Multiply is one of the four basic operations of arithmetic, along with addition, subtraction, and division. It is one of the most complicated and it is that to know how to multiply, it is necessary to know how to add. Since a multiplication consists of adding the same number a certain number of times. This means that 5×6, is that the number 5 is repeated 6 times, or what is the same, 5+5+5+5+5+5, which would be 30.
The elements of a multiplication is called a factor, and the result, a product. For this reason it is said that in a multiplication, in the same way as in an addition, the order of the factors does not alter the product, since 5×6 is the same as 6×5.
There are simple multiplications and others much more complex. The simple ones are of a single number, that is, there are only units. However, in those that have to multiply figures of more than one decimal, we will have to do several steps: the first is to multiply the number on the right by the entire column above; then the same with the number on the bottom left; and then add the two amounts.
It is important to know the multiplication tables , because that way it will be much faster and easier, otherwise you will have to be doing the multiplications all the time as if they were an addition, and that is incorrect. By this I mean that if you have to multiply 3 × 6, do not add 6 times the number 3, because this takes a lot of time. Ideally, you should know all the multiplication tables to speed up the process and know by heart that 3 × 6 and 6 × 3 are 18.
Using as an example a two-digit multiplication such as 56×32, we will have to do the following:
- Multiply 56×2, since two is the number in the bottom column that is furthest to the right. We do it in parts, first 6×2, which is 12, so we only keep 2 and take 1, and 5×2, which is 10, but we must add what we take. Therefore 56 × 2 is 112.
- We leave a space below the 2 of 112, and we begin to put the digits of the following multiplication in the second 1 of 1(1)2.
- We multiply 56×3. We do it again in parts, first 6 × 3, which is 18, we keep the 8 and we sign up that we take 1. And then 5 × 3, which is 15, plus the one we take. Therefore 56 × 3 is equal to 168.
- We add 112 from multiplying 56×2, + 168 from multiplying 56×3. The result is 1,792, because in the units column we have only left 2 out of 112, and the result of the second multiplication must begin to be placed to its left and not just below.
In the event that instead of having to multiply 2 quantities, they are 3, it would be done in the same way. If we had to do 56x32x11, we would do it two by two. That is, follow the steps from before until you reach the result of 1,792 and after that multiply this amount by 11. They are always done two by two.
In the event that instead of two figures the amount was three, it would also be done in the same way. If the quantity to multiply is 534×23 we would do it like this:
- First see which is the number that has more digits. That number will always be at the top, not because another result will come out, but because that way we will be saving an operation.
- Multiply 534×3, which is the number on the right of the bottom column. We would do it in parts, first 3×4, which is 12, and we note that we take 1; then 3×3, which is 9, plus the one from before would be 10, so we take 1 again; and finally 3×5 which is 15 plus the one from before 16. So the result of 534×3 is 1,602.
- You have to put the plus sign under the 2 of 1,602, and place the result of the second multiplication to its left, but never below that 2.
- Multiply 534×2, which is the number in the left column that we have left. We would continue to do it in parts. First 2×4 which is 8; then 2×3 which is 6; and finally 2×5 which is 10. So the result of 534×2 is 1,068.
- We add the two results, 1,602 of 534×3, + 1,068 of 534×2, taking into account that no other number should have been placed below the 2 of 1,602. So finally the result of multiplying 534 × 23 is 108,402.
If instead of two figures there are three, the same thing would be done, but always, after finishing with a column, you have to put the + symbol under the resulting number on the right, as with 2 of 1,602, because if not at doing the sum we will be doing it wrong and the result will not come out. This process will have to be repeated as many times as there are numbers. And in the event that the multiplication is 3 quantities or more, you should always do it two by two, and with the result of these two, multiply to the third quantity. Otherwise it won’t come out.
The fact of putting the + sign is because the number 3 of 23 is part of the units, but 2 of the tens, if its result is placed below the 2 of 1,602 we would be doing it as if the 2 were also a unit and not, is a ten, so you have to omit that first column on the right of the units and start in the second, which is the tens column. If there were more numbers, instead of x23 the operation would be for 423, with 4 you would have to do the same. Let run two places, the first that is the units and the second that is the tens and place the result in the third column that is yours, the hundreds.
Tips for multiplying
- Always put the + sign after multiplying each row, otherwise the final result will not come out, since the resulting number will be a very low amount.
- Multiply number by number, checking that the result of each one is correct.
- When doing it for the first time, repeat the operations a couple of times to check that they are correct, since it is not like adding and subtracting that with a simple operation we can know if we have done it correctly.
- Multiply by putting the figures one below the other, because if you do it in a horizontal line, it will be much more complicated, especially for the sum and to sign up if you take a number.
- Take a pen of another color or with the pencil put on top of each column if you take a number from its previous column or not so that you do not forget to add it, since otherwise, even by a couple of figures, the result will be wrong.
- Review the multiplication tables. If you don’t know them, even in the simple multiplications of a single number, it will cost you a lot and it will take longer, since you will do the multiplication as if it were an addition. Something that is not bad, because it is what it is, but the objective is to save time.
What do you need to multiply?
- Paper
- Pencil