Solve: Find the Missing Fraction in 2/12 + ? + 3/12 = 9/12

Q: Why do I add the known fractions first?

Adding the known fractions shows you what's already accounted for. Since $ \frac{2}{12} + \frac{3}{12} = \frac{5}{12} $, you need $ \frac{4}{12} $ more to reach $ \frac{9}{12} $!

Q: What if the denominators were different?

You'd need to find a common denominator first, then convert all fractions before adding. Lucky for us, all fractions already have 12 as the denominator!

Q: Can I simplify 4/12 to 1/3?

Yes! $ \frac{4}{12} = \frac{1}{3} $ when simplified. However, since all other fractions in the problem use 12 as the denominator, keeping it as 4/12 makes the most sense here.

Q: How do I know this isn't a trick question?

Always verify your answer by substituting back! When you add $ \frac{2}{12} + \frac{4}{12} + \frac{3}{12} $, you should get exactly $ \frac{9}{12} $.

Q: What if I got a different answer like 5/12?

Check your arithmetic! If you got $ \frac{5}{12} $, you might have added $ \frac{2}{12} + \frac{3}{12} $ and thought that was the answer. Remember to subtract this sum from the total!

Missing Addend with Same Denominators

Complete the missing fraction

$\frac{2}{12}+_—+\frac{3}{12}=\frac{9}{12}$

What is the missing fraction?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve for the unknown value!

00:11 First, match the unknown denominator to the given denominator.

00:15 Now, find the number that makes the numerator equal to the result's numerator.

00:20 Great! Substitute that number into the unknown numerator.

00:24 And there you have it! That's how you solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the missing fraction

$\frac{2}{12}+_—+\frac{3}{12}=\frac{9}{12}$

What is the missing fraction?

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Add the known fractions: We first add the fractions given on the left-hand side. So, $\frac{2}{12} + \frac{3}{12} = \frac{5}{12}$ .
Step 2: Subtract this sum from the total: We know the sum of all the fractions is $\frac{9}{12}$ . To find the missing fraction, we need to calculate $\frac{9}{12} - \frac{5}{12}$ .
Step 3: Perform the subtraction: Since the fractions have the same denominator, subtract numerators: $\frac{9 - 5}{12} = \frac{4}{12}$ .
Step 4: Verify your solution: Verify by adding all fractions including the missing one: $\frac{2}{12} + \frac{4}{12} + \frac{3}{12} = \frac{9}{12}$ , which confirms our answer.

Therefore, the missing fraction is $\frac{4}{12}$ .

Final Answer

$\frac{4}{12}$

Key Points to Remember

Essential concepts to master this topic

Rule: With same denominators, add numerators and keep denominator unchanged
Technique: Subtract known sum from total: $\frac{9}{12} - \frac{5}{12} = \frac{4}{12}$
Check: Add all fractions to verify: $\frac{2}{12} + \frac{4}{12} + \frac{3}{12} = \frac{9}{12}$ ✓

Common Mistakes

Avoid these frequent errors

Adding all given fractions including the total
Don't add 2/12 + 3/12 + 9/12 = 14/12! This treats the total as another addend instead of the sum. Always recognize that the fraction after the equals sign is the final result, not another piece to add.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{4}+\frac{1}{4}=$ $$

FAQ

Everything you need to know about this question

Why do I add the known fractions first?

Adding the known fractions shows you what's already accounted for. Since $\frac{2}{12} + \frac{3}{12} = \frac{5}{12}$ , you need $\frac{4}{12}$ more to reach $\frac{9}{12}$ !

What if the denominators were different?

You'd need to find a common denominator first, then convert all fractions before adding. Lucky for us, all fractions already have 12 as the denominator!

Can I simplify 4/12 to 1/3?

Yes! $\frac{4}{12} = \frac{1}{3}$ when simplified. However, since all other fractions in the problem use 12 as the denominator, keeping it as 4/12 makes the most sense here.

How do I know this isn't a trick question?

Always verify your answer by substituting back! When you add $\frac{2}{12} + \frac{4}{12} + \frac{3}{12}$ , you should get exactly $\frac{9}{12}$ .

What if I got a different answer like 5/12?

Check your arithmetic! If you got $\frac{5}{12}$ , you might have added $\frac{2}{12} + \frac{3}{12}$ and thought that was the answer. Remember to subtract this sum from the total!

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