Double-digit multiplication is an essential skill in our daily lives. People are constantly faced with the need to multiply something in their mind: the price tag in the store, a lot of products or the size of the discount. But how to multiply double-digit numbers quickly and without problems? Let's figure it out.
How to multiply a two-digit number by a single-digit?
Let's start with a simple task - how to multiply two-digit numbers by single-digit ones.
To begin with, a two-digit number is a number that consists of a certain number of tens and units.
In order to multiply a two-digit number by a single-digit number in a column, you need to write the desired two-digit number, and under it the corresponding single-digit number. Next, you should alternately multiply by a given number, first units, and then tens. If, when multiplying units, a number greater than 10 is obtained, then the number of tens should simply be transferred to the next digit, adding them.
Multiple Dozens by Dozens
Multiplying two-digit numbers by tens is a bit more difficult than multiplying by single-digit numbers. The basic procedure remains the same:
- Write down the numbers one under the other in a column, while the zero should be “sideways”, so as not to interfere with arithmetic operations.
- Multiply a two-digit number by the number of tens, do not forget about transferring some numbers to the next digits.
- The only thing that distinguishes this example from the previous one is that you need to add zero at the end of the resulting answer, so that the tens that were omitted at the beginning become taken into account.
How to multiply two two-digit numbers?
After you have fully figured out the multiplication of two-digit and single-digit numbers, you can begin to think how to multiply a column of two-digit numbers by each other. In fact, this action also should not require much effort from you, since the principle still remains the same.
- We write out these numbers in a column - units under units, dozens under dozens.
- We start the multiplication from one in the same way as in the examples with single digits.
- After you get the first number, multiplying units by a given number, you need to multiply tens by the same number in the same way. Note: the answer must be written strictly under dozens. The empty space under the units is unaccounted for zero. You can record it if you prefer.
- Multiplying dozens and units and getting two numbers written one under one, they need to be added to the column. The resulting value is the answer.
How to multiply two-digit numbers? To do this, it is not enough just to read or learn the instructions given. Remember, in order to master the principle of how to multiply double-digit numbers, first of all you need to constantly practice - solve as many examples as possible, use the calculator as little as possible.
How to multiply in the mind
Having learned to multiply brilliantly on paper, one may wonder how to quickly multiply double-digit numbers in the mind.
Of course, this is not an easy task. It requires some concentration, good memory, and the ability to hold a certain amount of information in the head. However, this can be learned by putting enough effort, especially if you choose the right algorithm. Obviously, it’s easiest to multiply by round numbers, so the simplest way is to factor the numbers.
- First you need to break one of these two-digit numbers into dozens. For example, 48 = 4 × 10 + 8.
- Next, you need to sequentially multiply first the units, and then the tens with the second number. These are operations that are quite difficult to perform in the mind, since you need to simultaneously multiply the numbers by each other and keep in mind the result that has already been obtained. Most likely, it will be difficult for you to cope with this task the first time, but if you are diligent enough, this skill can be developed, because you can only understand how to double-digit numbers in your mind correctly in practice.
Some tricks when multiplying double-digit numbers
But is there an easier way in the mind to multiply double-digit numbers, and how to do it?
There are a few tricks. They will help you easily and quickly double-digit numbers.
- When multiplied by eleven, you just need to put the sum of tens and units in the middle of this two-digit number. For example, we needed to multiply 34 by 11.
3 + 4 = 7
We put 7 in the middle, 374. This is the answer.
If adding adds a number greater than 10, then simply add one to the first number. For example, 79 × 11.
7 + 9 = 16
(7 + 1) 69 = 869
- It is sometimes easier to factor the number and multiply them sequentially. For example, 16 = 2 × 2 × 2 × 2, so you can just 4 times multiply the original number by 2.
14 = 2 × 7, so when performing mathematical operations, you can multiply first by 7, and then by 2.
- In order to multiply a number by numbers that are multiples of 100, for example, 50 or 25, you can multiply this number by 100, and then divide by 2 or 4, respectively.
- You also need to remember that sometimes when multiplying it is easier not to add, but to subtract numbers from each other.
For example, to multiply a number by 29, you can first multiply it by 30, and then subtract this number once from the resulting number. This rule is true for any tens.