Lesson 4: Use Partial Quotients to Divide

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

When a whole number (the dividend) cannot be evenly divided by another whole number (the divisor), the result is a quotient and a remainder.
The remainder is the amount left over and must be less than the divisor.
The relationship is:

Examples

• Find $125 \div 4$:

The quotient is $31$ with a remainder of $1$, written as $31 \text{ R}1$.

• Find $347 \div 8$:

The quotient is $43$ with a remainder of $3$, written as $43 \text{ R}3$.

Explanation

To divide whole numbers using long division, follow the divide, multiply, subtract, and bring down steps. If you have a non-zero number left after the final subtraction step and no more digits to bring down, that number is the remainder. The remainder represents the part of the dividend that is left over after creating as many equal groups as possible. Always make sure the remainder is smaller than the divisor.

Property

In an area model for division, the dividend is the total area, the divisor is a known side length, the quotient is the other side length, and the remainder consists of leftover units that do not form a complete rectangle. This is represented by the equation:

Examples