Which list shows fractions with denominators that are factors of 100?

Understand the Problem

The question is asking which list of fractions has denominators that are factors of the number 100. To solve it, we need to identify the factors of 100 and compare them with the denominators of each fraction listed.

Answer

B: $4, 5, 20, 50$

Steps to Solve

Identify Factors of 100
First, we need to find the factors of 100. The factors of 100 are all the integers that divide 100 without leaving a remainder.
The factors are:
$$ 1, 2, 4, 5, 10, 20, 25, 50, 100 $$
List Denominators from Each Option
Next, we will extract the denominators from each option:

Option A: $2, 4, 6, 8$
Option B: $4, 5, 20, 50$
Option C: $5, 10, 15, 20$
Option D: $10, 20, 30, 40$

Compare Denominators with Factors of 100
Now, we check which denominators are factors of 100:

For Option A: $2$ (yes), $4$ (yes), $6$ (no), $8$ (no) → Not all factors
For Option B: $4$ (yes), $5$ (yes), $20$ (yes), $50$ (yes) → All factors
For Option C: $5$ (yes), $10$ (yes), $15$ (no), $20$ (yes) → Not all factors
For Option D: $10$ (yes), $20$ (yes), $30$ (no), $40$ (no) → Not all factors

Conclusion
Only Option B has all denominators that are factors of 100.

The correct answer is B: $2, 4, 5, 20, 50$.

More Information

Option B contains denominators of $4$, $5$, $20$, and $50$. Each of these denominators can be evenly divided into $100$:

$100 \div 4 = 25$
$100 \div 5 = 20$
$100 \div 20 = 5$
$100 \div 50 = 2$

This shows that all denominators in Option B are indeed factors of 100.

Tips

Overlooking Non-Factors: Be careful to check each denominator thoroughly against the factors of 100.
Confusing Factors with Multiples: It's important to remember we're looking for factors, not numbers that can be multiplied to get 100.

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