Solve the Fraction Addition: 1/5 + 4/5 Step-by-Step

Fraction Addition with Same Denominators

Solve the following exercise:

15+45=? \frac{1}{5}+\frac{4}{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
00:07 Let's color the parts corresponding to each fraction
00:13 Let's combine all the colored parts and place in the numerator
00:25 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+45=? \frac{1}{5}+\frac{4}{5}=\text{?}

2

Step-by-step solution

To solve this problem, we need to add the fractions 15 \frac{1}{5} and 45 \frac{4}{5} . Let's follow these steps:

  • Step 1: Ensure the fractions have the same denominator.
    Both fractions, 15 \frac{1}{5} and 45 \frac{4}{5} , already have the same denominator, which is 5.
  • Step 2: Add the numerators while keeping the denominator the same.
    Compute 1+4=5 1 + 4 = 5 . This gives us the new fraction 55 \frac{5}{5} .
  • Step 3: Simplify the fraction if needed.
    The fraction 55 \frac{5}{5} simplifies to 1, since 5 divided by 5 is 1.
  • Step 4: Confirm against the answer choices.
    The simplified result 1 corresponds to choice number 2, which is 1.

Therefore, the solution to the problem is 1.

3

Final Answer

1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add numerators when denominators are the same
  • Technique: Calculate 1 + 4 = 5, then write 55 \frac{5}{5}
  • Check: Simplify 55=1 \frac{5}{5} = 1 since 5 ÷ 5 = 1 ✓

Common Mistakes

Avoid these frequent errors
  • Adding both numerators and denominators
    Don't add 1 + 4 and 5 + 5 to get 510 \frac{5}{10} = wrong answer! This changes the value of the fractions completely. Always keep the denominator the same and only add the numerators.

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. Since both fractions are already in fifths, we keep working in fifths. Adding denominators would change the piece size!

How do I know when fractions can be simplified?

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When the numerator and denominator can both be divided by the same number. Here, 55 \frac{5}{5} simplifies to 1 because both 5s divide by 5.

What if the denominators were different?

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Then you'd need to find a common denominator first! Convert both fractions so they have the same bottom number, then add the numerators.

Is 1 the same as 55 \frac{5}{5} ?

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Yes! Any fraction where the numerator equals the denominator equals 1. Think of it as 5 pieces out of 5 pieces = the whole thing = 1.

How can I visualize this problem?

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Picture a rectangle divided into 5 equal parts. You shade 1 part, then 4 more parts. Now all 5 parts are shaded = the whole rectangle = 1!

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