Compare Fractions: Find the Missing Symbol Between 7/4 and 2/4

Q: Why can I compare numerators when denominators are the same?

When fractions have the same denominator, they represent the same-sized pieces. So $ \frac{7}{4} $ means 7 pieces of size 1/4, while $ \frac{2}{4} $ means 2 pieces of the same size. More pieces = bigger value!

Q: What if the denominators were different?

If denominators are different, you need to find a common denominator first. Convert both fractions so they have the same denominator, then compare numerators.

Q: Can I convert to mixed numbers to make it easier?

Absolutely! $ \frac{7}{4} = 1\frac{3}{4} $ and $ \frac{2}{4} = \frac{1}{2} $. Since 1¾ > ½, this confirms our answer.

Q: What symbol should I use in my answer?

Use the greater than symbol (>) because 7 is greater than 2. Remember: the symbol points to the smaller number, so $ \frac{7}{4} > \frac{2}{4} $.

Fraction Comparison with Same Denominators

Fill in the missing answer:

$\frac{7}{4}☐\frac{2}{4}$

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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 The denominator is equal

00:08 When the denominators are equal, the fraction with the larger numerator is the larger fraction

00:11 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 answer:

$\frac{7}{4}☐\frac{2}{4}$

Step-by-step solution

Let's solve the problem step-by-step:

Both fractions in the problem, $\frac{7}{4}$ and $\frac{2}{4}$ , have the same denominator. This allows us to directly compare their numerators.

The numerators are 7 and 2, respectively. Therefore, we need to determine whether 7 is less than, greater than, or equal to 2.

Comparing 7 and 2:

$7 > 2$

Since 7 is greater than 2, it follows that:

$\frac{7}{4} > \frac{2}{4}$

The correct inequality symbol to fill in the blank is $>$ .

Thus, the solution to the problem is $\frac{7}{4} > \frac{2}{4}$ .

Therefore, the correct choice from the available options is choice 2: $>$ .

Final Answer

$>$

Key Points to Remember

Essential concepts to master this topic

Rule: When denominators are equal, compare numerators directly
Technique: Compare 7 and 2: since 7 > 2, then $\frac{7}{4} > \frac{2}{4}$
Check: Convert to decimals: 1.75 > 0.5 confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Comparing denominators instead of numerators
Don't compare the denominators when they're the same = wrong focus! This leads to confusion about which fraction is larger. Always compare the numerators when denominators are equal.

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 I compare numerators when denominators are the same?

When fractions have the same denominator, they represent the same-sized pieces. So $\frac{7}{4}$ means 7 pieces of size 1/4, while $\frac{2}{4}$ means 2 pieces of the same size. More pieces = bigger value!

What if the denominators were different?

If denominators are different, you need to find a common denominator first. Convert both fractions so they have the same denominator, then compare numerators.

How can I visualize this comparison?

Think of pizza slices! If both fractions represent quarters of a pizza, $\frac{7}{4}$ is 7 quarters (1¾ pizzas) and $\frac{2}{4}$ is 2 quarters (½ pizza). Clearly 1¾ > ½!

Can I convert to mixed numbers to make it easier?

Absolutely! $\frac{7}{4} = 1\frac{3}{4}$ and $\frac{2}{4} = \frac{1}{2}$ . Since 1¾ > ½, this confirms our answer.

What symbol should I use in my answer?

Use the greater than symbol (>) because 7 is greater than 2. Remember: the symbol points to the smaller number, so $\frac{7}{4} > \frac{2}{4}$ .

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