Dividing decimals by integers

In this lesson, we will learn:

• What are the division rules for decimals and integers?
• How to divide decimals with integers: using mental math (with regrouping), base ten (block) models, and long division

• Numbers that are integers can be defined as positive and negative whole numbers:

• What happens when we divide decimals with integers? It’s the same as multiplication!
• When dividing a decimal by a positive integer, the answer will be positive.
• When dividing a decimal by a negative integer, the answer will be negative.
• Negative decimals are also possible, so the full set of rules are:

• When dividing decimals with integers, there are multiple ways to write a division statement, and it’s important to know where to put the dividend (the number being divided) and the divisor (the number you will divide by):
• writing the statement from left to right (dividend ÷ divisor =), ex. 20 ÷ 5 =
• writing the statement in long division format (divisor)$\frac{}{dividend}$), ex. 5) $\overline{20}$
• writing the statement in the form of a fraction ($\large \frac{dividend}{divisor}$), ex. $\frac{20}{5}$


• When dividing decimals with integers we can use three methods:
$\qquad$ 1. Using mental math (and regrouping)
$\qquad$ 2. Using base ten (block models)
$\qquad$ 3. Using the long division algorithm


• When using mental math, we use our division table knowledge and:
• Divide each place value by the integer
• If you are unable to divide, you will need to regroup to create a bigger number in the smaller neighbor place value (ex. 1 ones = 10 tenths, 1 tenths = 10 hundredths, 1 hundredth = 10 thousandths)


• We can also show decimal and integer division using base ten (block) models.
• We will deal with each place value separately when deciding how to represent the decimals.
• Then, decide whether your answer will be positive or negative. And, interpret the integer division as follows:
• i.e. ÷ 2 means out of every two blocks, keep one block
• i.e. ÷ 3 means out of every three blocks, keep one block
• i.e. ÷ 4 means out of every four blocks, keep one block


• To divide decimals and integers using the standard algorithm for long division:
• Write your division statement into the long division format and determine whether your answer will be positive or negative
• Line up the decimal place in the dividend and the quotient (the answer); this will decide how many decimal places there will be in your answer