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Get Started Now- Intro Lesson: a1:57
- Intro Lesson: b5:01
- Intro Lesson: c2:36
- Intro Lesson: d4:04
- Intro Lesson: e6:28
- Intro Lesson: f5:29
- Lesson: 1a1:25
- Lesson: 1b1:28
- Lesson: 1c1:27
- Lesson: 2a2:33
- Lesson: 2b2:29
- Lesson: 2c3:21
- Lesson: 3a5:06
- Lesson: 3b6:01
- Lesson: 3c6:36
- Lesson: 4a2:23
- Lesson: 4b2:50
- Lesson: 4c2:25

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

- 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)
- 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
, and (2) another where a whole is represented by a__hundred block____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!)

$\qquad$ 2. Using base ten (block models)

$\qquad$ 3. Using the long multiplication algorithm

Ex. Multiply 4.56 × 7

- IntroductionIntroduction 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 mathd)Multiplying decimals with integers using regroupinge)Multiplying decimals with integers using base ten (block) modelsf)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 solvea)-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)

10.

Decimals

10.1

What are decimals?

10.2

Multiplying decimals by powers of 10

10.3

Dividing decimals by powers of 10

10.4

Coverting between decimals and fractions

10.5

Comparing and ordering decimals and fractions

10.6

Multiplying decimals with integers

10.7

Dividing decimals with integers

10.8

Word problems for decimals and integers