Solve the Fraction Addition: 3/4 + 2/20 Step-by-Step

Q: Why can't I just add the tops and bottoms separately?

Because $ \frac{3}{4} $ means 3 pieces of size $ \frac{1}{4} $, while $ \frac{2}{20} $ means 2 pieces of size $ \frac{1}{20} $. You can't add different-sized pieces until you make them the same size!

Q: How do I find the common denominator?

Look for the least common multiple (LCM) of the denominators. Since 20 is already a multiple of 4, use 20 as your common denominator. Convert $ \frac{3}{4} $ by multiplying top and bottom by 5.

Q: Do I always use the bigger denominator?

Not always! Sometimes you need a number bigger than both denominators. For example, $ \frac{1}{6} + \frac{1}{4} $ needs denominator 12, not 6 or 4. Find the LCM to be sure.

Q: Should I simplify my final answer?

Check if you can! For $ \frac{17}{20} $, since 17 and 20 share no common factors, it's already in simplest form. Always try to reduce fractions to lowest terms.

Q: What if the fractions have the same denominator already?

Lucky you! Just add the numerators and keep the same denominator. For example: $ \frac{5}{20} + \frac{3}{20} = \frac{8}{20} $. Much easier!

Fraction Addition with Different Denominators

$\frac{3}{4}+\frac{2}{20}=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to get to the smallest common denominator

00:06 Therefore multiply by 5, to get the common denominator 20

00:09 Remember to multiply both numerator and denominator

00:16 Let's calculate the multiplications

00:22 Let's add under the common denominator

00:30 Let's calculate the numerator

00:34 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

$\frac{3}{4}+\frac{2}{20}=$

Step-by-step solution

To solve $\frac{3}{4} + \frac{2}{20}$ , let's follow these steps:

Step 1: Convert $\frac{3}{4}$ to a fraction with the denominator $20$ .
Multiply both the numerator and denominator of $\frac{3}{4}$ by $5$ , as $20 \div 4 = 5$ :
We have: $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$
Step 2: The fraction $\frac{2}{20}$ is already in the correct form with a denominator of $20$ .
Step 3: Add the fractions $\frac{15}{20}$ and $\frac{2}{20}$ :
Since they have the same denominator, we combine the numerators directly: $\frac{15}{20} + \frac{2}{20} = \frac{15 + 2}{20} = \frac{17}{20}$

Therefore, the sum of the fractions is $\frac{17}{20}$ .

Final Answer

$\frac{17}{20}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions
Technique: Convert $\frac{3}{4}$ to $\frac{15}{20}$ by multiplying by 5
Check: $\frac{15}{20} + \frac{2}{20} = \frac{17}{20}$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 3+2=5 and 4+20=24 to get $\frac{5}{24}$ ! This ignores that fractions represent parts of different-sized wholes. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just add the tops and bottoms separately?

Because $\frac{3}{4}$ means 3 pieces of size $\frac{1}{4}$ , while $\frac{2}{20}$ means 2 pieces of size $\frac{1}{20}$ . You can't add different-sized pieces until you make them the same size!

How do I find the common denominator?

Look for the least common multiple (LCM) of the denominators. Since 20 is already a multiple of 4, use 20 as your common denominator. Convert $\frac{3}{4}$ by multiplying top and bottom by 5.

Do I always use the bigger denominator?

Not always! Sometimes you need a number bigger than both denominators. For example, $\frac{1}{6} + \frac{1}{4}$ needs denominator 12, not 6 or 4. Find the LCM to be sure.

Should I simplify my final answer?

Check if you can! For $\frac{17}{20}$ , since 17 and 20 share no common factors, it's already in simplest form. Always try to reduce fractions to lowest terms.

What if the fractions have the same denominator already?

Lucky you! Just add the numerators and keep the same denominator. For example: $\frac{5}{20} + \frac{3}{20} = \frac{8}{20}$ . Much easier!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime