Solve the Fraction Addition: 1/4 + 6/12 Step-by-Step

Fraction Addition with Common Denominators

Solve the following equation:

14+612= \frac{1}{4}+\frac{6}{12}=

❤️ 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
00:05 Let's solve this problem.
00:08 First, multiply the fraction by 3 to get a common denominator.
00:13 Remember to multiply both the numerator and the denominator.
00:17 Now, calculate the products. Take your time.
00:25 Next, add the fractions using the common denominator.
00:29 Calculate the new numerator carefully.
00:33 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

14+612= \frac{1}{4}+\frac{6}{12}=

2

Step-by-step solution

We must first identify the lowest common denominator between 4 and 12.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 12.

In this case, the common denominator is 12.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 12.

We'll multiply the first fraction by 3

We'll multiply the second fraction by 1

1×34×3+6×112×1=312+612 \frac{1\times3}{4\times3}+\frac{6\times1}{12\times1}=\frac{3}{12}+\frac{6}{12}

Finally we'll combine and obtain the following:

3+612=912 \frac{3+6}{12}=\frac{9}{12}

3

Final Answer

912 \frac{9}{12}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find least common denominator before adding fractions
  • Technique: Convert 14 \frac{1}{4} to 312 \frac{3}{12} by multiplying by 3
  • Check: Verify 312+612=912 \frac{3}{12} + \frac{6}{12} = \frac{9}{12} by adding numerators ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 14+612 \frac{1}{4} + \frac{6}{12} as 716 \frac{7}{16} ! This treats fractions like separate addition problems instead of parts of a whole. Always find the LCD first and convert both fractions before adding only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

Why can't I just add 1+6 and 4+12?

+

Fractions represent parts of a whole, not separate numbers! Adding 14+612 \frac{1}{4} + \frac{6}{12} as 716 \frac{7}{16} is like adding 1 quarter to 6 twelfths - they're different sized pieces!

How do I know 12 is the LCD of 4 and 12?

+

The LCD is the smallest number both denominators divide into evenly. Since 12 ÷ 4 = 3 and 12 ÷ 12 = 1, both work perfectly! You could use 24 or 36, but 12 is the least common denominator.

Do I need to simplify my final answer?

+

Yes! 912 \frac{9}{12} can be simplified to 34 \frac{3}{4} by dividing both numerator and denominator by their greatest common factor (3).

What if the denominators were harder numbers like 6 and 8?

+

Use the same process! Find multiples: 6: 6, 12, 18, 24... and 8: 8, 16, 24... The LCD would be 24, then convert both fractions to have denominator 24.

Why multiply the first fraction by 3?

+

To get from denominator 4 to denominator 12, you multiply by 3 (since 4 × 3 = 12). Whatever you do to the denominator, you must also do to the numerator to keep the fraction equal!

🌟 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