Solve: Find the Missing Fraction in 3/10 + ? + 3/10 = 9/10

Q: Why don't I add the denominators when they're the same?

When denominators are the same, they represent the same-sized pieces. You're just counting how many pieces total! Think of it like: 3 tenths + ? + 3 tenths = 9 tenths.

Q: How do I find the missing fraction step by step?

First, add the known fractions: $ \frac{3}{10} + \frac{3}{10} = \frac{6}{10} $. Then subtract from the total: $ \frac{9}{10} - \frac{6}{10} = \frac{3}{10} $. That's your missing fraction!

Q: What if the denominators were different?

If denominators don't match, you'd need to find a common denominator first, then convert all fractions before adding. Luckily, this problem has matching denominators!

Q: How do I check if my answer is correct?

Substitute your answer back into the original equation: $ \frac{3}{10} + \frac{3}{10} + \frac{3}{10} = \frac{9}{10} $. If both sides are equal, you're right!

Fraction Addition with Missing Addends

Complete the missing fraction

$\frac{3}{10}+_—+\frac{3}{10}=\frac{9}{10}$

What is the missing fraction?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 According to the calculation, we know that the unknown denominator equals the given denominator

00:07 Let's find the number that completes the numerators to the result numerator

00:17 This is the appropriate number, so we'll substitute it in the unknown numerator

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the missing fraction

$\frac{3}{10}+_—+\frac{3}{10}=\frac{9}{10}$

What is the missing fraction?

Step-by-step solution

To find the missing fraction in the equation $\frac{3}{10} + \_ + \frac{3}{10} = \frac{9}{10}$ , we need to determine what must be added to the sums of the known fractions to reach the total sum.

Step 1: Calculate the sum of known fractions. We have:

$\frac{3}{10} + \frac{3}{10}$

Add the numerators together, since both fractions have the same denominator:

$3 + 3 = 6$

Thus, the combined fraction is:

$\frac{6}{10}$

Step 2: To find the missing fraction, subtract the sum of known fractions from the total:

$\frac{9}{10} - \frac{6}{10} = \frac{3}{10}$

This shows that the missing fraction is indeed $\frac{3}{10}$ .

Therefore, the solution to the problem is $\frac{3}{10}$ .

Final Answer

$\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Same Denominators: Add numerators directly when denominators match
Technique: Subtract known sum from total: $\frac{9}{10} - \frac{6}{10} = \frac{3}{10}$
Check: Verify by adding all three fractions: $\frac{3}{10} + \frac{3}{10} + \frac{3}{10} = \frac{9}{10}$ ✓

Common Mistakes

Avoid these frequent errors

Adding all denominators together
Don't add 10 + 10 + 10 = 30 to get $\frac{9}{30}$ ! This changes the value of fractions completely. Always keep the same denominator when fractions have matching denominators 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 when they're the same?

When denominators are the same, they represent the same-sized pieces. You're just counting how many pieces total! Think of it like: 3 tenths + ? + 3 tenths = 9 tenths.

How do I find the missing fraction step by step?

First, add the known fractions: $\frac{3}{10} + \frac{3}{10} = \frac{6}{10}$ . Then subtract from the total: $\frac{9}{10} - \frac{6}{10} = \frac{3}{10}$ . That's your missing fraction!

What if the denominators were different?

If denominators don't match, you'd need to find a common denominator first, then convert all fractions before adding. Luckily, this problem has matching denominators!

Can I solve this problem a different way?

Yes! You could think: "What plus 6 tenths equals 9 tenths?" Since $6 + 3 = 9$ , the answer is $\frac{3}{10}$ . Both methods work!

How do I check if my answer is correct?

Substitute your answer back into the original equation: $\frac{3}{10} + \frac{3}{10} + \frac{3}{10} = \frac{9}{10}$ . If both sides are equal, you're right!

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