Patterns in Multiplying Decimals by Powers of 10

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: 1 to 100 even numbers.
Even numbers

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

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:  1 to 100 odd numbers.
                    Odd numbers

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

There are 2 equal groups of 9. and

There are 3 equal groups of 6.

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,

Exercise:

1. If you multiply two odd numbers, will the product be even or odd. Explain with an example?
2. 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=____.
3. 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.