Solve the Fraction Equation: Finding the Missing Number in ? + 1/3 = 2/5

Q: Why can't I just add the numerators and denominators?

Because fractions represent parts of different wholes! Adding $ \frac{1}{3} $ and $ \frac{2}{5} $ is like adding 1 piece of a 3-slice pizza to 2 pieces of a 5-slice pizza - you need equal slice sizes first!

Q: How do I find the LCD of 3 and 5?

Since 3 and 5 are both prime numbers, their LCD is simply 3 × 5 = 15. For other numbers, list multiples of each denominator until you find the smallest common one.

Q: What does it mean to isolate the question mark?

Isolating means getting the unknown value by itself on one side. Since we have $ ? + \frac{1}{3} = \frac{2}{5} $, we subtract $ \frac{1}{3} $ from both sides to get $ ? = \frac{2}{5} - \frac{1}{3} $.

Q: Why is my answer 1/15 and not something bigger?

Because $ \frac{2}{5} $ is only slightly larger than $ \frac{1}{3} $! When you subtract $ \frac{6}{15} - \frac{5}{15} $, you get a small difference of $ \frac{1}{15} $.

Q: Can I convert to decimals instead?

Yes, but be careful with rounding! $ \frac{1}{3} ≈ 0.333... $ and $ \frac{2}{5} = 0.4 $, so 0.4 - 0.333... ≈ 0.067. However, working with fractions gives you the exact answer.

Fraction Equations with Common Denominators

$?+\frac{1}{3}=\frac{2}{5}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:05 Arrange the equation and isolate the unknown

00:13 Find the smallest common denominator

00:17 Multiply each fraction by the second denominator to find the common denominator

00:23 Remember to multiply both numerator and denominator

00:36 Calculate the multiplications

00:43 Add under the common denominator

00:46 Calculate the numerator

00:50 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

$?+\frac{1}{3}=\frac{2}{5}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the common denominator for $\frac{1}{3}$ and $\frac{2}{5}$ .
Step 2: Rewrite each fraction using this common denominator.
Step 3: Perform the fraction subtraction.
Step 4: Simplify the resulting fraction, if needed.

Now, let's work through each step:

Step 1: Find the common denominator.

The denominators of the fractions are 3 and 5. The least common multiple of 3 and 5 is 15.

Step 2: Rewrite each fraction with the common denominator of 15.

$\frac{1}{3} = \frac{5}{15}$ , and $\frac{2}{5} = \frac{6}{15}$ .

Step 3: Subtract $\frac{5}{15}$ from $\frac{6}{15}$ .

$\frac{6}{15} - \frac{5}{15} = \frac{1}{15}$ .

Step 4: Simplification.

The fraction $\frac{1}{15}$ is already in its simplest form.

Therefore, the solution to the equation is $\frac{1}{15}$ .

Final Answer

$\frac{1}{15}$

Key Points to Remember

Essential concepts to master this topic

Isolation: Subtract one fraction from both sides to isolate variable
Common Denominator: Convert $\frac{1}{3} = \frac{5}{15}$ and $\frac{2}{5} = \frac{6}{15}$ using LCD 15
Verification: Check $\frac{1}{15} + \frac{1}{3} = \frac{1}{15} + \frac{5}{15} = \frac{6}{15} = \frac{2}{5}$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions without finding common denominator
Don't just add numerators and denominators separately like 1/3 + 2/5 = 3/8! This ignores the different denominators and gives completely wrong results. Always find the LCD first, then convert both fractions before adding or subtracting.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just add the numerators and denominators?

Because fractions represent parts of different wholes! Adding $\frac{1}{3}$ and $\frac{2}{5}$ is like adding 1 piece of a 3-slice pizza to 2 pieces of a 5-slice pizza - you need equal slice sizes first!

How do I find the LCD of 3 and 5?

Since 3 and 5 are both prime numbers, their LCD is simply 3 × 5 = 15. For other numbers, list multiples of each denominator until you find the smallest common one.

What does it mean to isolate the question mark?

Isolating means getting the unknown value by itself on one side. Since we have $? + \frac{1}{3} = \frac{2}{5}$ , we subtract $\frac{1}{3}$ from both sides to get $? = \frac{2}{5} - \frac{1}{3}$ .

Why is my answer 1/15 and not something bigger?

Because $\frac{2}{5}$ is only slightly larger than $\frac{1}{3}$ ! When you subtract $\frac{6}{15} - \frac{5}{15}$ , you get a small difference of $\frac{1}{15}$ .

Can I convert to decimals instead?

Yes, but be careful with rounding! $\frac{1}{3} ≈ 0.333...$ and $\frac{2}{5} = 0.4$ , so 0.4 - 0.333... ≈ 0.067. However, working with fractions gives you the exact answer.

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