Elsa used the multiplication table below to write ratios that are equivalent to StartFraction 12 Over 4 EndFraction.

Question

A multiplication table.

One number is missing from the equivalent ratio, as shown.

StartFraction blank Over 12 EndFraction

What is the missing number?
6
18
24
36

Answer 1

To find the missing number in the equivalent ratio \( \frac{\text{blank}}{12} \) that is equivalent to \( \frac{12}{4} \), we can first simplify \( \frac{12}{4} \):

\[ \frac{12}{4} = 3 \]

Now, to find an equivalent ratio, we will set up the equivalent ratio \( \frac{3}{1} \) (since 3 is the simplified form of \( \frac{12}{4} \)) and express it in terms of the new ratio \( \frac{x}{12} \):

To find \( x \), we can set up the proportion:

\[ \frac{3}{1} = \frac{x}{12} \]

Now, cross-multiply:

\[ 3 \cdot 12 = 1 \cdot x \]

This simplifies to:

\[ 36 = x \]

Thus, the missing number is \( 36 \).