Adding Fractions with Unlike Denominators: 2/5 and 1/4

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

Because $ \frac{2}{5} $ and $ \frac{1}{4} $ represent parts of different-sized wholes! You need equal-sized pieces (same denominator) before you can count how many pieces you have total.

Q: How do I find the LCD of 5 and 4?

Since 5 and 4 share no common factors, their LCD is their product: 5 × 4 = 20. List multiples if unsure: 5, 10, 15, 20 and 4, 8, 12, 16, 20.

Q: What if my denominators were bigger numbers?

The process stays the same! Find the LCM of the denominators, convert both fractions, then add. For larger numbers, use prime factorization to find the LCM more easily.

Q: Do I always need to simplify my final answer?

Yes, always check! Look for common factors between numerator and denominator. In this case, 13 is prime and doesn't divide 20, so $ \frac{13}{20} $ is already simplified.

Q: Can I convert to decimals instead?

You could convert to decimals ($ \frac{2}{5} = 0.4 $, $ \frac{1}{4} = 0.25 $), but keeping fractions gives you the exact answer without rounding errors.

Fraction Addition with Common Denominators

$\frac{2}{5}+\frac{1}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to find the least common denominator

00:06 Multiply each fraction by the other denominator to find the common denominator

00:09 Remember to multiply both numerator and denominator

00:24 Calculate the multiplications

00:30 Add under the common denominator

00:34 Calculate the numerator

00:38 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

$\frac{2}{5}+\frac{1}{4}=$

Step-by-step solution

To solve the problem, let's follow a structured approach:

Step 1: Determine the least common multiple (LCM) of the denominators (5 and 4). The LCM of 5 and 4 is 20.
Step 2: Adjust each fraction to have the common denominator of 20.
For $\frac{2}{5}$ , multiply both numerator and denominator by 4 to get $\frac{8}{20}$ .
For $\frac{1}{4}$ , multiply both numerator and denominator by 5 to get $\frac{5}{20}$ .
Step 3: Now, add the two fractions:
$\frac{8}{20} + \frac{5}{20} = \frac{8 + 5}{20} = \frac{13}{20}$ .
Step 4: Verify if the fraction needs simplification. In this case, $\frac{13}{20}$ is already in its simplest form.

The resulting fraction after adding $\frac{2}{5}$ and $\frac{1}{4}$ is $\frac{13}{20}$ .

Final Answer

$\frac{13}{20}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD of denominators before adding fractions
Technique: Convert $\frac{2}{5}$ to $\frac{8}{20}$ and $\frac{1}{4}$ to $\frac{5}{20}$
Check: Verify $\frac{13}{20}$ cannot simplify further: 13 and 20 share no common factors ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 2+1=3 and 5+4=9 to get $\frac{3}{9}$ = wrong answer! This ignores that fractions represent parts of different wholes. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{3}{4}:\frac{5}{6}=\text{?}$

FAQ

Everything you need to know about this question

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

Because $\frac{2}{5}$ and $\frac{1}{4}$ represent parts of different-sized wholes! You need equal-sized pieces (same denominator) before you can count how many pieces you have total.

How do I find the LCD of 5 and 4?

Since 5 and 4 share no common factors, their LCD is their product: 5 × 4 = 20. List multiples if unsure: 5, 10, 15, 20 and 4, 8, 12, 16, 20.

What if my denominators were bigger numbers?

The process stays the same! Find the LCM of the denominators, convert both fractions, then add. For larger numbers, use prime factorization to find the LCM more easily.

Do I always need to simplify my final answer?

Yes, always check! Look for common factors between numerator and denominator. In this case, 13 is prime and doesn't divide 20, so $\frac{13}{20}$ is already simplified.

Can I convert to decimals instead?

You could convert to decimals ( $\frac{2}{5} = 0.4$ , $\frac{1}{4} = 0.25$ ), but keeping fractions gives you the exact answer without rounding errors.

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Adding Fractions with Unlike Denominators: 2/5 and 1/4

Fraction Addition with Common Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

How do I find the LCD of 5 and 4?

What if my denominators were bigger numbers?

Do I always need to simplify my final answer?

Can I convert to decimals instead?

🌟 Unlock Your Math Potential

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