How to Solve Multi Digit Multiplication Problems Easily
In our earlier classes, we learned about all four maths operations: addition, subtraction, multiplication and division. And from all the operations, our favourites were addition and multiplication because they were simpler than subtraction and division. But today in this article, we will learn about multi-digit multiplication in a very easy and enjoyable way. Doing multiplication is fun if it's done in the right way. So in this article, we will learn about 5 digit multiplication, which we might call hard multiplication. Here we provided multiplication practice problems and 3-digit multiplication worksheets to clear your concepts.
What is Multiplication?
Multiplication is an important arithmetic operation; it helps to find the total number of items quickly. It's the operation representing the basic idea of repeated addition of the same number. So we can say that it's a method of finding the product of two or more numbers. We use multiplication in our everyday life. Do you want to know how?
So let's say you went to a grocery store to buy 5 apples, which cost 10 rupees. How much money do you need to pay to buy those 5 apples? Do you know the answer? Ok, stop, don't waste your time adding them repeatedly; just multiply 5 by 10, so the answer is 50. So you will need 50 rupees to buy those 5 apples.
Here we understand multiplication and why we need it, we find it interesting, too, so don't worry. We are not going to stop here. We are going to explore multiplication a little bit more. We are going to learn about multi-digit multiplication.
Symbol of Multiplication
While doing multiplication, there are many symbols which are used to denote the most interesting arithmetic operation, i.e. multiplication. So let's check what symbols are used to denote multiplication.
Cross sign “X”, dot sign “.”, and the star sign “*”. And remember, if there is no symbol after the bracket, there is also multiplication between the numbers. Confused? Don't worry. Let's check it with an example 5(7)= 35.
Symbol of multiplication
Formula for Multiplication
The multiplication formula is very simple. Let's see what it is, Multiplicand x Multiplier = Product. Where multiplicand refers to the first number, the total number of objects in each group. Then Multiplier is the second number which is the number of equal groups.
And the last is the product which is the final result that we get after multiplying the multiplicand and the multiplier.
Example: If a multiplier is 6 and multiplicand is 5, the product is 30.
12 x 10 = 120
Multiplication
Rules for Multiplication
If any number is multiplied by 0, the product will be 0.
Example: $5 \times 0 = 0$
The multiplication of two integers is an integer.
Example: $5 \times 5 = 25$
The order of the number does not matter when they are multiplied together.
Example: $25 \times 5 = 125$ or $5 \times 25 = 125$
If any number multiplied by 1 is equal to the original number.
Example: $5 \times 1 = 5$
Solved Example
Let's learn about multiplication by looking at solved examples based on 5-digit multiplication and 3-digit multiplication:
Q 1. Multiply 123 x 3
Ans: Step-1. Write the number one below the other as per the places of their digits.
Multiplication
Step-2. Multiply the ones digit of the top number by the ones digit of the bottom number.
Multiplication
Step-3. Multiply the tens digits of the top by the ones digit of the bottom number and you will get your answer.
Multiplication
Q 2. Multiply 36953 x 3
Ans: Step-1. Write the number one below the other as per the places of the digit.
Step-2. Now by multiplying the tens place, if there is a carry of number, shift it to another number at the top of the hundreds place.
Step-3. By multiplying in this way, you will get your answer. i.e. 110859.
5-digit multiplication
Multiplication Practice Problems
Here are some practice problems based on hard multiplication:
Q 1. 343 x 213
Ans. 73,059
Q 2. 369 x 15
Ans. 5535
Q 3. 513 x 33
Ans. 16,929
3 Digit Multiplication Worksheets
3-Digit Multiplication Worksheets
Summary
So in this article, we learned about many wonderful things related to multiplication. We learned about multiplication, like what multiplication is and what are the symbols of multiplication. We learned the formula of multiplication. We also discussed the rules for multiplication to make hard multiplication easy.
We just did not end there. We also did some multiplication practice problems as we know that maths is not learned by reading. It's learned by solving by doing questions.
That's why we have provided a 3-digit multiplication worksheet to clear all your doubts.
FAQs on Multi Digit Multiplication Made Simple
1. How do you do multi-digit multiplication?
To perform multi-digit multiplication, you multiply each digit of one number by each digit of the other number and then add the results appropriately. The standard approach, often known as the long multiplication method, involves these steps:
- Write the numbers on top of each other, aligning the digits to the right.
- Multiply the bottom number's rightmost digit by each digit of the top number, writing the result below.
- Shift one place to the left, then multiply with the next digit of the bottom number, writing the results accordingly.
- Continue this process for all digits of the bottom number.
- Add all the partial products to get the final answer.
Step 1: $234 imes 6 = 1404$
Step 2: $234 imes 50 = 11700$
Step 3: Add the results: $1404 + 11700 = 13104$.
Vedantu provides detailed step-by-step explanations and live interactive sessions to help students master multi-digit multiplication efficiently.
2. Is there a 7s multiplication trick?
Yes, there are several tricks and shortcuts for learning the multiplication table of 7. One helpful trick is to break the number into easier components using distributive property. For example:
- $7 imes 8 = (7 imes 10) - (7 imes 2) = 70 - 14 = 56$
3. What is an example of a multi digit number?
A multi-digit number is any number with more than one digit. Examples include:
- 23
- 456
- 1,234
4. What are the 4 types of multiplication?
The four main types of multiplication methods commonly taught in mathematics are:
- Repeated Addition: Treating multiplication as adding a number multiple times (e.g., $3 imes 4 = 4 + 4 + 4$).
- Using Arrays: Representing multiplication visually with rows and columns.
- Long Multiplication (Column Method): The standard written method for multi-digit numbers.
- Short Multiplication: Used when multiplying a large number by a single-digit number.
5. What are some efficient strategies for teaching multi-digit multiplication?
Efficient strategies for teaching multi-digit multiplication include:
- Visual aids such as grids or area models to represent multiplication concepts.
- Breaking the problem into parts using the distributive property: $36 imes 24 = (30 + 6) imes (20 + 4)$.
- Step-by-step guided examples and interactive problem-solving.
- Utilizing practice worksheets and quizzes for reinforcement.
6. What is the expanded algorithm for multi-digit multiplication?
The expanded algorithm for multi-digit multiplication involves breaking numbers into their place values and multiplying each part separately. For example, to multiply 23 by 45:
- Break numbers into place values: $23 = 20 + 3$, $45 = 40 + 5$
- Multiply each component:
- $20 imes 40 = 800$
- $20 imes 5 = 100$
- $3 imes 40 = 120$
- $3 imes 5 = 15$
- Add the partial products: $800 + 100 + 120 + 15 = 1035$
7. How can students check their answers after doing multi-digit multiplication?
Students can check their answers in multi-digit multiplication by:
- Reverse operation (division): Divide the product by one of the factors to see if you get the other factor.
- Estimation: Round the numbers and multiply to get an approximate result, ensuring the answer is reasonable.
- Using Vedantu’s online tools and live guidance to verify solutions
8. How does multi-digit multiplication help solve real-world math problems?
Multi-digit multiplication is essential for solving real-world math problems such as calculating total cost, determining area, or understanding large quantities in science and business. Examples include:
- Finding the total price: If one book costs $45$ and a student buys $23$ books, total cost is $45 imes 23 = 1035$.
- Calculating area: A rectangular field of $125$ meters by $48$ meters requires $125 imes 48 = 6000$ square meters of grass seed.
9. What common mistakes occur in multi-digit multiplication and how can they be avoided?
Common mistakes in multi-digit multiplication include:
- Misaligning numbers during calculation.
- Forgetting to add a zero when moving to the next digit.
- Adding partial products incorrectly.
- Double-check alignment of digits in each step.
- Carefully add zeros in the correct places for place value.
- Recheck addition of partial products.
10. What resources does Vedantu offer to help students improve in multi-digit multiplication?
Vedantu provides a range of resources to support mastery of multi-digit multiplication, including:
- Live interactive classes with step-by-step demonstrations.
- Comprehensive study materials, worksheets, and mock tests.
- Personalized doubt-solving sessions with qualified teachers.
- Concept videos and practice quizzes tailored for different grades.
