Dividing decimals by integers

Dividing decimals by integers

Lessons

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

Notes:

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

Decimals: Multiplying decimals by integers

  • 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:

Decimals: Multiplying decimals by integers

  • 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)dividend\frac{}{dividend} ), ex. 5) 20\overline{20}
    • writing the statement in the form of a fraction (dividenddivisor\large \frac{dividend}{divisor} ), ex. 205\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

Decimals: Multiplying decimals by integers
  • Introduction
    Introduction to multiplying and dividing decimals with integers:
    a)
    What are the division rules for integers?

    b)
    What are the different formats that you can write a division statement?

    c)
    Dividing decimals with integers using mental math

    d)
    Dividing decimals with integers using regrouping

    e)
    Dividing decimals with integers using base ten (block) models

    f)
    Dividing decimals with integers using long multiplication


  • 1.
    Rewriting decimal-integer division statements and predicting answers
    Write each decimal and integer division statement into long division format and fraction format. Then, state whether the answer will be positive or negative.
    a)
    60.25 ÷ -5 =

    b)
    309.18 ÷ 3 = ?

    c)
    48.36 ÷ -4 = ?


  • 2.
    Dividing decimals with integers without regrouping
    Use mental math to divide the following! First decide if your answer is positive or negative. Then divide each place value with the integer value.
    a)
    12.084 ÷ 4 =

    b)
    8.622 ÷ -2 =

    c)
    15.936 ÷ -3 =


  • 3.
    Dividing decimals with integers WITH regrouping
    Divide each decimal by each integer (regroup if necessary). Circle whether the answer will be positive or negative and rewrite the answer as a standard form decimal.
    a)

    Decimals: Multiplying decimals by integers

    b)

    Decimals: Multiplying decimals by integers

    c)

    Decimals: Multiplying decimals by integers


  • 4.
    Dividing decimals with integers by using base ten (block) models
    Use base ten (block) models to represent the division statement, then solve.
    a)
    5.68 ÷ 2 =

    b)
    6.39 ÷ -3 =

    c)
    8.42 ÷ -4 =


  • 5.
    Long division with decimals and integers
    Use the long division algorithm to divide each decimal with the integer given.
    a)
    6.7 ÷ - 4 =

    b)
    3.25 ÷ 5 =

    c)
    8.491 ÷ -7 =