Multiplication Part 2
Standard 4th | Mathematics
What is Multiplication?
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.
Example: If there are 6 boxes of cupcakes and each box has 9 cupcakes, find the total number of cupcakes.
Solution: We can solve this question by addition but it would take longer to add these to get the answer. That is, 9 + 9 + 9 + 9 + 9 + 9 = 54 cupcakes. In other words, when we have larger numbers to work upon, then multiplication is useful.
Now, let us use multiplication to solve this problem. We will multiply the number of boxes with the number of cupcakes in each box. If we multiply 6 × 9, we will get the total number of cupcakes, which is 6 × 9 = 54 cupcakes. Thus, we can see that we get the same result in a shorter period of time. This is the reason why multiplication is also termed as repeated addition.
Multiplication Symbol (×)
In mathematics, we have different symbols. The multiplication symbol is one of the commonly used math symbols. In the example given above, we learnt about the multiplication of two numbers 6 and 9. If we observe the expression of multiplication (6 × 9 = 54), we can see that the symbol (×) connects the two numbers and completes the given expression. Apart from the cross symbol (×), multiplication is also denoted by the mid-line dot operator (⋅), and by the asterisk sign (*).
Multiplication Formula
The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:
- Multiplicand: The first number (factor).
- Multiplier: The second number (factor).
- Product: The final result after multiplying the multiplicand and multiplier.
- Multiplication symbol: '×' (which connects the entire expression)
Let us understand the multiplication formula with the help of the following expression.
7(multiplicand) × 5 (multiplier) = 35 (product)
Using this basic concept of multiplication let us learn how to solve multiplication problems.
How to Solve Multiplication Problems?
While solving multiplication problems, one-digit numbers can be multiplied in a simple way by using the multiplication tables, but for larger numbers, we split the numbers into columns using their respective place values, like ones, tens, hundreds, thousands, and so on. There are two types of multiplication problems:
- Multiplication without regrouping
- Multiplication with regrouping
Let us understand the two cases with the help of examples.
Multiplication Without Regrouping
Multiplication of two numbers without regrouping involves smaller numbers where there is no need to take a carry-over to the next higher place value. It is the basic level that could help a learner understand the basics of multiplication before moving on to the higher level of problems including regrouping. Let us understand this with the help of the example given below.
Example: Multiply 3014 by 2.
Solution:
- Step 1: Start with the digit in ones place. (2 × 4 = 8)
- Step 2: Multiply 2 with the digit in tens place. (2 × 1 = 2)
- Step 3: Now, multiply 2 with the digit in hundreds place. (2 × 0 = 0)
- Step 4: Now multiply 2 with the digit in thousands place. (2 × 3 = 6)
- Step 5: 3014 × 2 = 6028.
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