Solve the Fraction Addition: 1/4 + 3/4 Step by Step

Fraction Addition with Like Denominators

14+34= \frac{1}{4}+\frac{3}{4}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Let's add under the common denominator
00:09 Let's calculate the numerator
00:13 Any number divided by itself always equals 1
00:16 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

14+34= \frac{1}{4}+\frac{3}{4}=

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Step-by-step solution

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

  • Step 1: Identify the denominators of the fractions.
  • Step 2: Because the denominators are the same, add the numerators.
  • Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Both fractions, 14 \frac{1}{4} and 34 \frac{3}{4} , have the same denominator, 4.
Step 2: Since the denominators are the same, we can add the numerators: 1+3=4 1 + 3 = 4 .
Step 3: The resulting fraction is 44 \frac{4}{4} , which simplifies to 1 1 .

Therefore, the solution to the problem is 1 1 .

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Rule: When denominators match, add only the numerators together
  • Technique: Add numerators: 1 + 3 = 4, keep denominator: 4
  • Check: Verify 44=1 \frac{4}{4} = 1 by simplifying completely ✓

Common Mistakes

Avoid these frequent errors
  • Adding both numerators and denominators
    Don't add 1+3=4 and 4+4=8 to get 48 \frac{4}{8} = wrong answer! This breaks fraction rules and gives incorrect results. Always keep the same denominator and add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{4}\times\frac{3}{2}= \)

FAQ

Everything you need to know about this question

Why don't I add the denominators too?

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The denominator tells you the size of each piece. Since both fractions are fourths, you're adding pieces of the same size. Only count how many pieces: 1 fourth + 3 fourths = 4 fourths.

How do I simplify 44 \frac{4}{4} ?

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When the numerator and denominator are the same, the fraction equals 1. Think of it as 4 pieces out of 4 total pieces = the whole thing!

What if the denominators were different?

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Then you'd need to find a common denominator first. But here, both fractions already have the same denominator (4), so you can add directly!

Can I convert to decimals instead?

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Yes! 14=0.25 \frac{1}{4} = 0.25 and 34=0.75 \frac{3}{4} = 0.75 , so 0.25 + 0.75 = 1.00. But working with fractions is often more precise.

Is there a shortcut for this type of problem?

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Yes! When denominators are the same:

  • Add the top numbers
  • Keep the bottom number
  • Simplify if possible
That's it!

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