Solve 3/7 + 2/7: Adding Fractions with Like Denominators

Fraction Addition with Same Denominators

37+27= \frac{3}{7}+\frac{2}{7}=

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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 color the appropriate number of squares, according to the given data
00:16 Now let's count and add to the numerator in the new fraction
00:21 The denominator equals the number of cells we divided
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

37+27= \frac{3}{7}+\frac{2}{7}=

2

Step-by-step solution

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

  • Step 1: Identify the fractions and check the denominators.
  • Step 2: Add the numerators since the denominators are the same.
  • Step 3: Reduce the fraction to its simplest form if possible.

Now, let's work through each step:
Step 1: We observe that the fractions are 37\frac{3}{7} and 27\frac{2}{7}, both having the same denominator, 7.
Step 2: Since the denominators are the same, we can directly add the numerators: 3+2=53 + 2 = 5.
Step 3: This results in the fraction 57\frac{5}{7}. As the fraction is already in its simplest form, no further simplification is needed.

Therefore, the solution to the problem is 57 \frac{5}{7} .

3

Final Answer

57 \frac{5}{7}

Key Points to Remember

Essential concepts to master this topic
  • Same Denominators: Keep denominator unchanged, add only the numerators
  • Technique: Add numerators: 3+2=5 3 + 2 = 5 , keep denominator 7
  • Check: Verify 57 \frac{5}{7} cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors
  • Adding both numerators and denominators
    Don't add denominators: 37+27514 \frac{3}{7} + \frac{2}{7} ≠ \frac{5}{14} ! This creates a completely different fraction that's much smaller than the correct answer. Always keep the same denominator and add only 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 we add the denominators too?

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The denominator tells us what size pieces we're working with. Since both fractions have sevenths, we're adding pieces of the same size, so the denominator stays 7.

What if I got 5/14 as my answer?

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That means you accidentally added the denominators! 514 \frac{5}{14} is much smaller than 57 \frac{5}{7} . Remember: same denominators = add only numerators.

Do I need to simplify 5/7?

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No! 57 \frac{5}{7} is already in simplest form because 5 and 7 share no common factors other than 1.

How can I visualize this problem?

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Think of a pizza cut into 7 equal slices. You eat 3 slices, then 2 more slices. Total: 5 slices out of 7, which is 57 \frac{5}{7} !

What if the denominators were different?

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If denominators are different, you'd need to find a common denominator first. But here, both fractions already have the same denominator (7), making this much easier!

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