The basic operations of Mathematics are the ones that we must handle perfectly well to advance in deeper studies. It’s like knowing how to read and write, you could never study history or any science if you don’t know the basics for reading and writing, you can’t interpret a text if you don’t read it correctly and understand what it says, beyond the single words.
Something similar happens in Mathematics, you cannot multiply if you do not know how to add, you cannot divide if you do not know how to add, subtract and multiply, thus Mathematics becomes more complex and based on previous knowledge.
Multiplication is a repeated addition, that is, knowing how to add can learn to multiply. What happens is that if we are working with small numbers we can apply this definition, such as multiplying 75 x 3, we could solve it by adding 3 times 75 without resorting to multiplication, but if we have to multiply larger numbers of two and three digits this would be impossible.
The multiplication algorithm is valid for all numerical sets, we will work with natural numbers but it can then be extended to integers and decimals.
At Doncomos.com we will show you the multiplication procedures and algorithms so that you also know how to teach multiplication.
What do you need to teach multiplication?
- Multiplication tables
- Paper, pencil
- Computer with Internet connection
Instructions to teach multiplication
- To learn to multiply, we will start from the basics, which is the meaning of multiplication: it is a repeated addition. When we multiply 4 x 2 we are saying: 4 times 2, that is, 2 + 2 + 2 + 2 = 8, but it is directly written: 4 x 2 = 8
- These multiplications of two one-digit numbers constitute the multiplication tables, which are those that are learned at school since childhood and constitute the basis of multiplications with numbers of two or more figures, decimal numbers, fractions, etc.
- The numbers that we multiply are called factors, and the result of the multiplication is called a product.
- We can see the multiplication tables in the following table so as not to write them separately, it is a double entry table in which you will find the result at the intersection of the row and the column where the numbers you want to multiply are located. Remember that multiplication is commutative so you can look up the numbers in any order.
- Two properties to take into account for all multiplication is that “every number multiplied by 0 gives zero” and that every number (except 0) multiplied by 1 gives the same number.” For example:
- 5 x 0 = 0 and 5 x 1 = 5 ; 8 x 0 = 0 and 8 x 1 = 8 but 0 x 0 = 0 and 0 x 1 = 0.
- That is why = is called the absorbing element of multiplication (it makes the number become zero) and 1 is called the neutral element of multiplication (it makes the number stay the same, remember, except for zero).
- If we multiply natural numbers we will always obtain another natural number as a result.
- If we multiply by 10; 100, 1000, etc we simply add to the first factor as many zeros as the second has. For example:
- Now we will see the multiplication algorithm by a number. If we have to multiply the number 238x 4 we must locate the factors as shown in the figure.
- Let’s remember the position of the figures, U: units, D: tens, C: hundreds, UM: units of thousands, DM: tens of thousands, etc.
- We begin to multiply the 4 by the 8 because it is always done in that order: first by the U, then by the D, etc., that is to say from right to left . From the number 32 (results of 4 x 8) we place the 2 as the unit of the result and we write the 3 very small on the tens column.
- Now we will multiply the 4 by the tens, that is, by the 3 , and to the result obtained we will add the tiny 3 that we had written precisely in the D column.
- 4 x 3 = 12 then: 12+ 3 = 15. Again we separate the number obtained as a result: we place the 5 in the tens place and the little 1 in the hundreds column as you see in the figure.
- We repeat the procedure 4 x 2 = 8 then 8 + 1 = 9. Since 9 has only one number we directly write it in the result (it will occupy the hundreds place).
- Finally we multiply: 4 x 1 = 4 and write it in the UM place. And we have solved the multiplication. The final result is 4,952
- When we multiply by a two-digit number we must do the same process that we already saw starting with the units of the second factor. Suppose we want to multiply 238 x 34.
- When we are going to multiply by the tens we do the same procedure except that the first number obtained must be placed one unit to the left:
- 3 x 8 = 24, we put the 4 in column D and the tiny 2 in column C. We continue with the same procedure until completing the second line of numbers. Finally, we first add the units, then the tens, that is, by columns: The final result will be 42,092.
- In the same way if we want to multiply by three-digit numbers: first we multiply the units of the second factor, then the tens (moving one place) and then the hundreds (also moving one place with respect to the second number). The columns of the units, tens, hundreds, units of a thousand and tens of thousands of the three numbers must be well ordered to be able to add correctly. Now we can add the three numbers arriving at the final result. In the figure you will see the multiplication solved.
- If we have doubts, we check with a calculator or we can resort to any of the games to learn to multiply that exist on the Web.
- It’s always good to know how to multiply without having to resort to a calculator because maybe at some point you need to do it and you don’t have one handy.
Tips for teaching multiplication
- Remember that multiplication is commutative, this means that the order of the factors does not alter the product, this benefits us in that if you have to multiply 25 x 45623, it is convenient to write it 45623 x 25 since you will obtain the same result and you will work less.
- When you do the multiplication by two or three figures you must be very orderly to place the numbers. Otherwise when you go to do the sum you can make a mistake if they are not well in columns.
- Learn more math tricks here in an easy and simple way.