Division - Division as Repeated Subtraction

Division is the method of distributing a group of items into equal parts. Imagine you have a basket of $12$ apples and you want to give an equal number to $3$ friends; division helps you find out that each friend gets $4$ apples.

Division as Repeated Subtraction is a way to find the answer by subtracting the same number over and over again until you reach zero. If you have $20$ and you keep subtracting $5$, you are performing the division $20 \div 5$.

On a number line, repeated subtraction is visualized as jumping backward from a starting number. To solve $15 \div 3$, you start at $15$ and make equal jumps of $3$ backward ($15 \rightarrow 12 \rightarrow 9 \rightarrow 6 \rightarrow 3 \rightarrow 0$). The total number of jumps you take is the quotient.

The number you are dividing is called the Dividend. The number you are dividing by (or subtracting repeatedly) is called the Divisor. The final answer, which tells you how many times the divisor was subtracted, is called the Quotient.

The symbol for division is $\div$. In a math sentence like $18 \div 6 = 3$, $18$ is the dividend, $6$ is the divisor, and $3$ is the quotient.

Division is the inverse (opposite) of multiplication. If $4 \times 2 = 8$, then $8 \div 2 = 4$. You can visualize this as building a tower of blocks (multiplication) versus taking the tower apart block by block (division).

When you divide any number by $1$, the quotient is always the number itself (e.g., $7 \div 1 = 7$). When you divide a number by itself, the quotient is always $1$ (e.g., $9 \div 9 = 1$).