Question
Karima, Brenda, Xavier, and Jody are looking for ratios which are equivalent to 4:8 in the columns of the multiplication table below.
A multiplication table.
Karima says that only the numbers in columns 4 and 8 form equivalent ratios for 4:8.
Brenda says that only Karima’s ratios and the numbers in columns 2 and 4 form equivalent ratios for 4:8.
Xavier says that Karima’s ratios, Brenda’s ratios, and the numbers in columns 1 and 2 form equivalent ratios for 4:8.
Jody says that any pair of columns with even numbers forms equivalent ratios for 4:8.
Who is correct?
Karima
Brenda
Xavier
Jody
Mark this and return
A multiplication table.
Karima says that only the numbers in columns 4 and 8 form equivalent ratios for 4:8.
Brenda says that only Karima’s ratios and the numbers in columns 2 and 4 form equivalent ratios for 4:8.
Xavier says that Karima’s ratios, Brenda’s ratios, and the numbers in columns 1 and 2 form equivalent ratios for 4:8.
Jody says that any pair of columns with even numbers forms equivalent ratios for 4:8.
Who is correct?
Karima
Brenda
Xavier
Jody
Mark this and return
Answers
GPT-4o mini
To determine who is correct, we need to analyze the ratios formed by the columns of the multiplication table in relation to the ratio 4:8. First, we simplify 4:8:
\[
4:8 = \frac{4}{8} = \frac{1}{2}
\]
So, any pair of ratios that simplifies to 1:2 will be equivalent to 4:8.
Now, let's examine each person's claims based on the even columns of the multiplication table:
1. **Karima** claims that **only the numbers in columns 4 and 8** form equivalent ratios for 4:8.
- Column 4 contains multiples of 4 (4, 8, 12, 16, ...).
- Column 8 contains multiples of 8 (8, 16, 24, 32, ...).
- The ratio of any number in column 4 to an equivalent number in column 8 will always simplify to 1:2.
- **Karima is partially correct**, but it's not the only set of equivalent ratios.
2. **Brenda** claims that **Karima’s ratios and the numbers in columns 2 and 4** form equivalent ratios for 4:8.
- Column 2 contains multiples of 2 (2, 4, 6, 8, ...).
- For example, the ratio of (2, 4) simplifies to 1:2, and the ratios of 2 & 4 or 4 & 8 still maintain the 1:2 ratio.
- **Brenda is also partially correct**, as she includes equivalent ratios from column 4. But she still may not have captured all equivalent ratios.
3. **Xavier** claims that **Karima’s ratios, Brenda’s ratios, and the numbers in columns 1 and 2** form equivalent ratios for 4:8.
- Column 1 contains multiples of 1 (1, 2, 3, 4, ...).
- Although 1:2 and any higher equivalents are valid (like 4:8), pairs where one number is 1 and the other is higher will not preserve the 1:2 ratio. For instance, the number 2 and 1 will not form ratios that simplify directly to match column pairs forming 1:2 through 4:8.
- **Xavier is incorrect**, because he includes column 1, which does not universally form the necessary ratios.
4. **Jody** claims that **any pair of columns with even numbers** forms equivalent ratios for 4:8.
- While many even numbers do share ratios simplifying to 1:2, not all pairs of even number columns do. For instance, while column 2 and column 4 do, column 2 and column 6 do not simplify correctly when cross-referenced.
- **Jody is also incorrect**, as this statement is too broad – not every even pair forms a 1:2 ratio.
In conclusion, **Brenda is the most correct** because she accurately identifies a broader range of ratios that simplify to the correct ratio. The correct answer is:
**Brenda**
\[
4:8 = \frac{4}{8} = \frac{1}{2}
\]
So, any pair of ratios that simplifies to 1:2 will be equivalent to 4:8.
Now, let's examine each person's claims based on the even columns of the multiplication table:
1. **Karima** claims that **only the numbers in columns 4 and 8** form equivalent ratios for 4:8.
- Column 4 contains multiples of 4 (4, 8, 12, 16, ...).
- Column 8 contains multiples of 8 (8, 16, 24, 32, ...).
- The ratio of any number in column 4 to an equivalent number in column 8 will always simplify to 1:2.
- **Karima is partially correct**, but it's not the only set of equivalent ratios.
2. **Brenda** claims that **Karima’s ratios and the numbers in columns 2 and 4** form equivalent ratios for 4:8.
- Column 2 contains multiples of 2 (2, 4, 6, 8, ...).
- For example, the ratio of (2, 4) simplifies to 1:2, and the ratios of 2 & 4 or 4 & 8 still maintain the 1:2 ratio.
- **Brenda is also partially correct**, as she includes equivalent ratios from column 4. But she still may not have captured all equivalent ratios.
3. **Xavier** claims that **Karima’s ratios, Brenda’s ratios, and the numbers in columns 1 and 2** form equivalent ratios for 4:8.
- Column 1 contains multiples of 1 (1, 2, 3, 4, ...).
- Although 1:2 and any higher equivalents are valid (like 4:8), pairs where one number is 1 and the other is higher will not preserve the 1:2 ratio. For instance, the number 2 and 1 will not form ratios that simplify directly to match column pairs forming 1:2 through 4:8.
- **Xavier is incorrect**, because he includes column 1, which does not universally form the necessary ratios.
4. **Jody** claims that **any pair of columns with even numbers** forms equivalent ratios for 4:8.
- While many even numbers do share ratios simplifying to 1:2, not all pairs of even number columns do. For instance, while column 2 and column 4 do, column 2 and column 6 do not simplify correctly when cross-referenced.
- **Jody is also incorrect**, as this statement is too broad – not every even pair forms a 1:2 ratio.
In conclusion, **Brenda is the most correct** because she accurately identifies a broader range of ratios that simplify to the correct ratio. The correct answer is:
**Brenda**