Determine the ratio between the three numbers 𝑎, 𝑏, and 𝑐 given that 𝑎 to 𝑏 is equal to 10 to one and 𝑏 to 𝑐 is equal to two to one.
So we want to know the ratio between all three numbers: 𝑎 to 𝑏 to 𝑐.
We know that 𝑎 to 𝑏 is 10 to one. And 𝑏 to 𝑐 is two to one. So by presenting the two ratios vertically, we can use the least common multiple of the shared term 𝑏 to make equivalent ratios.
Then, we can write their ratio among all three terms. So we need to make 𝑏 equal between the two ratios. So for 𝑎 to 𝑏, we have 10 to one, so 𝑏 is one. But for 𝑏 to 𝑐, we have two to one, so 𝑏 is two.
So what’ll be the least common multiple between one and two? It would be two.
So we need to make one turn into two. And we can do that by multiplying by two. However, if we multiply the one by two, we must also multiply the 10 by two to keep their ratio equivalent.
10 times two is 20. And one times two is two. So we multiplied by two to get the 20 to two ratio. And then, we go ahead and just bring down the two to one ratio. So now notice the 𝑏s are identical.
And now we can write a ratio among all three terms: 20 to two to one. So this would be our ratio between the three numbers 𝑎, 𝑏, and 𝑐.