🧮 Average & Total Basics

The one line that cracks almost every average question is the same formula read backwards:

$\text{total}=\text{average}\times\text{count}$

Why it matters: totals can be added and subtracted, but averages cannot. So the moment a question gives you an average, multiply by the count to get a total you can actually work with.

• Missing number: find the total with it and the total without it; the gap is the number. If a total of 6 numbers is $132$ and one is $12$, the other five sum to $120$, so their average is $120\div5$.

• Combining groups: add every group's total, add every group's count, divide once. Never average the averages unless the groups are the same size — a larger group always drags the answer towards its own value.