Division - Relationship between Multiplication and Division

Multiplication and Division are inverse operations, which means they are opposites. If multiplication combines equal groups to find a total, division takes a total and splits it into equal groups. For example, if you have 3 groups of 4 stars, you have 12 stars in total ($3 \times 4 = 12$); conversely, if you take those 12 stars and put them into 3 rows, each row will have 4 stars ($12 \div 3 = 4$).

A Fact Family consists of three numbers that can be used to create two multiplication and two division equations. Imagine a triangle with the number $15$ at the top vertex and $3$ and $5$ at the bottom two vertices. From this visual, we get: $3 \times 5 = 15$, $5 \times 3 = 15$, $15 \div 3 = 5$, and $15 \div 5 = 3$.

Every multiplication fact (where the factors are different) gives two division facts. For example, the multiplication fact $6 \times 2 = 12$ allows us to derive $12 \div 6 = 2$ and $12 \div 2 = 6$. Visually, if you have 12 blocks arranged in 2 rows of 6, you can see it as 12 shared into 2 groups or 12 shared into 6 groups.

The components of a division sentence relate directly to multiplication. In the equation $20 \div 5 = 4$, $20$ is the Dividend (Total), $5$ is the Divisor (Number of groups), and $4$ is the Quotient (Number in each group). This is the exact reverse of $5 \times 4 = 20$, where the factors are $5$ and $4$ and the product is $20$.

Dividing a number by itself always results in 1, because any number multiplied by 1 is itself. For example, $8 \div 8 = 1$. Visually, if you have 8 chocolates and you give them to 8 children, each child gets exactly 1 chocolate because $8 \times 1 = 8$.

Dividing a number by 1 always results in the number itself. For example, $7 \div 1 = 7$. If you have 7 apples and put them into 1 basket, that basket contains all 7 apples because $1 \times 7 = 7$.

You can check the correctness of a division answer using multiplication. If you calculate $18 \div 3 = 6$, you can verify it by multiplying the quotient ($6$) by the divisor ($3$). Since $6 \times 3 = 18$, your division is correct.