Lesson 1: Making Sense of Division

Property

Division is a process of splitting a total quantity. In this operation, we call the number being divided the dividend and the number dividing it the divisor. The result is the quotient.

Examples

• The expression $81 \div 9$ is read as eighty-one divided by nine, and the result is the quotient of eighty-one and nine.
• The expression $48 \div 6$ is read as forty-eight divided by six, and the result is the quotient of forty-eight and six.
• The expression $5)\overline{45}$ is read as forty-five divided by five, and the result is the quotient of forty-five and five.

Property

Division can be understood as finding the number of times a divisor can be repeatedly subtracted from a dividend until nothing remains. The quotient represents how many times the divisor "fits into" the dividend. This relationship can be expressed as:

Property

By comparing the dividend ($a$) and the divisor ($b$), we can predict if the quotient will be greater than, less than, or equal to 1.

• If the dividend is larger than the divisor ($a > b$), the quotient is greater than 1: $\frac{a}{b} > 1$
• If the dividend is smaller than the divisor ($a < b$), the quotient is less than 1: $\frac{a}{b} < 1$
• If the dividend is equal to the divisor ($a = b$), the quotient is exactly 1: $\frac{a}{b} = 1$