Compare Fractions: Determine if 1/5 is Greater or Less Than 3/4

Q: Why can't I just compare 1 and 3 directly?

Because different denominators mean different-sized pieces! Think of it like comparing 1 slice of a 5-piece pizza to 3 slices of a 4-piece pizza - you need to cut them into equal pieces first.

Q: How do I find the common denominator?

Find the Least Common Multiple (LCM) of both denominators. For 5 and 4, you can multiply them together: $ 5 \times 4 = 20 $ since they share no common factors.

Q: Is there a faster way than finding common denominators?

Yes! You can cross multiply: $ \frac{1}{5} $ vs $ \frac{3}{4} $ becomes $ 1 \times 4 = 4 $ vs $ 3 \times 5 = 15 $. Since 4 \( \frac{1}{5} .

Q: What if the fractions have really big denominators?

Look for patterns first! Sometimes you can see that one fraction is clearly much smaller (like $ \frac{1}{100} $) or use benchmark fractions like $ \frac{1}{2} $ to estimate quickly.

Q: How do I know which fraction is bigger without calculating?

Visual thinking helps! $ \frac{1}{5} $ is 1 out of 5 equal parts, while $ \frac{3}{4} $ is 3 out of 4 parts. Since $ \frac{3}{4} $ is close to 1 whole and $ \frac{1}{5} $ is much smaller, $ \frac{3}{4} $ is clearly bigger.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 We are looking for the right sign. Let's go!

00:09 We want to find a common denominator. Ready?

00:13 We do this by multiplying each fraction by the other's denominator. Let's multiply.

00:18 Remember, multiply both top and bottom numbers of each fraction.

00:26 Now, let's repeat the same steps for the second fraction.

00:30 Make sure you multiply by the denominator of the second fraction.

00:35 Don't forget to multiply both the numerator and the denominator.

00:40 Great! Now we have common denominators. Well done!

00:45 When denominators are the same, bigger numerators mean bigger fractions.

00:54 And that's the solution to our problem! Nice work!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Fill in the missing sign:

$\frac{1}{5}☐\frac{3}{4}$

2

Step-by-step solution

To compare the fractions $\frac{1}{5}$ and $\frac{3}{4}$ , we'll use the following steps:

Step 1: Find a common denominator for the fractions.
Step 2: Convert each fraction to an equivalent fraction with the common denominator.
Step 3: Compare the numerators of the equivalent fractions.

Step 1: The denominators of the two fractions are 5 and 4. To find a common denominator, we multiply these together, getting $5 \times 4 = 20$ . So, our common denominator is 20.

Step 2: Convert each fraction to have the denominator of 20.

$\frac{1}{5}$ : Multiply the numerator and denominator by 4 to get $\frac{1 \times 4}{5 \times 4} = \frac{4}{20}$ .
$\frac{3}{4}$ : Multiply the numerator and denominator by 5 to get $\frac{3 \times 5}{4 \times 5} = \frac{15}{20}$ .

Step 3: Now compare the numerators of the equivalent fractions:

$\frac{4}{20}$ compared to $\frac{15}{20}$ (both having the denominator of 20):

$4 < 15$ implies $\frac{4}{20} < \frac{15}{20}$ .

Therefore, $\frac{1}{5} < \frac{3}{4}$ .

Thus, the correct mathematical sign to fill in is $<$ .

Therefore, the missing sign in the expression $\frac{1}{5} ☐ \frac{3}{4}$ is $<$ .

3

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to same denominator before comparing numerators
Technique: Find LCD: 1/5 = 4/20 and 3/4 = 15/20
Check: Compare numerators with same denominator: 4 < 15 ✓

Common Mistakes

Avoid these frequent errors

Comparing numerators without converting denominators
Don't compare 1 to 3 directly without converting = wrong comparison! Different denominators mean different-sized pieces, so you can't compare numerators directly. Always find a common denominator first.

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

Why can't I just compare 1 and 3 directly?

+

Because different denominators mean different-sized pieces! Think of it like comparing 1 slice of a 5-piece pizza to 3 slices of a 4-piece pizza - you need to cut them into equal pieces first.

How do I find the common denominator?

+

Find the Least Common Multiple (LCM) of both denominators. For 5 and 4, you can multiply them together: $5 \times 4 = 20$ since they share no common factors.

Is there a faster way than finding common denominators?

+

Yes! You can cross multiply: $\frac{1}{5}$ vs $\frac{3}{4}$ becomes $1 \times 4 = 4$ vs $3 \times 5 = 15$ . Since 4 < 15, we get $\frac{1}{5} < \frac{3}{4}$ .

What if the fractions have really big denominators?

+

Look for patterns first! Sometimes you can see that one fraction is clearly much smaller (like $\frac{1}{100}$ ) or use benchmark fractions like $\frac{1}{2}$ to estimate quickly.

How do I know which fraction is bigger without calculating?

+

Visual thinking helps! $\frac{1}{5}$ is 1 out of 5 equal parts, while $\frac{3}{4}$ is 3 out of 4 parts. Since $\frac{3}{4}$ is close to 1 whole and $\frac{1}{5}$ is much smaller, $\frac{3}{4}$ is clearly bigger.

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Compare Fractions: Determine if 1/5 is Greater or Less Than 3/4

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