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:
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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.
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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.
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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.
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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