Solve: Adding 3/8 + 2/3 - Unlike Denominators Practice

Fraction Addition with Different Denominators

Solve the following exercise:

38+23= \frac{3}{8}+\frac{2}{3}=

❤️ 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 Multiply each fraction by the second denominator to find the common denominator
00:07 Make sure to multiply both numerator and denominator
00:15 Calculate the multiplications
00:21 Add with the common denominator
00:24 Calculate the numerator
00:28 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

38+23= \frac{3}{8}+\frac{2}{3}=

2

Step-by-step solution

Let's try to find the least common multiple (LCM) between 8 and 3

To find the least common multiple, we need to find a number that is divisible by both 8 and 3

In this case, the common multiple is 24

Now we'll multiply each fraction by the appropriate number to reach the denominator 24

We'll multiply the first fraction by 3

We'll multiply the second fraction by 8

3×38×3+2×83×8=924+1624 \frac{3\times3}{8\times3}+\frac{2\times8}{3\times8}=\frac{9}{24}+\frac{16}{24}

Now we'll combine and get:

9+1624=2524 \frac{9+16}{24}=\frac{25}{24}

3

Final Answer

2524 \frac{25}{24}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find LCD before adding fractions with different denominators
  • Technique: Convert 38 \frac{3}{8} to 924 \frac{9}{24} and 23 \frac{2}{3} to 1624 \frac{16}{24}
  • Check: Verify LCD is correct: 24 ÷ 8 = 3 and 24 ÷ 3 = 8 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 3 + 2 = 5 and 8 + 3 = 11 to get 5/11! This completely ignores fraction rules and gives a wrong answer. Always find the LCD first, convert both fractions, 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

How do I find the LCD of 8 and 3?

+

Since 8 and 3 share no common factors, multiply them together: 8 × 3 = 24. For numbers that aren't relatively prime, find the smallest number both denominators divide into evenly.

Why can't I just add 3/8 + 2/3 directly?

+

You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add 3 slices of pizza cut into 8 pieces with 2 slices cut into 3 pieces.

What if my answer is an improper fraction like 25/24?

+

That's perfectly correct! 2524 \frac{25}{24} can be converted to 1124 1\frac{1}{24} if needed, but improper fractions are valid answers in mathematics.

How do I multiply 3/8 by 3 to get the same denominator?

+

Multiply both the numerator and denominator by 3: 3×38×3=924 \frac{3 \times 3}{8 \times 3} = \frac{9}{24} . This keeps the fraction's value the same while changing its form.

Can I simplify 25/24 further?

+

No! Since 25 and 24 share no common factors (25 = 5² and 24 = 2³ × 3), the fraction 2524 \frac{25}{24} is already in simplest form.

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations