Compare Fractions: Determine the Correct Symbol Between 1/4 and 5/6

Q: How do I find the LCD of 4 and 6?

List the multiples of each number: 4: 4, 8, 12, 16... and 6: 6, 12, 18... The smallest number that appears in both lists is 12!

Q: Can I use decimals instead of finding common denominators?

Yes! Convert $ \frac{1}{4} = 0.25 $ and $ \frac{5}{6} ≈ 0.833 $. Since 0.25 common denominators give exact comparisons.

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

Try cross-multiplication! For $ \frac{1}{4} $ vs $ \frac{5}{6} $: compare 1×6 = 6 and 4×5 = 20. Since 6

Q: Why can't I just compare 1 and 5?

Because the denominators are different! $ \frac{1}{4} $ means 1 out of 4 equal parts, while $ \frac{5}{6} $ means 5 out of 6 equal parts. You need the same-sized parts to compare fairly.

Q: How do I remember which way the inequality sign points?

Think of it like a hungry alligator! The open mouth always faces the larger number. So in $ \frac{1}{4} , the mouth opens toward \( \frac{5}{6} $ because it's bigger.

Fraction Comparison with Common Denominators

Fill in the missing sign:

$\frac{1}{4}☐\frac{5}{6}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's choose the right math sign.

00:08 Next, we'll find a common denominator.

00:12 So, multiply each fraction by the other's denominator.

00:16 Be sure to multiply both the top number and the bottom number.

00:25 We'll do the same for the second fraction, as well.

00:29 Again, multiply both numerator and denominator.

00:34 Great! Now, both fractions have the same bottom number.

00:39 With equal denominators, the larger numerator means a larger fraction.

00:45 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$\frac{1}{4}☐\frac{5}{6}$

Step-by-step solution

To solve this problem, we'll compare the fractions: $\frac{1}{4}$ and $\frac{5}{6}$ .

Step 1: Determine the least common denominator (LCD) of the fractions' denominators, 4 and 6. The LCM of 4 and 6 is 12.
Step 2: Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 12:

$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Step 3: Convert $\frac{5}{6}$ to an equivalent fraction with a denominator of 12:

$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$

Step 4: Compare the numerators: $\frac{3}{12}$ compared to $\frac{10}{12}$ .

Since $3$ is less than $10$ , we conclude that $\frac{1}{4}$ is less than $\frac{5}{6}$ .

Thus, the missing sign is $<$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD to convert fractions before comparing
Technique: Convert $\frac{1}{4}$ to $\frac{3}{12}$ and $\frac{5}{6}$ to $\frac{10}{12}$ using LCD 12
Check: Compare numerators: 3 < 10, so $\frac{1}{4}$ < $\frac{5}{6}$ ✓

Common Mistakes

Avoid these frequent errors

Comparing denominators instead of numerators
Don't compare 4 and 6 directly to determine which fraction is larger = wrong comparison! This ignores the actual fraction values. Always find common denominators first, then compare the numerators of the equivalent fractions.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{25}☐\frac{1}{5}$

FAQ

Everything you need to know about this question

How do I find the LCD of 4 and 6?

List the multiples of each number: 4: 4, 8, 12, 16... and 6: 6, 12, 18... The smallest number that appears in both lists is 12!

Can I use decimals instead of finding common denominators?

Yes! Convert $\frac{1}{4} = 0.25$ and $\frac{5}{6} ≈ 0.833$ . Since 0.25 < 0.833, we get the same answer. But common denominators give exact comparisons.

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

Try cross-multiplication! For $\frac{1}{4}$ vs $\frac{5}{6}$ : compare 1×6 = 6 and 4×5 = 20. Since 6 < 20, the first fraction is smaller.

Why can't I just compare 1 and 5?

Because the denominators are different! $\frac{1}{4}$ means 1 out of 4 equal parts, while $\frac{5}{6}$ means 5 out of 6 equal parts. You need the same-sized parts to compare fairly.

How do I remember which way the inequality sign points?

Think of it like a hungry alligator! The open mouth always faces the larger number. So in $\frac{1}{4} < \frac{5}{6}$ , the mouth opens toward $\frac{5}{6}$ because it's bigger.

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