Miguel tells his teacher that [tex]$\frac{1}{5}$[/tex] is the same as [tex]$20 \%$[/tex]. Which best justifies Miguel's answer?
A. 5 goes into 100 twenty times, so [tex]$20 \%$[/tex] is the answer.
B. 5 goes into 20 four times, and 5 times 4 is 20, so [tex]$20 \%$[/tex] is the answer.
C. 5 goes into 100 twenty times, and 1 times 20 is 20, so [tex]$20 \%$[/tex] is the answer.
D. 5 goes into 20 four times, and 5 times 4 times 1 is 20, so [tex]$20 \%$[/tex] is the answer.
Answer (1)
Recognizes that 5 1 needs to be expressed as a percentage.
Analyzes each justification to determine its clarity and correctness.
Identifies that '5 goes into 100 twenty times, so 20% is the answer' correctly implies 5 1 = 100 20 = 20% .
Concludes that the best justification is the one that directly relates dividing 100 by 5 to finding the equivalent percentage: $\boxed{5 goes into 100 twenty times, so 20% is the answer.}
Explanation
Problem Analysis Miguel claims that 5 1 is equivalent to 20% . We need to identify the best justification for this statement among the given options.
Analyzing Justifications Let's analyze each justification:
Justification 1: "5 goes into 100 twenty times, so 20% is the answer." This implies 5 1 = 100 20 = 20% , which is correct.
Justification 2: "5 goes into 20 four times, and 5 times 4 is 20, so 20% is the answer." This justification is not clear and doesn't directly explain the equivalence.
Justification 3: "5 goes into 100 twenty times, and 1 times 20 is 20, so 20% is the answer." This also implies 5 1 = 100 20 = 20% , which is correct.
Justification 4: "5 goes into 20 four times, and 5 times 4 times 1 is 20, so 20% is the answer." This justification is also unclear.
Comparing Correct Justifications Comparing Justification 1 and Justification 3, both are correct and explain why 5 1 is equal to 20% . However, Justification 1 is more concise and directly relates 5 going into 100 to the percentage.
Selecting the Best Justification Therefore, the best justification is: 5 goes into 100 twenty times, so 20% is the answer.
Final Answer The best justification for Miguel's answer is that 5 goes into 100 twenty times, meaning 5 1 = 100 20 , which is equal to 20% .
Examples
Imagine you're sharing a pizza with 5 friends, and you each get one slice. That means you get 5 1 of the pizza. Now, if you cut the pizza into 100 tiny slices, your share of 5 1 would be 20 of those tiny slices, which is 20% of the whole pizza. This shows how fractions and percentages are related in everyday situations.
