Fractions Exercises – Learn Fractions

Fractions! Big problem to learn them. One of our biggest headaches is math. At the beginning, we learn to count. Easy! But year by year, the matter is getting more cumbersome. And suddenly, we come to the dreaded fractions. If the basic operations are already difficult (read add, subtract, multiply and divide), how can we understand those complicated fractions?

When we come across fractions, we ask ourselves why do we have to learn that and what is it for us? If it’s worth anything, you’ll tell yourself in the middle of a big sigh of annoyance. Although you may not believe it, knowledge about fractions is very useful.  That was very clear to the Egyptians when they invented the “fractional numbers” many centuries ago. They were especially useful when dealing with the Nile River and its floods, or with construction calculations.

In your daily life, knowledge of fractions is very necessary. Even in the kitchen you use it; for example, when calculating amounts of flour or sugar to make cookies. When you get together with your friends and order a large pizza, they will surely divide it in equal portions. You have to be fair! That everyone wants to eat.

That is why it is important that you learn to perform operations with fractions. You don’t know when you will need to use that knowledge. So get ready. Cautious is worth two. Perhaps you feel that you are too old to start learning mathematics. Well, you are never too old to learn something.

Don’t be discouraged. We will help you understand fractions. You may be just entering the world of fractions, or you need to teach them to your students and you don’t know how. With us you will not only learn about fractions, you will also see exercises that clarify the panorama for you. We will explain how to do operations with fractions, in a simple and enjoyable way. You will see that it is not as complicated as it seems.

Instructions

The first thing we should know is that the universe of numbers is diverse and very complex:

1. The numbers with which we learned to count as children ,the first ones we know, are  the natural ones. Remember: one, two, three….
2. But there are other types of numbers, one of those are the In this group is that we find the fractions.

Let’s get into fractions

1. We have, then, that the fractions are rational numbers and represent one or more portions of a whole (unit).
2. Therefore, a unit, viewed as a whole, can be divided into a number of equal parts, or fractions. Whether it is a cake, an apple or a pizza, for example, we can separate them (all) into identical portions.
3. Next, look at the structure of a fraction. Every fraction is made up of two numbers that are written separated by a vertical or perpendicular line (1/2).
4. We call the upper number the numerator; to the bottom, denominator.
5. The numerator represents the portions that interest us; the dominator, to all the portions into which the unit is divided. For this reason, the numerator must always be less than the denominator.
6. Let’s specify what we’ve seen so far. If we divide an apple into four (equal) portions and take two, we have 2/4. But we can also divide it into eight parts, into ten, into twelve, and let’s stop cutting. The more parts the apple is divided into, the smaller each portion will be.
7. You have no problem reading the numerator, it is a cardinal number. Remember that it is the portion that interests you of the total (that is, the unit).
8. As for the denominator, as it is the number in which the unit is divided, then you use partitive. Let’s go back to the example of the apple. If they are 2/4, we read two fourths; 2/8, we read two eighths ; and 2/10, two tenths . But if the denominator is greater than 10, then we add the suffix -avos. So 2/12, is two twelfths ; 3/15, three fifteenths. Extremely easy!

Some exercises

Knowing the fractions better, and knowing both how to read and write them, let’s proceed to do exercises. Let’s start with operations with like fractions, those that have the same denominator.

1. To add, simply add the numerators and keep the denominator. Therefore, 2/4 +1/4 = 3/4. You can do the same with subtraction: 3/4 – 1/4 = 2/4.
2. But the denominators are not always the same, we speak then of heterogeneous fractions. Here the matter is complicated. What should we do? We must achieve that the two fractions have the same denominator; that is, we proceed to equalize them.
3. How do we equate two different denominators? To do so, it is necessary to appreciate that two different fractions (with different numerators and denominators) do not really have to be.
4. Is it possible for two apparently different fractions to be equal? Let’s go back to the apple: if you divide it in two and take one of the halves, you have ½. If, on the other hand, you divide it into four and take two quarters (2/4), you have exactly the same amount; that is, half. So 1/2 and 2/4 constitute the same portion of the total. We call these fractions
5. To add 1/4 + 1/2, we equalize the denominators like this:1/4 + 2/4 = 3/4.  Because we know that 1/2 is equivalent to 2/4.
6. If you need to multiply fractions, you multiply their numerators and then their denominators. The product of each multiplication is put in its rightful place. Then, to multiply 6/8 x 3/6 x 4/7, we first multiply 6 x 3 x 4; and then 8 x 6 x 7. Pay attention to the following exercise:
7. When the result is a fraction that is very difficult to understand, as in the previous exercise, we must reduce or simplify it. To do this, we find the smallest equivalent fraction that is possible. How? with its dividers.
8. To find the divisors of 32, let’s think of numbers that divide it exactly. For this, when dividing it cannot give us a decimal number as a result. In the case of 32, we have: 2, 4, 8 and 16. And what numbers are divisors of 120?; Well, 2, 3, 4, 5, 6, 8, 15, 20, 24, 40 and 60. You can check it with a calculator, so you will understand it more quickly.
9. Once the divisors of the numerator and denominator have been determined, we identify the ones common to both, which in our case are 2, 4 and 8. You must take the largest of all and with it divide both the numerator and the denominator.
10. We can now simplify the fraction 32/120. By dividing the numerator (32 ÷ 8) and the denominator (120 ÷ 8), we get 4/15. As you can see, 4/15 is more understandable than 32/120.
11. But what happens when you can’t find common divisors? In that case, the fraction is impossible to reduce. Don’t suffer trying! They call this type of fractions irreducible for a reason.
12. Finally, to divide fractions, multiply in the form of a cross. How do you do it? Simple: numerator 1 x denominator 2 (to find the numerator) and denominator 1 x numerator 2 (for the denominator).

There are also mixed fractions. We find them very easily in cooking recipes. For example, if the recipe calls for one and a half cups of sugar, you have a mixed fraction (1½). As you can see the first number is an integer; the second, a fraction. They also call them improper.

What do you need:

• Knowing how to perform basic mathematical operations (understand adding, subtracting, multiplying and dividing).
• A good calculator is ideal, but you can do the necessary operations with your mobile or your computer.
• Patience and care when performing the necessary operations.
• A significant taste for numbers is not too much.

Tips

1. If you don’t understand fractions, circle one. Divide it into the portions marked by the denominator; and then color the portions indicated by the numerator. There you have your fraction. It is not difficult and it will clear the picture for you.
2. If there are apps that help you learn or teach fractions, use them. For the little ones, just grab your mobile and look for them in the Play Store.
3. Also resort to the web; there they will provide you with multiple resources for teaching or learning fractions. There are bloggers interested in math, and fractions!
4. A very useful example of the use of fractions is the division of time. What do you mean quarter to one? It is very simple, you have divided the hour into four parts of fifteen minutes each. Therefore, if it is a quarter to one, it is fifteen minutes. And if you say it’s a quarter past one, you’re using a mixed number made up of the unit (1 hour) plus the fraction ¼. You therefore have 1 ¼ (1:15).
5. So yes, you use fractions a lot, and mixed fractions too. But you don’t realize it.
6. One of the best ways to teach fractions, then, is to show how useful they are in reality. We learn more easily what we consider relevant and useful for our lives. Do not forget. And if you also do it in a playful way, much better.
7. Remember that, at least in terms of fractions, if you know how to divide, you will win.