# Multiplying decimals by integers

### Multiplying decimals by integers

#### Lessons

In this lesson, we will learn:

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

Notes:

• What is an integer?
• If we look at the number line of whole numbers, there are opposite numbers (on the left side of the zero) that are negative which mirror the positive numbers (on the right side). These are all integers:

• What happens when we multiply decimals with integers?
• When multiplying a decimal by a positive integer, the answer will be positive.
• When multiplying a decimal by a negative integer, the answer will be negative.
• Mostly we will look at positive decimals for this lesson, but it is also possible to have negative decimals too

• where (-) × (+) = (-) and (-) × (-) = (+)

• When multiplying 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 multiplication algorithm

• When using mental math, we use our times tables knowledge and:
• Multiply each place value by the integer separately (using times tables)
• You will need to regroup if you get a double-digit product in a place value
• Regroup into the next biggest place value (ex. 10 thousandths = 1 hundredth; 10 hundredths = 1 tenth, 10 tenths = 1 ones)

• We can also show decimal and integer multiplication using base ten (block) models.
• Don’t forget there are two types of models: (1) one where a whole is represented by a hundred block, and (2) another where a whole is represented by a thousand cube
• Multiply each type of block by the integer value and draw
• Regroup whenever you see 10 of a type of block into the next bigger type of block (ones $\,$$\,$ tens $\,$$\,$ hundreds $\,$$\,$ thousands)

• Ex. When one whole = hundred block, use blocks to solve for 1.3 × 3

• To multiply decimals and integers using the standard algorithm for long multiplication:
• First, ignore the decimal and whether or not the integer is negative
• Do long multiplication as you would with whole numbers
• The number of decimal places in your question will be the number of decimal places in your answer
• You can always decide if your answer will be positive or negative at the end (or you could have made a note at the beginning too, just don’t forget to do it!)

Ex. Multiply 4.56 × 7

• Introduction
Introduction to multiplying and dividing decimals with integers:
a)
What are integers?

b)
What are the multiplication rules for decimals and integers?

c)
Multiplying decimals with integers using mental math

d)
Multiplying decimals with integers using regrouping

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

f)
Multiplying decimals with integers using long multiplication

• 1.
Multiplying decimals with integers without regrouping
Use mental math to multiply the following! First decide if your answer is positive or negative. Then multiply each place value with the integer value.
a)
4 × 8.2 =

b)
-2 × 4.13 =

c)
-3 × 2.131 =

• 2.
Multiplying decimals with integers WITH regrouping
Multiply each decimal and integer pair. Regroup if necessary, circle whether the answer will be positive or negative and rewrite the answer as a standard form decimal.
a)

b)

c)

• 3.
Multiplying decimals with integers using base ten (block) models
Use base ten (block) models to show each multiplication statement and solve
a)
-2 × 2.156 =

b)
8 × 3.84 =

c)
-6 × 0.937 =

• 4.
Long multiplication with decimals and integers
Use the long multiplication algorithm to multiply each decimal with the integer given.
a)

b)

c)