Solve 1/12 + 7/12: Adding Fractions with Like Denominators

Fraction Addition with Same Denominators

112+712= \frac{1}{12}+\frac{7}{12}=

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Step-by-step video solution

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00:00 Solve
00:04 Add under the common denominator
00:08 Calculate the numerator
00:11 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

112+712= \frac{1}{12}+\frac{7}{12}=

2

Step-by-step solution

To solve this problem, we'll use the approach of adding fractions with a common denominator:

  • Step 1: Identify that the fractions 112 \frac{1}{12} and 712 \frac{7}{12} have a common denominator, which is 12.
  • Step 2: Since the denominators are the same, we add the numerators: 1+7=8 1 + 7 = 8 .
  • Step 3: Keep the common denominator, which is 12.

Therefore, the sum of the fractions is 812\frac{8}{12}.

Thus, the solution to the problem is 812 \frac{8}{12} .

3

Final Answer

812 \frac{8}{12}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add numerators when denominators are the same
  • Technique: Keep denominator 12, add numerators: 1 + 7 = 8
  • Check: Verify 112+712=812 \frac{1}{12} + \frac{7}{12} = \frac{8}{12} by counting parts ✓

Common Mistakes

Avoid these frequent errors
  • Adding both numerators and denominators
    Don't add 1+7 and 12+12 to get 824 \frac{8}{24} ! This gives a completely wrong answer because you're changing the size of the pieces. Always keep the same denominator 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 pieces of size 112 \frac{1}{12} , we keep that size and just count how many pieces we have total!

Do I need to simplify 812 \frac{8}{12} ?

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You can! 812 \frac{8}{12} simplifies to 23 \frac{2}{3} by dividing both parts by 4. But for this problem, either answer is correct since the question asks for the exact form.

What if the denominators were different?

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Then you'd need to find a common denominator first! But in this problem, both fractions already have the same denominator (12), so you can add directly.

How can I picture this problem?

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Imagine a pizza cut into 12 equal slices. You have 1 slice, then get 7 more slices. Now you have 812 \frac{8}{12} of the whole pizza!

Is there a pattern for adding fractions?

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  • Same denominator: Add numerators, keep denominator
  • Different denominators: Find common denominator first, then add

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