What is Multiplication?
Multiplication is Repeated Addition, a way of adding the same number over and over. It helps us count things quickly. Imagine you have three baskets of apples, and each basket has 5 apples. Instead of counting the apples one by one, multiplication helps you figure out how many apples you have in total.
How Does Multiplication Work?
We have 3 baskets with 5 apples each. Let’s count the total number of apples using multiplication.
Total Number of Apples = 3 x 5
This means we are adding the number 5 three times:
5 + 5 + 5 = 15
So, 3 x 5 equals 15.
We have 3 groups, and each group has 5 items. So, the total number of items is 3×5 = 15. Multiplication tells us how many items we have in total.
Understanding Multiplication with Arrays
We can also use arrays to help us see how multiplication works. An array is a group of objects arranged in rows and columns. If we want to multiply 4 x 6, we can create an array with 4 rows and 6 dots in each row.
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Here, we have 4 rows and 6 dots in each row, with a total of 24 dots. So, 4 x 6 = 24. This shows that multiplication helps us find the total number of objects in all the rows.
Multiplication Tables
Multiplication tables are a helpful tool that makes multiplication easier. By learning these tables, we can quickly figure out how to multiply numbers without having to add them over and over again. For example, when we know that 3 x 4 equals 12, we don’t need to count it each time. Multiplication tables help us remember important multiplication facts, making math quicker and more fun. The more we practice these tables, the faster we’ll be able to solve problems in our head!
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Commutative Property of Multiplication
The commutative property of multiplication means that the order in which you multiply numbers doesn’t change the answer. For example, if you multiply 2 x 3 or 3 x 2, both will give you 6. This rule tells us that the result is the same no matter which number comes first. It’s like swapping the numbers around, but still getting the same answer! This property helps make multiplication easier because you can rearrange numbers in a way that’s more comfortable for you when solving problems.
2-Digit by 1-Digit Multiplication
To multiply a double-digit number with a single-digit number, we split the two-digit number into tens and ones and multiply each digit separately with the one-digit number.
Without Carry Over
Let’s look at the steps in detail with the example 21 x 3.
Step 1: Multiply the ones digit (1) of the two-digit number by the one-digit number (3).
1×3 = 3
Step 2: Multiply the tens digit (2) of the two-digit number by the one-digit number (3).
2×3 = 6
This gives us the answer 6 tens and 3 ones = 63
21 x 3 = 63
Practice: 81×5, 92×3
With Carry Over
If the answer is our first step is a two-digit number, what do we do? Let’s look at this with the example 23 x 4.
Step 1: Multiply the ones digit (3) of the two-digit number by the one-digit number (4).
3×4 = 12
Step 2: We can write down 2 in the ones place of the answer and carry over 1 to the tens place.
Step 3: Multiply the tens digit (2) of the two-digit number by the one-digit number (4) and then add the carried over digit (1) to the answer.
2×4 = 8 8+1 = 9
This gives us the answer 9 tens and 2 ones = 92
23 x 4 = 92
Practice: 64×7, 58×2
2-Digit by 2-Digit Multiplication
Let’s see how to multiply two double-digit numbers with the example 41 x 12. This is equivalent to the sum of 41 x 2 ones and 41 x 1 ten.
Step 1: Multiply the first number with the ones digit (2) of the second number.
1×2 = 2
4×2 = 8
41×2 = 82
Step 2: Before we multiply the first number with the tens digit (2) of the second number, we need to fill the ones place in the next step with 0, as tens multiplied by any digit will end with zero.
Step 3: Multiply the first number with the tens digit (1) of the two-digit number.
1×1 = 1
4×1 = 4
41×1 = 41
Step 4: Add the numbers in both the rows.
82+410 = 492
Practice: 35×61, 37×52
FAQs on Multiplication
- Multiplication can be represented by the symbols ×, ·, or by placing numbers next to each other in parentheses.
- Examples: 4×7=28, 4⋅7=28, (4)(7)=28.
- Yes, multiplication is commutative, meaning the order of the factors does not affect the product.
- Example: 3×5=5×3=15.
- Yes, multiplication is associative, so changing the grouping of numbers does not affect the product.
- Example: (2×3)×4=2×(3×4)=24.
- The distributive property states that ax(b+c)=(axb)+(axc).
- Example: 3x(4+2)=(3×4)+(3×2)=12+6=18.