Question

find the number that makes the ratio equivalent to 8:16. \boxed{ }:96

Explanation:

Step1: Simplify the given ratio

The ratio \(8:16\) can be simplified by dividing both parts by their greatest common divisor, which is 8. So, \(\frac{8}{8}:\frac{16}{8}=1:2\). This means the first number is half of the second number in an equivalent ratio.

Step2: Find the missing number

We have the ratio \(\square:96\) and we know the simplified ratio is \(1:2\). Let the missing number be \(x\). So, \(\frac{x}{96}=\frac{1}{2}\) (since the ratio \(x:96\) is equivalent to \(1:2\)). To find \(x\), we can cross - multiply: \(2x = 96\times1\). Then, solve for \(x\) by dividing both sides by 2: \(x=\frac{96}{2}=48\). We can also think of it as finding the scale factor. The second term in the original ratio is 16 and in the new ratio is 96. The scale factor is \(\frac{96}{16} = 6\). Then, multiply the first term of the original ratio (8) by the scale factor (6): \(8\times6 = 48\).

Answer:

48