Solve the Fraction Addition: 1/5 + 3/5 Step-by-Step

Fraction Addition with Common Denominators

Solve the following exercise:

15+35=? \frac{1}{5}+\frac{3}{5}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's divide our complete rectangle into 5 parts
00:08 Let's color the parts corresponding to each fraction
00:13 Let's combine all the colored parts and place in the numerator
00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

15+35=? \frac{1}{5}+\frac{3}{5}=\text{?}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the common denominator.
  • Step 2: Add the numerators and keep the common denominator.

Now, let's work through each step:
Step 1: Both fractions 15 \frac{1}{5} and 35 \frac{3}{5} have the common denominator of 5.
Step 2: Add the numerators: 1+3=4 1 + 3 = 4 .
Thus, we get 45 \frac{4}{5} .

Therefore, the solution to the problem is 45 \frac{4}{5} . This corresponds to choice 4.

3

Final Answer

45 \frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominators: Keep the same denominator when fractions match
  • Add Numerators: Add top numbers only: 1 + 3 = 4
  • Verify: Count visual parts: 1 section + 3 sections = 4 sections total ✓

Common Mistakes

Avoid these frequent errors
  • Adding both numerators and denominators
    Don't add 1+3=4 and 5+5=10 to get 4/10! This creates a completely different fraction that doesn't represent the actual sum. Always keep the common denominator unchanged and only add the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \)\( \frac{4}{5}+\frac{1}{5}= \)

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. Since both fractions have fifths, we're still working with fifths after adding. Only the number of pieces (numerators) changes!

What if the denominators were different?

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Then you'd need to find a common denominator first by converting the fractions. But here, both fractions already have the same denominator (5), so you can add directly!

How can I visualize this problem?

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Think of a rectangle divided into 5 equal parts. You have 1 part shaded plus 3 more parts shaded = 4 parts shaded total out of 5 parts.

Can I simplify 4/5 further?

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No, 45 \frac{4}{5} is already in lowest terms because 4 and 5 share no common factors other than 1. This is your final answer!

What does the visual diagram show?

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The rectangle is divided into 5 equal sections. The shaded part represents 15 \frac{1}{5} , and when you add 35 \frac{3}{5} , you get 45 \frac{4}{5} of the rectangle shaded.

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