Karima, Brenda, Xavier, and Jody are looking for ratios which are equivalent to 4:8 in the columns of the multiplication table below.

Question

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

Answer 1

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