Given that 21 over 𝑎 is equal to seven over nine which is equal to 𝑏 over 36, find the values of 𝑎 and 𝑏.
First, we can just copy down the proportion. We notice that our only full fraction is the one in the middle — seven over nine. We can use this seven over nine to help us find 𝑎 and 𝑏.
I know that to go from seven to 21, you multiply seven by three. I also know that when we’re working with fractions, if I multiply the numerator by a value, I must multiply the denominator by the same value. And that means that 𝑎 must be equal to nine times three. Nine times three is 27. 𝑎 is equal to 27.
We can use this same process to find 𝑏. I notice that nine times four equals 36. If I multiply the denominator by a value, I must multiply the numerator by the same value. Seven times four equals 28. 𝑏 must be equal to 28.
The completed proportion looks like this: 21 over 27 is equal to seven over nine which is equal to 28 over 36.