Solve the Fraction Equation: Finding the Missing Addend in 1/5 + ? = 3/5

Q: Why do I subtract instead of add to find the missing fraction?

Think of it like this: if you have 1 piece + ? pieces = 3 pieces total, you need to find how many more pieces you need. You subtract: 3 - 1 = 2 pieces!

Q: What if the fractions had different denominators?

You'd need to find a common denominator first, then convert both fractions before subtracting. But since $ \frac{1}{5} $ and $ \frac{3}{5} $ already have the same denominator, we can work directly with the numerators.

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

Simply add your answer to the given fraction! $ \frac{1}{5} + \frac{2}{5} = \frac{3}{5} $. If you get the target sum, you're right!

Q: Can I solve this using a different method?

Yes! You can also think of it as solving the equation $ \frac{1}{5} + x = \frac{3}{5} $ by moving $ \frac{1}{5} $ to the right side, which gives the same result.

Q: What if I get confused about which fraction to subtract?

Remember: subtract the smaller fraction from the larger one. Since $ \frac{3}{5} > \frac{1}{5} $, you calculate $ \frac{3}{5} - \frac{1}{5} $ to find the missing piece.

Fraction Addition with Missing Addend

Complete the missing fraction

$\frac{1}{5}+_—=\frac{3}{5}$

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

00:07 According to the calculation, we know that the denominator of the unknown equals the given denominator

00:12 Let's find the number that completes the numerator to the result's 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

$\frac{1}{5}+_—=\frac{3}{5}$

What is the missing fraction?

Step-by-step solution

To find the missing fraction $x$ in the equation $\frac{1}{5} + x = \frac{3}{5}$ , we can follow these steps:

Step 1: Start with the given equation: $\frac{1}{5} + x = \frac{3}{5}$ .
Step 2: Subtract $\frac{1}{5}$ from both sides to solve for $x$ :

$x = \frac{3}{5} - \frac{1}{5}$

Step 3: Since the fractions have the same denominator, subtract the numerators directly:

$x = \frac{3 - 1}{5} = \frac{2}{5}$

Thus, the missing fraction is $\frac{2}{5}$ .

Therefore, the solution to the problem is $\frac{2}{5}$ .

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Subtraction Method: Isolate the unknown by subtracting the known fraction from both sides
Same Denominators: Subtract numerators directly: $\frac{3}{5} - \frac{1}{5} = \frac{2}{5}$
Verification: Check by adding: $\frac{1}{5} + \frac{2}{5} = \frac{3}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions instead of subtracting to solve
Don't add $\frac{1}{5} + \frac{3}{5} = \frac{4}{5}$ thinking that's the answer! This gives you the sum of both known fractions, not the missing one. Always subtract the given fraction from the total to find the missing addend.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why do I subtract instead of add to find the missing fraction?

Think of it like this: if you have 1 piece + ? pieces = 3 pieces total, you need to find how many more pieces you need. You subtract: 3 - 1 = 2 pieces!

What if the fractions had different denominators?

You'd need to find a common denominator first, then convert both fractions before subtracting. But since $\frac{1}{5}$ and $\frac{3}{5}$ already have the same denominator, we can work directly with the numerators.

How can I check if my answer is correct?

Simply add your answer to the given fraction! $\frac{1}{5} + \frac{2}{5} = \frac{3}{5}$ . If you get the target sum, you're right!

Can I solve this using a different method?

Yes! You can also think of it as solving the equation $\frac{1}{5} + x = \frac{3}{5}$ by moving $\frac{1}{5}$ to the right side, which gives the same result.

What if I get confused about which fraction to subtract?

Remember: subtract the smaller fraction from the larger one. Since $\frac{3}{5} > \frac{1}{5}$ , you calculate $\frac{3}{5} - \frac{1}{5}$ to find the missing piece.

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