

Step-by-step solution

To solve the problem of adding 15\frac{1}{5} and 25\frac{2}{5}, follow these steps:

Step 1: Identify the denominators

Both fractions, 15\frac{1}{5} and 25\frac{2}{5}, have the common denominator of 5. This simplifies the addition process since we only need to add the numerators.

Step 2: Add the numerators

When adding fractions with the same denominator, keep the denominator unchanged:

15+25=1+25 \frac{1}{5} + \frac{2}{5} = \frac{1 + 2}{5}

Step 3: Perform the addition

Add the numerators: 1+2=3 1 + 2 = 3 . So, the sum is:

35 \frac{3}{5}

Therefore, the solution to the problem is 35 \frac{3}{5} .

3

Final Answer

35 \frac{3}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add numerators, keep the same denominator when adding fractions
  • Technique: 15+25=1+25=35 \frac{1}{5} + \frac{2}{5} = \frac{1+2}{5} = \frac{3}{5}
  • Check: Verify that 3 parts out of 5 equals the sum ✓

Common Mistakes

Avoid these frequent errors
  • Adding both numerators and denominators
    Don't add 15+25 \frac{1}{5} + \frac{2}{5} as 310 \frac{3}{10} ! This creates a completely different value and breaks the fraction rules. Always keep the same denominator and only add the numerators when denominators match.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{2}{4}+\frac{1}{4}= \)\( \)

FAQ

Everything you need to know about this question

Why don't I add the denominators too?

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The denominator tells us what size pieces we're working with. Both fractions have pieces of size 15 \frac{1}{5} , so we're just counting how many of those pieces we have total: 1 piece + 2 pieces = 3 pieces.

What if the denominators were different?

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Great question! If denominators are different, you'd need to find a common denominator first. But since both fractions have 5 as the denominator, we can add directly.

How do I visualize this problem?

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Think of a pizza cut into 5 equal slices. You have 1 slice, then get 2 more slices. In total, you have 3 out of 5 slices, which is 35 \frac{3}{5} of the pizza!

Is my answer in simplest form?

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35 \frac{3}{5} is already in simplest form because 3 and 5 don't share any common factors other than 1. No further simplification needed!

Can I convert this to a decimal?

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Yes! 35=0.6 \frac{3}{5} = 0.6 because 3 ÷ 5 = 0.6. But for fraction problems, it's usually best to keep your answer as a fraction unless specifically asked to convert.

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