## What are multiplicative problems?

The **multiplicative problems** They are problems related to the mathematical operations of multiplication, and have a certain level of difficulty whose solution is not always visible to the naked eye. Multiplication is taught to children in elementary school, after learning the operations of addition and subtraction, also called addition and subtraction.

It is important to teach children that multiplication of whole numbers is really addition, but it is essential to learn to multiply in order to do such addition more quickly and easily.

It is essential to choose well the first problems that will be used to teach children to multiply, since they must be problems that they can understand and can see the usefulness of learning to multiply.

It is not enough to simply teach them the multiplication tables mechanically, it is much more attractive to show them their use through situations that arise in everyday life, such as when their parents go shopping.

## Examples of multiplicative problems

There are a large number of problems that can be used to teach a child to apply the multiplication tables, below are some problems with their solutions.

**1. How many books are left to order?**

A librarian has to order the books on the library shelves. At the end of Friday afternoon, the librarian realizes that he still has to order 78 boxes of books, which have 5 books each. How many books will the librarian have to order next week?

**Solution**: In this problem, it should be noted that all the boxes have the same number of books. Therefore, 1 box represents 5 books, 2 boxes represent 5 + 5 = 10 books, 3 boxes represent 5 + 5 + 5 = 15 books. But performing all these sums is a very extensive process.

Carrying out all the above sums is equivalent to multiplying the number of books in each box by the number of boxes left to order. That is to say, **5×78**therefore, we multiply this figure and we will know that the librarian lacks ordering **390** books.

**2. How many boxes does the farmer need?**

A farmer needs to pack the coffee obtained in his last harvest in boxes. The total harvest is 20,000 kilos and the boxes in which he is going to pack them have a maximum capacity of 100 kilos. How many boxes does the farmer need to pack the entire crop?

**Solution**: The first thing to note is that all the boxes have the same capacity (100 kilos). So if the farmer uses 2 boxes, then he can only pack 100 + 100 = 200 kilos. If he uses 4 boxes, then he will pack 200 + 200 = 400 kilos.

As before, doing all this amount of addition is a very long process. The key is to find a number that when multiplied by 100 the result is 20,000.

Investigating in detail, it can be seen that said number is 200, since 200 x 100 = 20,000.

Therefore, the farmer needs 200 boxes to pack the entire crop.

**3. How many windows are there?**

Maria has just moved into a building and would like to know how many windows the building has on the front. The building has 13 floors and on each floor there are 3 windows.

**Solution**: In this problem you can count the number of windows floor by floor and add them to get the answer.

But, since each floor has the same number of windows, it is much faster to multiply the number of floors by the number of windows on each floor. This is 13 x 3, therefore the building has 39 windows.

**4. How many tiles are needed?**

Javier is a bricklayer who is building a bathroom floor. So far Javier has placed 9 tiles (squares) on the bathroom floor, as shown in the figure below. How many tiles does it take to cover the entire bathroom floor?

**Solution**: One way to solve this problem is to finish filling in the figure by drawing the missing tiles and then counting them.

But, according to the image, the bathroom floor fits 5 tiles horizontally and 4 vertically. So the entire bathroom floor will have a total of 5 x 4 = 20 tiles.

**5. What is the total number of days?**

The months January, March, May, July, August, October and December have 31 days each. What is the total number of days that all these months add up to?

**Solution**: in this exercise a data is given explicitly, which is the number of days (31). The second data is implicitly given in the months (7). Therefore, we can multiply the number of days by the number of months, 7 x 31, and the result is 217.

### 6. Eggs from the farm

On a farm, 415 eggs are collected daily. In 14 days, how many eggs are collected?

**Solution**: we multiply 415 x 14, which gives the amount of 5,810 eggs.

### 7. Savings

Maria has to take out the trash every Monday, Wednesday, and Friday of each week, and the parents pay her $8 per week. If Maria wants to raise $64, how many weeks will she have to save?

**Solution**: you have to find the number that, multiplied by 8, gives 64. The answer is 8, that is, in 8 weeks, Maria will have saved 64 dollars: 8 x 8 = 64.

### 8. Student ticket

José pays 25 pesos to go to school and return home. How much does José spend in a week, knowing that he studies from Monday to Friday?

**Solution:** The answer is obtained by multiplying 25 by the 5 days that he goes from home to school and returns: 25 x 5 = 125 pesos.