Solve the Fraction Equation: 3/4 - 1/6 Step-by-Step

Fraction Subtraction with Unlike Denominators

Solve the following equation:

34−16= ? \frac{3}{4}-\frac{1}{6}=\text{ ?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together!
00:08 First, we need to find the least common denominator.
00:12 To do this, we'll multiply both by 3 and 2 to find a common denominator.
00:18 Remember, multiply both the top, which is the numerator, and the bottom, which is the denominator.
00:23 Now, let's do the calculations together. Get ready to multiply!
00:32 Next, subtract using the common denominator we found.
00:36 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

34−16= ? \frac{3}{4}-\frac{1}{6}=\text{ ?}

2

Step-by-step solution

In this question, we need to find a common denominator.

However, we don't have to multiply the denominators by each other as there is a lowest common denominator: 12.

3×33×4 \frac{3\times3}{3\times4}

1×26×2 \frac{1\times2}{6\times2}

912−212=9−212=712 \frac{9}{12}-\frac{2}{12}=\frac{9-2}{12}=\frac{7}{12}

3

Final Answer

712 \frac{7}{12}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find lowest common denominator before subtracting fractions
  • Technique: Convert 34 \frac{3}{4} to 912 \frac{9}{12} and 16 \frac{1}{6} to 212 \frac{2}{12}
  • Check: Verify 912−212=712 \frac{9}{12} - \frac{2}{12} = \frac{7}{12} is in simplest form ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting numerators and denominators separately
    Don't subtract 3-1=2 and 4-6=-2 to get 2−2 \frac{2}{-2} ! This completely ignores fraction rules and gives wrong results. Always find a common denominator first, then subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \frac{3}{2}-\frac{1}{2}=\text{?} \)

FAQ

Everything you need to know about this question

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

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Fractions represent parts of a whole. You can only combine fractions when they have the same-sized parts (same denominator). Different denominators mean different-sized pieces!

How do I find the LCD of 4 and 6?

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List multiples of each: 4, 8, 12, 16... and 6, 12, 18... The first number that appears in both lists is your LCD. For 4 and 6, it's 12!

Do I always need to simplify my final answer?

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Yes! Always check if your answer can be simplified. For 712 \frac{7}{12} , since 7 and 12 share no common factors, it's already in simplest form.

What if the LCD is really big? Is there an easier way?

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The LCD is actually the smallest common denominator! Using it makes your numbers smaller and easier to work with than just multiplying the denominators together.

Can I convert to decimals instead?

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You could, but fractions are often more exact. Converting 34 \frac{3}{4} and 16 \frac{1}{6} to decimals gives repeating decimals that are harder to work with!

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