Lesson 7: Concepts of Division (Optional)

Property

Division is the process of splitting a quantity into equal groups. For whole numbers, the equation $a \div b = c$ means that the total amount $a$ is split into $b$ equal groups with $c$ in each group, or that $a$ is split into groups of size $b$ resulting in $c$ groups.

Examples

• If 20 cookies are shared equally among 4 friends, each friend gets $20 \div 4 = 5$ cookies.
• If you have 15 apples and you put them into bags of 5, you will have $15 \div 5 = 3$ bags.
• $56 \div 7 = 8$

Explanation

Division helps us solve problems involving separating a total amount into equal parts. This can be thought of in two ways: sharing a total among a known number of groups, or finding how many groups of a certain size fit into the total. For example, $12 \div 3$ can mean "12 shared into 3 groups" (4 in each group) or "how many groups of 3 are in 12" (4 groups). This foundational concept of division with whole numbers provides the basis for understanding division with other types of numbers, like fractions.

Property

Solving a division problem, such as $A \div B = ?$, is the same as finding the unknown factor in the related multiplication equation, $B \times ? = A$.
The quotient of the division is the unknown factor.

Examples