Determine the Symbol Between Fractions: 1/4 ☐ 5/16

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

The numerators represent different-sized parts! One-fourth is a larger piece than one-sixteenth. You need equal-sized parts (same denominator) to make a fair comparison.

Q: How do I find the least common denominator between 4 and 16?

Since 16 is a multiple of 4 (4 × 4 = 16), the LCD is simply 16. When one denominator divides evenly into the other, the larger number is your LCD.

Q: What if both fractions need to be converted?

Find the LCD of both denominators, then convert both fractions to have that denominator. For example, comparing $ \frac{2}{3} $ and $ \frac{3}{4} $ requires LCD of 12.

Q: Is there a faster way to compare fractions?

You can cross-multiply: multiply 1 × 16 = 16 and 4 × 5 = 20. Since 16 \( \frac{1}{4} . This works but common denominators show the relationship more clearly.

Q: How do I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number. Since $ \frac{4}{16} $ is smaller, the arrow points from $ \frac{1}{4} $ toward $ \frac{5}{16} $, giving us

Fraction Comparison with Common Denominators

Fill in the missing sign:

$\frac{1}{4}☐\frac{5}{16}$

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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'll multiply the fraction by 4

00:09 Remember to multiply both numerator and denominator

00:20 Now we have a common denominator between the fractions

00:23 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:

$\frac{1}{4}☐\frac{5}{16}$

Step-by-step solution

To solve this problem, we'll compare the two fractions, $\frac{1}{4}$ and $\frac{5}{16}$ , by converting them to have a common denominator:

Step 1: Identify the denominators of the two fractions: 4 and 16.
Step 2: Find the least common denominator (LCD). The smallest number both 4 and 16 can divide into is 16.
Step 3: Convert $\frac{1}{4}$ to have a denominator of 16: Multiply both the numerator and the denominator of $\frac{1}{4}$ by 4 to obtain $\frac{4}{16}$ .
Step 4: Now we compare the two fractions: $\frac{4}{16}$ and $\frac{5}{16}$ .
Step 5: Since both fractions have the same denominator, compare the numerators: 4 and 5.

Based on the comparison, 4 is less than 5, which means $\frac{4}{16}$ is less than $\frac{5}{16}$ .

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

Final Answer

$<$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to common denominator before comparing
Technique: Multiply $\frac{1}{4}$ by 4/4 to get $\frac{4}{16}$
Check: With same denominator, compare numerators: 4 < 5 ✓

Common Mistakes

Avoid these frequent errors

Comparing fractions without common denominators
Don't compare 1/4 and 5/16 directly by looking at numerators and denominators separately = wrong comparisons! This ignores that the parts are different sizes. Always convert to common denominators first to ensure accurate comparison.

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 the numerators 1 and 5 directly?

The numerators represent different-sized parts! One-fourth is a larger piece than one-sixteenth. You need equal-sized parts (same denominator) to make a fair comparison.

How do I find the least common denominator between 4 and 16?

Since 16 is a multiple of 4 (4 × 4 = 16), the LCD is simply 16. When one denominator divides evenly into the other, the larger number is your LCD.

What if both fractions need to be converted?

Find the LCD of both denominators, then convert both fractions to have that denominator. For example, comparing $\frac{2}{3}$ and $\frac{3}{4}$ requires LCD of 12.

Is there a faster way to compare fractions?

You can cross-multiply: multiply 1 × 16 = 16 and 4 × 5 = 20. Since 16 < 20, we know $\frac{1}{4} < \frac{5}{16}$ . This works but common denominators show the relationship more clearly.

How do I remember which symbol to use?

Think of the symbols as arrows pointing to the smaller number. Since $\frac{4}{16}$ is smaller, the arrow points from $\frac{1}{4}$ toward $\frac{5}{16}$ , giving us <.

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