![Multiply and Divide Whole Numbers](/multiply_and_divide_whole_numbers/images/multiply-and-divide-whole-numbers-mini-logo.jpg)
- Multiply and Divide Whole Numbers
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- Multiplication as Repeated Addition
- Single Digit Multiplication
- Multiplication by 10, 100, and 1000
- Multiplication Without Carry
- Multiplication With Carry
- Multiplication With Trailing Zeros: Problem Type 1
- Multiplication With Trailing Zeros: Problem Type 2
- Multiplication of 2-digit Numbers With 2-digit Numbers
- Multiplication of a Single Digit Number With Large Numbers
- Multiplication of Large Numbers
- Multiples Problem Type 1
- Multiples Problem Type 2
- Division Facts
- Fact Families for Multiplication and Division
- Multiplication or Division of Whole Numbers (Word problems)
- Multiplication and Addition or Subtraction of Whole numbers (Word problems)
- Unit Rates and Ratios of Whole Numbers (Word problems)
- Division Without Carry
- Division With Carry
- Division Involving Zero
- Whole Number Division: 2-digit by 2-digit, No Remainder
- Whole Number Division: 3-digit by 2-digit, No Remainder
- Division With Trailing Zeros: Problem Type 1
- Division With Trailing Zeros: Problem Type 2
- Quotient and Remainder: Problem type 1
- Quotient and Remainder: Problem type 2
- Quotient and Remainder (Word problems)
Multiplication as Repeated Addition
Let us consider an example to understand multiplication as a repeated addition operation. Suppose there are some toy cars divided into 6 groups each having 4 toy cars. The total number of toy cars can be found by adding 4 repeatedly 6 times as shown below.
4 + 4 + 4 + 4 + 4 + 4 = 24
![Divided into 6](/multiply_and_divide_whole_numbers/images/1.1.jpg)
The same result is also obtained by multiplication operation. Since 4 is being repeatedly added take 4 and multiply it with the number of groups which is 6.
So 4 × 6 = 24 (Read as 4 times 6 equals 24)
Here 4 and 6 care called as factors and the resulting number is called as product.
The way multiplication is related to repeated addition can be explained in this way, i.e. multiplying a × b is the same as adding a repeatedly b number of times.
For example, for objects arranged in 4 rows and 5 columns (20 in all);
5 + 5 + 5 + 5 and 4 × 5 represents the total number of objects.
When you multiply, you add equal groups together to find the total.
![Divided into 6](/multiply_and_divide_whole_numbers/images/1.2.jpg)
Write the number of keys that you see. Write it as both an addition and multiplication problem
2 + 2 + 2 + 2 =
4 × 2 =
Solution
Step 1:
We see 2 keys in each group. There are 4 groups.
To simplify, there are 4 groups of 2 keys or
2 + 2 + 2 + 2 = 8
Step 2:
This can also be written as a multiplication problem.
4 groups and each group has 2 keys so we can multiply
4 × 2 = 8
Step 3:
So,
2 + 2 + 2 + 2 = 8
4 × 2 = 8
Rewrite the following repeated addition as a multiplication sentence
2 + 2 + 2 + 2 +2 + 2 = 12
Solution
Step 1:
Here 2 is being repeatedly added, so first write a 2. Then we count the number of times it is being added. This is 6 times.
Step 2:
So the multiplication sentence would be
2 × 6 = 12