Solve the Fraction Equation: Finding the Missing Addend in 1/2 + ? = 2/5

Q: Why is the answer negative when both given fractions are positive?

Great observation! When $ \frac{1}{2} $ is larger than $ \frac{2}{5} $, we need a negative number to make the sum smaller. Think of it as: $ \frac{1}{2} + (-\frac{1}{10}) = \frac{2}{5} $

Q: How do I know which fraction is larger?

Convert both to the same denominator first! $ \frac{1}{2} = \frac{5}{10} $ and $ \frac{2}{5} = \frac{4}{10} $. Now you can see that $ \frac{5}{10} > \frac{4}{10} $, so $ \frac{1}{2} > \frac{2}{5} $.

Q: Can I solve this by moving the fraction to the other side?

Absolutely! You can rewrite $ \frac{1}{2} + ? = \frac{2}{5} $ as $ ? = \frac{2}{5} - \frac{1}{2} $. This is the subtraction method and gives the same answer: $ -\frac{1}{10} $.

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

Substitute it back! $ \frac{1}{2} + (-\frac{1}{10}) = \frac{5}{10} - \frac{1}{10} = \frac{4}{10} = \frac{2}{5} $ ✓. The left side equals the right side, so your answer is correct!

Fraction Subtraction with Missing Addends

$\frac{1}{2}+?=\frac{2}{5}$

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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 Arrange the equation and isolate the unknown

00:14 Find the smallest common denominator

00:18 Multiply each fraction by the second denominator to find common denominator

00:25 Remember to multiply both numerator and denominator

00:32 Calculate the multiplications

00:39 Add under the common denominator

00:42 Calculate the numerator

00:45 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

$\frac{1}{2}+?=\frac{2}{5}$

Step-by-step solution

To solve the problem $\frac{1}{2} + x = \frac{2}{5}$ , we need to find $x$ . We will achieve this by following these steps:

Calculate a common denominator for the fractions $\frac{1}{2}$ and $\frac{2}{5}$ .
Subtract $\frac{1}{2}$ from $\frac{2}{5}$ once both fractions have equivalent denominators.
Determine the simplified result for $x$ .

Here's the solution:

Step 1: The denominators for $\frac{1}{2}$ and $\frac{2}{5}$ are 2 and 5. The least common denominator is 10.

Step 2: Convert each fraction to have the denominator of 10.

Convert $\frac{1}{2}$ to $\frac{5}{10}$ because $\frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}$ .

Convert $\frac{2}{5}$ to $\frac{4}{10}$ because $\frac{2 \cdot 2}{5 \cdot 2} = \frac{4}{10}$ .

Step 3: Subtract the converted $\frac{1}{2}$ from $\frac{2}{5}$ .

This gives us $\frac{4}{10} - \frac{5}{10} = -\frac{1}{10}$ .

Therefore, the value of $x$ that satisfies the equation is $-\frac{1}{10}$ .

Final Answer

$-\frac{1}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: To find missing addend, subtract known addend from sum
Technique: Find LCD first: $\frac{2}{5} - \frac{1}{2} = \frac{4}{10} - \frac{5}{10}$
Check: Substitute back: $\frac{1}{2} + (-\frac{1}{10}) = \frac{5}{10} - \frac{1}{10} = \frac{4}{10} = \frac{2}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without finding common denominator first
Don't just add numerators and denominators separately like $\frac{1}{2} + \frac{2}{5} = \frac{3}{7}$ ! This gives completely wrong results because you're adding parts of different-sized wholes. Always find the LCD first, then convert both fractions before adding or subtracting.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{9}+\frac{1}{9}=\text{?}$

FAQ

Everything you need to know about this question

Why is the answer negative when both given fractions are positive?

Great observation! When $\frac{1}{2}$ is larger than $\frac{2}{5}$ , we need a negative number to make the sum smaller. Think of it as: $\frac{1}{2} + (-\frac{1}{10}) = \frac{2}{5}$

How do I know which fraction is larger?

Convert both to the same denominator first! $\frac{1}{2} = \frac{5}{10}$ and $\frac{2}{5} = \frac{4}{10}$ . Now you can see that $\frac{5}{10} > \frac{4}{10}$ , so $\frac{1}{2} > \frac{2}{5}$ .

What if I forget to find the LCD?

Without the LCD, you can't properly add or subtract fractions! Always find the least common multiple of the denominators first. For 2 and 5, the LCM is 10.

Can I solve this by moving the fraction to the other side?

Absolutely! You can rewrite $\frac{1}{2} + ? = \frac{2}{5}$ as $? = \frac{2}{5} - \frac{1}{2}$ . This is the subtraction method and gives the same answer: $-\frac{1}{10}$ .

How do I check if my negative answer is correct?

Substitute it back! $\frac{1}{2} + (-\frac{1}{10}) = \frac{5}{10} - \frac{1}{10} = \frac{4}{10} = \frac{2}{5}$ ✓. The left side equals the right side, so your answer is correct!

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