Lesson 2: Fluently Divide Whole Numbers and Decimals

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

To divide a whole number by a whole number and find a decimal quotient, perform long division.
If there is a remainder, place a decimal point in the dividend and the quotient.
Then, annex zeros to the dividend and continue the division process until the remainder is zero or you reach the desired number of decimal places.

Examples

• $13 \div 4 = 3.25$

Dividing 13 by 4 gives 3 with a remainder of 1. Adding a decimal point and a zero makes 10, which divided by 4 gives 2, and bringing down another zero gives 10 ÷ 4 = 2.5, resulting in 3.25.

• $99 \div 12 = 8.25$

Dividing 99 by 12 gives 8 with a remainder of 3. Adding a decimal point and a zero turns it into 30, which divided by 12 gives 2 with a remainder of 6. Bringing down another zero makes 60 ÷ 12 = 5, so the result is 8.25.

• $7 \div 8 = 0.875$

Dividing 7 by 8 gives 0 with a remainder of 7. Adding a decimal point and a zero gives 70 ÷ 8 = 8 remainder 6. Bringing down another zero gives 60 ÷ 8 = 7 remainder 4, and another zero gives 40 ÷ 8 = 5, so the final answer is 0.875.

Explanation

When a whole number division results in a remainder, you can continue dividing to find an exact decimal answer. This is done by adding a decimal point and zeros to the end of the dividend. Remember to place the decimal point in your answer (the quotient) directly above the new decimal point in the dividend. This process converts the remainder into a decimal part of the quotient.

Property

How to divide decimal numbers:
Step 1. Make the divisor a whole number by moving the decimal point all the way to the right. Move the decimal point in the dividend the same number of places to the right, writing zeros as needed.
Step 2. Divide. Place the decimal point in the quotient above the decimal point in the dividend.
Step 3. Write the quotient.

Examples