The Multiplication and Division Link

Multiplication and division are like a pair of shoes—they belong together! In math, we call them inverse operations. This means they do the exact opposite of each other. Multiplication takes small, equal groups and puts them together to find a big total. Division takes that big total and breaks it back down into small, equal groups. If multiplication 'builds' a tower of blocks, division 'takes it apart' block by block. Because they are opposites, if you know one multiplication fact, you can use it to solve two different division problems!

A fact family is a group of math facts that all use the same three numbers. Just like people in a family are related, these numbers are stuck together! For any three numbers like $3$, $5$, and $15$, you can make four different facts: two multiplication and two division.

1. $3 \times 5 = 15$ 2. $5 \times 3 = 15$ 3. $15 \div 3 = 5$ 4. $15 \div 5 = 3$

Notice how the biggest number ($15$) is always the answer in multiplication, but it is always the starting number in division!

Sometimes, a math problem has a 'hole' in it, like $4 \times ? = 20$. Because multiplication and division are linked, you can use a related fact to find the answer. To solve $4 \times ? = 20$, you can ask yourself: 'How many groups of $4$ fit into $20$?' This is the same as solving $20 \div 4$. By using the operation you know best, you can solve the one that looks tricky!