𝑔 gallons is equal to 𝑙 liters. Using the fact that 4.5 liters is equal to one gallon, write a formula for 𝑔 in terms of 𝑙.
It might help to think of this a little bit like a ratio. The ratio of 𝑔 to 𝑙 is one to 4.5. For every one gallon, we have 4.5 liters.
To create a formula for 𝑔 in terms of 𝑙, we’re going to divide. We’re going to divide 𝑔, the number of gallons, by 𝑙, the number of liters. Here, that’s one divided by 4.5.
Now, 4.5 as a denominator of a fraction isn’t particularly nice. So we’re going to double. We’re gonna multiply it by two, both the numerator and the denominator of this fraction. And doing so, we get 𝑔 over 𝑙 is the same as two-ninths.
Next, we’re going to multiply both sides of this equation by 𝑙. Remember we’re trying to make 𝑔 the subject. And at the moment, 𝑔 is being divided by 𝑙. The opposite of dividing by 𝑙 is multiplying by 𝑙. And that tells us 𝑔 is equal to two-ninths multiplied by 𝑙.
Our formula for 𝑔 in terms of 𝑙 is 𝑔 is equal to two-ninths 𝑙.