Table of Contents
- What is a Multiple of 10?
- Multiples of 10
- What do you observe in Multiples of 10?
- Strategy to Multiply with 10
- Tape diagram
- Using Number line
- How do we use Multiplication with 5 to calculate Multiplication with 10?
- What is the Distributive property of Multiplication?
- Distributive property in Multiplication with 10
- Commutative property in Multiplication with 10
- Associative property in Multiplication with 10
- Solved Examples
- Frequently Asked Questions
What is a Multiple of 10?
When an integer is multiplied by ten, the result is a multiple of ten. 10 is the sum of the first three prime numbers 1+2+3+4.
The multiple of 10 is easy to memorize.
Example: Olivia has 2 pairs of 10 chocolates.
10 × 2 = 20 or 10 + 10 = 20.
Multiples of 10
We first multiply 10 by 1, which is 10. Then we will multiply 10 by 2, which is 20. This list is infinite; we can make as many multiples of ten as we like.
Examples: 10, 20, 30, 40, 50.
Multiplication table:
10 × 1 = 10 |
|---|
10 × 2 = 20 |
10 × 3 = 30 |
10 × 4 = 40 |
10 × 5 = 50 |
10 × 6 = 60 |
10 × 7 = 70 |
10 × 8 = 80 |
10 × 9 = 90 |
10 × 10 = 100 |
What do you observe in Multiples of 10?
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and so on are all multiples of ten. These multiples are obtained by multiplying 10 by 1, 2, 3,…, 10, in that order. All of these multiples appear to form a sequence with a difference of 10 between two consecutive products.
Strategy to Multiply with 10
- Tape diagram
- Using Number line
1) Tape diagram: In this method, we combine 10 boxes. The number of boxes is a number by which we multiply 10.
It is also called the repeated addition method.
Example: 6 × 10 = 60
It can be represented using a tape diagram as follows:
10 | 10 | 10 | 10 | 10 | 10 |
|---|
10 + 10 + 10 + 10 + 10 + 10 = 60
or
\(\begin{matrix}
\\10
\\\times 6
\\ \_\_\_\_\_
\\ 60
\\ \_\_\_\_\_
\end{matrix}\)
2) Using a number line:
Draw a line with an interval of 10 between two numbers. A jump of 10 represents the multiplication of 10 by a number.
Example:
Here as we can see that between 0 to 10 the interval can be written as 10 × 1 = 10.
How do we use Multiplication with 5 to calculate Multiplication with 10?
10 is the multiple of two prime numbers: 5 × 2 = 10. To find the multiple of a number by 10, we can multiply by 2 and 5.
Example: 10 × 7=70
The number 70 can be written as a multiplication of five and two.
70 = 10 × 7 = 5 × 2 × 7
What is the Distributive property of Multiplication?
When we multiply a value by the sum of two or more numbers, we use the distributive property of multiplication over addition.
Example: 10 × (2 + 6) (distribute the 10 to the 2 and the 6)
= 20 + 60
= 80.
Distributive property in Multiplication with 10
Distribute (8 + 2) over 10,
10 (8 + 2) = 10 × 8 + 10 × 2 (distribute the 10 to the 8 and the 2)
= 80 + 20
= 100.
Commutative property in Multiplication with 10
The order in which we multiply the numbers does not affect the final product, according to the commutative property of multiplication.
Example: 10 × 5 = 5 × 10
The result of both equations will be 50.
Associative property in Multiplication with 10
The associative property of multiplication states that no matter how the numbers are grouped, the product of three or more numbers remains the same.
Example: 2 × (3 × 10) = (3 × 2) × 10
L.H.S,
2 × (3 × 10) = 2 × 30 = 60
R.H.S,
(3 × 2) × 10 = 6 × 10 = 60
As we can observe, multiplication is associative.
Solved Multiple of Ten Examples
Example 1: Thomas has 5 nickels and his friend has 78¢. Who has more money?
Answer:
1 nickel = 5¢
The total money Thomas has:
5 × 5 = 25¢
It is given that Thomas’ friend has 78¢, which is greater than 25¢. So, Thomas’s friend has more money than Thomas.
Example 2: Fill in the blank
10 × ☐ = 60
Answer:
60 can be written as 10 + 10 + 10 + 10 + 10 + 10.
So, 10 × 6 = 60.
Example 3: Use the distributive property to find products.
6 × 4 = 6 × (…….+……. )
Answer:
4 can be written as the sum of 2 + 2, or 3 + 1.
When choose 2 + 2,
6 × 4 = 6 × (2 + 2) (distribute the 6 to the 2 and the 2)
= 6 × 2 + 6 × 2
= 12 + 12
= 24.
If we choose 4 = 3 + 1,
6 × 4 = 6 × (3+1 ) (distribute the 6 to the 3 and the 1)
= 6 × 3 + 6 × 1
= 18 + 6
= 24.
So, the result will be 6 × 4 = 6 × (2 + 2 ) or 6 × 4 = 6 × (3 + 1 ).
A 0 appears at the end of all multiples of ten. Simply look for a zero at the end of your numbers to find them.
We can use multiplication of 10 with 5 and 2. We know that 2 × 5 = 10.
We can use 2 and 5 both to find the multiplication of a number by 10.
When a number is multiplied by 10, we get 0 at the end. Since 0 is the even number, multiples of 10 are an even number.