Multiplication
In the previous classes, we have learnt how to multiply a number by 1-digit and 2-digit numbers. Here we will learn more about multiplication.
The numbers that are multiplied are called factors and the answer is called the product
9 x 8 = 72
9 and 8 are factors and 72 is the product.
9 and 8 are factors and 72 is the product.
- Multiplication by a 1-Digit Number
- Multiplication by 10, 100, 1000
- Multiplication by 20, 30, 40, ..., 90
- Multiplication by 200, 300, 400, ..., 900
- Multiplication by 2000, 3000, 4000, ..., 9000
- Multiplication by 2 or 3-Digit Numbers
- Estimating Products
Multiplication by a 1-Digit Number
Let's multiply 125 by 5
Step 1: Write the numbers in columns
125
x 5
Step 2: Multiply 5 with the digit in ones place. 5 x 5 = 25. We write 5 in the ones place and 2 carry over to tens place.
2
125
x 5
5
Step 3: Multiply 5 with the digit in tens place, then add the carried over 2. (5 x 2) + 2 = 12. We write 2 in the tens place and 1 carry over to hundreds place.
1
125
x 5
25
Step 4: Multiply 5 with the digit in hundreds place, then add the carried over 1. (5 x 1) + 1 = 6. We write 6 in the hundreds place.
125
x 5
625
125 x 5 = 625
125
x 5
Step 2: Multiply 5 with the digit in ones place. 5 x 5 = 25. We write 5 in the ones place and 2 carry over to tens place.
2
125
x 5
5
Step 3: Multiply 5 with the digit in tens place, then add the carried over 2. (5 x 2) + 2 = 12. We write 2 in the tens place and 1 carry over to hundreds place.
1
125
x 5
25
Step 4: Multiply 5 with the digit in hundreds place, then add the carried over 1. (5 x 1) + 1 = 6. We write 6 in the hundreds place.
125
x 5
625
125 x 5 = 625
Multiplication by 10, 100, 1000
Observe the following table.| 1 x 10 = 1 x 1 Ten = 1 Ten = 10 |
| 5 x 10 = 5 x 1 Ten = 5 Ten = 50 |
| 1 x 100 = 1 x 1 Hundred = 1 Hundred = 100 |
| 5 x 100 = 5 x 1 Hundred = 5 Hundred = 500 |
| 1 x 1000 = 1 x 1 Thousand = 1 Thousand = 1000 |
| 5 x 1000 = 5 x 1 Thousand = 5 Thousand = 5000 |
Multiplication by 20, 30, 40, ..., 90
To multiply a number by 20, 30... 90, multiply the number by 2, 3... 9 respectively and insert one zero on the right of the product.
| 5 x 10 | = 50 |
| 5 x 20 | = 100 |
| 5 x 30 | = 150 |
| 5 x 40 | = 200 |
| 5 x 50 | = 250 |
| 5 x 60 | = 300 |
| 5 x 70 | = 350 |
| 5 x 80 | = 400 |
| 5 x 90 | = 450 |
Multiplication by 200, 300, 400, ..., 900
To multiply a number by 200, 300... 900, multiply the number by 2, 3... 9 respectively and insert two zeroes on the right of the product.
| 8 x 200 | = 1600 |
| 8 x 300 | = 2400 |
| 8 x 400 | = 3200 |
| 8 x 500 | = 4000 |
| 8 x 600 | = 4800 |
| 8 x 700 | = 5600 |
| 8 x 800 | = 6400 |
| 8 x 900 | = 7200 |
Multiplication by 2000, 3000, 4000, ..., 9000
To multiply a number by 2000, 3000... 9000, multiply the number by 2, 3... 9 respectively and insert three zeroes on the right of the product.
| 8 x 2000 | = 16000 |
| 8 x 3000 | = 24000 |
| 8 x 4000 | = 32000 |
| 8 x 5000 | = 40000 |
| 8 x 6000 | = 48000 |
| 8 x 7000 | = 56000 |
| 8 x 8000 | = 64000 |
| 8 x 9000 | = 72000 |
Multiplication by 2 or 3-Digit Numbers
Let's multiply 24 by 12
Step 1: Write the numbers in column form.
24
x 12
Step 2: Multiply 3 with the digit in ones place. 2 x 4 = 8, we write 8 in the ones place.
24
x 12
8
Step 3: Multiply 3 with the digit in tens place. 2 x 2 = 4, we write 4 in the tens place.
24
x 12
48
Step 4: We are done with the first digit. Now we will start with the second digit 1. Since 1 is in tens place, we start writing the product from the tens place in the next line.Multiply 1 with the digit in ones place. 1 x 2 = 4, we write 4 in the tens place.
24
x 12
48
4
Step 5: Multiply 1 with the digit in tens place. 1 x 2 = 2, we write 2 in the hundreds place.
24
x 12
48
24
Step 6: Now add the two products obtained in the above 2 steps.
24
x 12
48
24
288
24 x 12 = 288
24
x 12
Step 2: Multiply 3 with the digit in ones place. 2 x 4 = 8, we write 8 in the ones place.
24
x 12
8
Step 3: Multiply 3 with the digit in tens place. 2 x 2 = 4, we write 4 in the tens place.
24
x 12
48
Step 4: We are done with the first digit. Now we will start with the second digit 1. Since 1 is in tens place, we start writing the product from the tens place in the next line.Multiply 1 with the digit in ones place. 1 x 2 = 4, we write 4 in the tens place.
24
x 12
48
4
Step 5: Multiply 1 with the digit in tens place. 1 x 2 = 2, we write 2 in the hundreds place.
24
x 12
48
24
Step 6: Now add the two products obtained in the above 2 steps.
24
x 12
48
24
288
24 x 12 = 288
Let's multiply 205 by 390
2 0 5
x 3 9 0
0 0 0
1 8 4 5 0
6 1 5 0 0
7 9 9 5 0
x 3 9 0
0 0 0
1 8 4 5 0
6 1 5 0 0
7 9 9 5 0
Estimating Products
We can estimate the products in many ways.Estimate the product 46 x 27
Method 1:
We will round up both the numbers.46 x 27 → 50 x 30 = 1500
Method 2:
We will round the first number up and the other down.46 x 27 → 50 x 20 = 1000
Method 3:
We will round one first number down and the other up.46 x 27 → 40 x 30 = 1200
Method 4:
We will round down both the numbers.46 x 27 → 30 x 20 = 600
Actual Product = 46 x 27 = 1242
We can see that the method 3 of rounding one number down and the other one up, gives an estimated product that is closer to the actual product.