Unit rate with fractions

Welcome! I'm really looking forward to working with you on mastering unit rates with fractions.

Before we dive in, let me ask you a quick question so I can tailor our pace perfectly: Are you learning this for a specific grade level or math class, and how comfortable are you already with dividing fractions?

I'm in middle school but struggle a bit with dividing fractions

Thanks for sharing that! Being in middle school is the perfect time to master this, and don't worry about the fraction division part—we'll break it down step-by-step so it makes complete sense. Let's start with the basics of what a actually is before we bring in any tricky fractions.

Imagine you go to the store and buy a pack of 3 sports drinks for $6. That relationship is a rate! We can write it as a fraction:

\frac{\text{\$6}}{\text{3 sports drinks}}

But if we want to find out how much just one sports drink costs, we are looking for a unit rate. A is a special rate where the denominator (the bottom number of our fraction) is simplified to exactly 1.

To turn our drink rate into a unit rate, we want to change that bottom 3 into a 1. To keep the fraction equivalent, we divide both the top and the bottom by 3:

\frac{\text{\$6} \div 3}{\text{3 drinks} \div 3} = \frac{\text{\$2}}{\text{1 drink}}

So, our unit rate is $2 per drink! How does this feel so far? Does the idea of making the bottom number 1 to find a "unit rate" make sense?