### Key Concepts

- Even numbers and odd numbers
- Multiplication patterns in even and odd numbers

## 4.5 Multiplication patterns: Even and odd numbers.

**Even numbers**: Even numbers are whole numbers that can be divided by 2 with none left over.

- Even numbers have 0, 2, 4, 6 or 8 in the ones place.

** An even number can only be formed by multiplication in three ways:**

- Even x odd
- Odd x even
- Even x even

**Odd numbers**: Odd numbers are whole numbers that cannot be divided by 2 with none left over.

- Odd numbers have 1, 3, 5, 7 or 9 in the ones place.

An odd number can only be formed by multiplication in one way:

- Odd x odd = odd.

### 4.5.1 Even numbers and odd numbers

**Even numbers**: Even numbers are whole numbers that can be divided by 2 with none left over.

Examples for even numbers:

- Even numbers have 0, 2, 4, 6 or 8 in the ones place.

E.g.: 12, 24, 26, 48, 20

**Example:** Highlighted numbers in the table are even numbers from 1 to 100

**Odd numbers**: use patterns to understand the effects of

Example for odd numbers:

- Odd numbers have 1, 3, 5, 7 or 9 in the ones place.

E.g.: 11, 23, 35, 37, 49.

**Example: **Highlighted numbers in the table are odd numbers from 1 to 100

### 4.5.2 Multiplication patterns in even and odd numbers.

Marty says that the product of an even number and an odd number is always even. Is he correct?

### Solution:

Even numbers greater than 0 can be shown as two equal groups.

Think about 2 x 5 and 2 x 7.

2 is even number.

2 x 5 means 2 equal groups of 5.

2 x 5 = 10.

2 x 7 means 2 equal groups of 7.

2 x 7 = 14.

There are always 2 equal groups.

### Generalize:

All even numbers are multiples of 2.

Think about 6 x 3.

You can think of 6 as 3 groups of 2.

Using properties, we can write.

6 x 3 = (2 x 3) x 3 as

6 x 3= 2 x (3 x 3)

So, 6 x 3 = 2 x 9

6 equal groups of 3 = 2 equal groups of 9

So, the product will be even.

**Example 2:**

Marty says that the product of two odd numbers is always odd. Is he correct?

**Solution:**

An odd number cannot be divided by 2 with none left over.

Think about 5 x 7.

5 cannot be divided by 2 with none left over.

7 cannot be divided by 2 with none left over.

35 is odd.

Both factors are odd.

Odd numbers cannot be divided into two equal groups with none left over.

So, odd number x odd number = odd number

## Exercise:

- If you multiply two odd numbers, will the product be even or odd. Explain with an example?
- 8 x 6 =?

8 can be divided by 2? ______.

6 can be divided by 2? _____.

8 x 6 is even or odd.

8 x 6=____. - Circle the numbers that are even.

4. Identify even or odd numbers for the numbers given below:

5. Mike says that the following patterns are true.

a. Odd x even = odd

b. Even x odd =even

Is he correct explain.

6. Find the product and write weather the product is even or odd.

7. Mercy is making party bags for Skylar’s birthday party. She puts 6 bags with 4 toys each bag. How many toys did Mercy put?

8. Emma gives you 3 stickers and Esther gives you 3 times than Emma. How many stickers are there?

9. Ryan has 4 bags of apples. Each bag has 5 apples. How many apples did Ryan have? Is it an even or odd number

10. Kate pack his bag with 15 note books. Does he have an even or odd number of books?

**Concept map:**

### What have we learned:

- Understand even numbers and odd numbers.
- Identify the even numbers and odd numbers.
- Understand multiplication pattern in even and odd numbers.
- Generalize the all even numbers are multiples of 2.

#### Related topics

#### Addition and Multiplication Using Counters & Bar-Diagrams

Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2. Use factors to get the product 3. Write equations to find the unknown. Addition Equation: 8+8+8 =? Multiplication equation: 3×8=? Example 1: Andrew has […]

Read More >>#### Dilation: Definitions, Characteristics, and Similarities

Understanding Dilation A dilation is a transformation that produces an image that is of the same shape and different sizes. Dilation that creates a larger image is called enlargement. Describing Dilation Dilation of Scale Factor 2 The following figure undergoes a dilation with a scale factor of 2 giving an image A’ (2, 4), B’ […]

Read More >>#### How to Write and Interpret Numerical Expressions?

Write numerical expressions What is the Meaning of Numerical Expression? A numerical expression is a combination of numbers and integers using basic operations such as addition, subtraction, multiplication, or division. The word PEMDAS stands for: P → Parentheses E → Exponents M → Multiplication D → Division A → Addition S → Subtraction Some examples […]

Read More >>#### System of Linear Inequalities and Equations

Introduction: Systems of Linear Inequalities: A system of linear inequalities is a set of two or more linear inequalities in the same variables. The following example illustrates this, y < x + 2…………..Inequality 1 y ≥ 2x − 1…………Inequality 2 Solution of a System of Linear Inequalities: A solution of a system of linear inequalities […]

Read More >>
Comments: