Compare Fractions: Determine the Missing Sign Between 1/4 and 5/12

Q: Why can't I just compare the numerators since 1 is less than 5?

Because the denominators are different! When fractions have different denominators, you can't directly compare numerators. $ \frac{1}{4} $ means 1 part out of 4, while $ \frac{5}{12} $ means 5 parts out of 12 - these are different-sized pieces!

Q: What exactly does cross-multiplication tell me?

Cross-multiplication compares the cross products. When you get 1×12=12 and 5×4=20, you're essentially asking: 'Is 12 equal to 20?' Since 12

Q: Is there another way to compare these fractions?

Yes! You can find a common denominator. The LCD of 4 and 12 is 12, so: $ \frac{1}{4} = \frac{3}{12} $. Now compare $ \frac{3}{12} $ and $ \frac{5}{12} $ - clearly 3

Q: How do I remember which cross product goes with which fraction?

Think diagonally! Draw lines from the numerator of each fraction to the denominator of the other. The left cross product (1×12) represents the left fraction, and the right cross product (5×4) represents the right fraction.

Q: What if the cross products are equal?

Then the fractions are equal! When cross-multiplication gives the same result on both sides, you use the equals sign (=) between the fractions.

Fraction Comparison with Cross-Multiplication Method

Fill in the missing sign:

$\frac{1}{4}☐\frac{5}{12}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 We want to find a common denominator

00:06 Therefore we will multiply the fraction by 3

00:09 Remember to multiply both numerator and denominator

00:17 Now we have a common denominator between the fractions

00:24 When denominators are equal, the larger the numerator, the larger the fraction

00:28 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

Fill in the missing sign:

$\frac{1}{4}☐\frac{5}{12}$

Step-by-step solution

To solve this problem, we'll use the cross-multiplication method to compare the fractions $\frac{1}{4}$ and $\frac{5}{12}$ .

Step 1: Cross-multiply the fractions.
We multiply the numerator of the first fraction by the denominator of the second, and the numerator of the second fraction by the denominator of the first:
$1 \times 12 = 12$
$5 \times 4 = 20$
Step 2: Compare the results from cross-multiplication.
Now, compare the results: $12$ and $20$ .
Since $12 < 20$ , it follows that $\frac{1}{4} < \frac{5}{12}$ .

Therefore, the correct sign to fill in the blank is $<$ .

The solution to the problem is $\frac{1}{4} < \frac{5}{12}$ .

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Cross-multiply to compare fractions without finding common denominators
Technique: Multiply 1×12=12 and 5×4=20, then compare results
Check: Convert to decimals: 1/4=0.25 and 5/12≈0.417, so 0.25<0.417 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators and denominators separately
Don't just look at 1<5 and conclude 1/4<5/12 without considering denominators! This ignores that 4<12, making the first fraction potentially larger. Always use cross-multiplication or find equivalent fractions with common denominators.

Practice Quiz

Test your knowledge with interactive questions

Fill in the missing sign:

$\frac{5}{9}☐\frac{3}{9}$

FAQ

Everything you need to know about this question

Why can't I just compare the numerators since 1 is less than 5?

Because the denominators are different! When fractions have different denominators, you can't directly compare numerators. $\frac{1}{4}$ means 1 part out of 4, while $\frac{5}{12}$ means 5 parts out of 12 - these are different-sized pieces!

What exactly does cross-multiplication tell me?

Cross-multiplication compares the cross products. When you get 1×12=12 and 5×4=20, you're essentially asking: 'Is 12 equal to 20?' Since 12<20, the first fraction is smaller.

Is there another way to compare these fractions?

Yes! You can find a common denominator. The LCD of 4 and 12 is 12, so: $\frac{1}{4} = \frac{3}{12}$ . Now compare $\frac{3}{12}$ and $\frac{5}{12}$ - clearly 3<5!

How do I remember which cross product goes with which fraction?

Think diagonally! Draw lines from the numerator of each fraction to the denominator of the other. The left cross product (1×12) represents the left fraction, and the right cross product (5×4) represents the right fraction.

What if the cross products are equal?

Then the fractions are equal! When cross-multiplication gives the same result on both sides, you use the equals sign (=) between the fractions.

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