Two-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, the mass of products or the size of the discount. But how to multiply two-digit numbers quickly and without problems? Let's find out.
How to multiply a two-digit number by a one-digit number?
Let's start with a simple problem - how to multiply two-digit numbers by one-digit numbers.
For starters, a two-digit number is a number that consists of a certain number of tens and ones.
In order to multiply a two-digit number by a one-digit number in a column, you need to write the desired two-digit number, and under it the corresponding one-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 by adding them.
Multiplicationtwo-digit numbers into tens
Multiplying two-digit numbers by tens is not much more difficult than multiplying by single-digit numbers. The basic procedure remains the same:
- Write out the numbers one below the other in a column, while zero should be as if "on the side" so as not to interfere with arithmetic operations.
- Multiply a two-digit number by the number of tens, don't forget to move some digits to the next digits.
- The only thing that differs this example from the previous one is that you need to add a zero at the end of the resulting answer, so that the tens that were omitted at the beginning are taken into account.
How to multiply two two-digit numbers?
After you have completely figured out the multiplication of two-digit and single-digit numbers, you can start thinking about how to multiply two-digit numbers with a column on each other. In fact, this action should not require much effort from you either, since the principle is still the same.
- Write out these numbers in a column - units under units, tens under tens.
- Starting multiplication from one just like in the examples with single digits.
- After you get the first number by multiplying the units by this number, you need to multiply the tens by the same number in the same way. Attention: the answer must be written strictly under tens. The empty space under the units is an unaccounted for zero. You can write it down if you feel more comfortable.
- Multiplying both tens and ones and getting two numbers,written one under one, they need to be added in a column. The resulting value is the answer.
How to multiply two-digit numbers correctly? 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 two-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 mentally
After learning to multiply brilliantly on paper, one might wonder how to quickly multiply two-digit numbers in the mind.
Of course, this is not an easy task. It requires some concentration, a good memory, and the ability to keep a certain amount of information in your head. However, this can be learned with enough effort, especially if you choose the right algorithm. Obviously, it is easiest to multiply by round numbers, so the simplest way is to factorize numbers.
- First, you should split one of these two-digit numbers into tens. 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 quite complex operations to perform in the mind, since you need to simultaneously multiply numbers by each other and keep in mind the result that has already been obtained. Most likely, you will find it difficult to cope with this task the first time, but if you are diligent enough, this skill can be developed, because you understand how to correctly multiply two-digitnumbers in the mind, only in practice.
Some tricks for multiplying two-digit numbers
But is there an easier way to mentally multiply two-digit numbers, and how to do it?
There are a few tricks. They will help you multiply two-digit numbers quickly and easily.
When multiplying by eleven, you just need to put the sum of tens and ones in the middle of this two-digit number. For example, we needed to multiply 34 by 11
3 + 4=7
Put 7 in the middle, 374. This is the answer.
If the addition results in a number greater than 10, then you should simply add one to the first number. For example, 79 × 11.
7 + 9=16
(7 + 1)69=869
Sometimes it's easier to factor a number and multiply them sequentially. For example, 16=2 × 2 × 2 × 2, so you can simply multiply the original number by 2 4 times
14=2 × 7, so when performing mathematical operations, you can multiply first by 7, and then by 2.
- To multiply a number by multiples of 100, such as 50 or 25, you can multiply that 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 from the resulting number once. This rule is valid for any tens.
