Problems

1. Introduction

To make a problem is like make a trip. To make a trip, first we need to know where we want to go. If we do not know it, we will never take the right road. On a trip we use the car, bus, train, plane or other means.

To make a problem, we have to know well what it asks or what we have to obtain. For that, we use additions, subtractions, multiplications, divisions or other operations.

To make problems, we need two things: first, we must know how to do the operations (addition, subtraction, multiplication, division and other operations) and second, we must understand what the problem asks, that is, we have to know where we want to go. If we do not understand what we need to obtain, we will never solve the problem. We can say that we understand a problem when we express what the problem asks with other personal words, other than the statement.

In the problem there are three different parts: a) what the problem asks, the unknown quantity, b) what the statement says, the information of the problem, c) the solution that is achieved after making the correct operations.

Example: I have seven candies (information) and someone gives me 3 candies for my birthday (information). How many candies do I have now? (unknown quantity). After making the sum of 7 and 3, we know that I have 10 candies (solution).

 1. What the problem asks is... 2. What the statement says is... 3. The solution is...

2. - Calculate the greatest and the lowest

In many problems the first question that we can ask is: will the solution be greater or lower than the information that the statement gives us?

Example: I have 3 candies and my mother give me 5. How many candies do I have now? The first question is: Will I have more or less candies than before? Obviously I will have more, because 8 is greater than 3.

Example: I had 18 sheets and I spent 5. How many sheets do I have now? The question is: will I have more or less sheets than before?

Answer and indicate if in the result we will have more or less.

 1. A kilo of chocolates costs 7 euros, how much money will 10 kilos cost? 2. If 9 bottles cost 120 euros, how much money will a bottle cost? 3. I had 5 coins and I spent 3. How much money do I have? 4. I had 7 stickers and a friend gave me 8. How many stickers do I have now? 5. In a box there are 5 chocolates and I shared them among 10 guys. How much chocolates will each of them receive? 6. A family spends 200 euros daily. How much does the family spend in a week?

When we add is like we join in one amount two or more previous numbers.

Example: Antonio has 5 euros and I give him 2 euros. How much money does he have now? (More) The operation that we need to do is the addition. We will have 7 euros.

We must take care that the two quantities are of the same class. So we cannot add euros and candies, because what would be the result?

Subtraction is removing or separating one quantity of another.

Example: Joseph had 5 pens and he lost three. How many pens does he have? (Less). The correct operation is the subtraction and there are 2 pens.

Answer and indicate the operation that we have to do:

 1. Peter has 2 pens in the pocket and 3 in his briefcase. How many pens does he have in total? 2. Antonio has 5 stickers and I give him 3. How many stickers does he have now? 3. In the kitchen we had 14 apples and we ate six. How many apples do we have? 4. In one pile, we have 5 shoes and in another pile we have 12 shoes. What is the difference between the two piles? 5. Juan has 5 pens and someone gives him 5. How many pens does he have now? 6. Andrew is 11 and his brother Peter is 15. How many more years than Andrew is Peter??

4- Multiplication and division problems

Example: My dad gives me 2 euros on Sunday. How much money will I have in 3 Sundays? When we multiply, we repeat the sum of a number (2 euros) as many times as the other number indicates (three Sundays).

Example: We have 20 chocolates to distribute among 5 friends. How many chocolates will each of them receive? When we divide, we distribute a number in several equal parts. In this case 20: 5 = 4 chocolates.

Answers and indicate the operation that we have to do: multiplication or division:
 1. I have to put 50 bulbs in 10 boxes. How many bulbs will I put in each box? 2. An employee earns 100 euros daily. How much money will he earn in 30 days? 3. A box has 20 chocolates, how many chocolates will be in 7 boxes? 4. We want deliver 35 candies among 7 friends. How many candies will they receive? 5. In a purse there are 6 books. How many books will be in five purses? 6. I gave 15 euros to 3 cousins. How much money will each one receive?

5. - Review of the four operations

Answers and indicate the operation that we have to do: addition, subtraction, multiplication, division:

 1. I share out 20 stickers between 4 players. How many stickers will each one have? 2. I have three stickers in a pocket and 8 in another pocket. How many stickers do I have in total? 3. A worker earns 120 euros daily. How much money does he earn in 7 days? 4. I had 3 pens and I lost two. How many pens do I have now? 5. I had 5 images and I found 7. How many images do I have now? 6. We want share out 35 cakes between 5 friends. How many cakes will each one receive? 7. In a box there are three pencils, how many pencils will be in 8 boxes? 8. Isabel had 7 images and she gives me three. How many images does she have now?

6. Problems with one or more operations.

The previous problems have a single operation, but other problems have two or more operations.

Answers and indicate if they have one or two operations:
 1. A bus had 15 persons; 3 men up and 5 men down. How many people are in the bus? 2. An employee earns 130 euros daily and he spent 8 euros daily. How much money will he have in 30 days? 3. John had 5 candies and he ate two. How many candies does he have? 4. Maria had 5 boxes with 20 chocolates in each one. She ate 30 chocolates. How many chocolates does she have? 5. I had 5 toys and someone gave me 6 more. How many toys do I have now? 6. Carmen wants to share out 25 chocolates among her and her 5 friends. She did it and her aunt gives her 3 chocolates more. How many chocolates does Carmen have now?

| Educational applications | Mathematics | In Spanish | To print |

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