Multiplication

How do I find the product of two numbers?

Ever stuck on questions like what is 67 multiplied by 12? Or something like 107 multiplied by 19?

To multiply two numbers, you can easily do so using the following steps:

  1. Start with multiplying the smaller number with the rightmost digit of the bigger number. This will give you the rightmost digit of your product.

  2. Move to the left side with every step and get more and more digits for your product.
    If the number you get after multiplication with a digit is two or more digits, you should only set the rightmost digit in the product and keep the rest as carry-forward. When multiplying the next digit with the smaller number, add the carry-forward to the product you get from multiplication and treat it as the number to be added to the product (again while making sure that any additional digits are treated as carry-forward for the next number).

If the above step gives you two or more digits after you multiply the smaller number with the leftmost digit and add the carry-forward if any; then you should add the entire answer to the left side of the product.

Let's try this by multiplying 67 by 12:

  1. Multiplying the rightmost digit of 67 with 12, i.e., 7 × 12. Since 7 × 12 = 84, this gives us the last digit of the product, i.e. 4. This also gives a carry-forward of 8.

  2. Moving to the next digit in the first number, i.e., 6. Now, 6 × 12 = 72, but since we have 8 as carry-forward from the previous step, we add it to 72. This gives us the answer as 72 + 8 = 80. Since we had 4 as the last digit from the previous step, the product is 804.

Let's try the above method for 107 multiplied by 19:

  1. Multiplying the rightmost digit of 107 with 19, i.e. 7 × 19. Since 7 × 19 = 133, this gives us the last digit of the product, i.e. 3. This also gives a carry-forward of 13.

  2. Moving to the next digit in the first number, i.e., 0. Now, 0 × 19 = 0, but since we have 13 as carry-forward from the previous step, we add it to 0, i.e., 0 + 13 = 13. This gives us the next digit as 3. Therefore, the rightmost digits in the product are 33. This also gives us a carry-forward of 1.

  3. Moving to the next digit in the first number, i.e., 1. Now, 1 × 19 = 19, but since we have 1 as carry-forward from the previous step, we add it to 19. This gives us the answer as 19 + 1 = 20. Since we had 33 as the last two digits from the previous step, the product is 2033.

If you find the above method easy, you can increase your pace by practicing multiplication and setting checkpoints for whenever you might struggle in multiplication. In the above example, for instance, 7 × 19 is not everyone's cup of tea, however, 7 × 20 is a lot easier than that. To get 7 × 19, all one has to do is subtract 7 from 7 × 20, i.e., 140 - 7, hence resulting in 133.

Practice Questions:

  • 33 × 43 = ?

  • 56 × 17 = ?

  • 87 × 42 = ?

  • 71 × 78 = ?

  • 63 × 63 = ?