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Aceasta imagine are ca rol atragerea atentiei elevilor, prezentandu-le intr-o maniera amuzanta importanta cunoasterii notiunii de fractie.

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Tutorialele au rolul de a fixa notiunile predate.

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Adunarea si Scaderea Fractiilor ordinare.

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Elevii pot consulta manualele digitale in cazul in care intampina dificultati in intelegerea notiunilor predate. De asemenea, pot lucra exercitii suplimentare, in vederea aprofundarii cunostintelor.

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Adunarea si scaderea fractiilor (Clasa a V-a)

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Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

Mixed Numbers Calculator

Simplify Fractions Calculator

Decimal to Fraction Calculator

Fraction to Decimal Calculator

Big Number Fraction Calculator

Use this calculator if the numerators or denominators are very big integers.

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Division:

The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply

. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction would therefore be . Refer to the equations below for clarification.

Simplification:

It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome than . The calculator provided returns fraction inputs in both improper fraction form as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 10 ¹, the second 10 ², the third 10 ³, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10 ⁴, or 10,000. This would make the fraction

, which simplifies to , since the greatest common factor between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction

for example. To convert this fraction into a decimal, first convert it into the fraction of . Knowing that the first decimal place represents 10⁻¹, can be converted to 0.5. If the fraction were instead , the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.

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Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator. Use this calculator if the numerators or denominators are very big integers.

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Q1: How do you explain fraction to a child?
Ans: Fraction represents part of a whole and usually refers to quantities which are less than 1. It is written in the form a/b where 'a' is called the numerator and 'b' is called the denominator. You can explain fraction to a child by using real life objects like cake, pizza or chocolates and then ask him to divide it into equal parts to share among friends.
Q2: Who introduced fractions?
Ans: The word fraction actually comes from the Latin "fractio" which means to break. From as early as 1800 BC, the Egyptians were writing fractions. The Egyptians wrote all their fractions as unit fractions where they put a mouth picture (which meant part) above a number to make it into a unit fraction.The disadvantage of this system was that it is very difficult to do any calculations.The Babylonians were the first people to come up with a more sensible way of representing fractions in around 1800 BC.
Q3: How do you add fractions?
Ans: To add fractions, if denominators are the same, add the numerators keeping the denominator the same. To add fractions with different denominators we first need to convert both fractions into fractions with common denominator and then add them just as we add like fractions.
Q4: How do u subtract fractions?
Ans: To subtract fractions, if denominators are the same, subtract the numerators keeping the denominator the same. To subtract fractions with different denominators we first need to convert both fractions into fractions with common denominator and then subtract them just as we subtract like fractions.
Q5: In which grade adding and subtracting fractions is taught?
Ans: We teach adding and subtracting fractions in grade 4 and 5. In Grade 4 we teach addition and subtraction of like fractions and in Grade 5 addition and subtraction of unlike fractions is taught.
Q6: How do you add fractions with different denominators?
Ans: To add fractions with different denominators we first need to convert both fractions into fractions with common denominator. Common denominator will be a common multiple of both the denominators. Find the least common multiple and then multiply both the numerator and denominator of each fraction by a number that makes the denominator the least common multiple. Once both fractions have the same denominators, we can simply add the numerators keeping the denominator the same.
Q7: What do we call those fractions which are greater than 1?
Ans: Those fractions which are greater than 1 are called improper fractions or mixed numbers.

Games are played for fun, it is capable of releasing stress from an individual. But, games, on the other hand, can also serve a different purpose. It can be used for academics too. There are various math games that complement mathematics and illustrates its concepts in a very simple fashion that can be understood by the children of all grades with ease.

The era has changed, we have moved to a very advanced and sophisticated kind of world, and henceforth, the pattern of teaching should be changed too, especially in the lower grades. Many times, traditional learning methods (i.e. books) find themselves incapable of binding the reader`s attention, and as a consequence of which, the chapters seem boring to the children. Sometimes, due to this constant phenomenon, the reader judges the whole subject to be not interesting and ultimately finds himself/herself in a position where he/she is no longer interested in that subject ( let's say math), and just studies to mug up the concepts for good scores, and knows nothing about the fundamentals. If this happens, then further, it might lead to worse situations. Hence, children should get their fundamentals cleared in the lower grades itself.

The solution to this problem is the involvement of math games that can prove to be very productive learning activities.

Benefits of learning through math games over traditional learning methods: There are innumerable benefits of learning through math games. Children enjoy playing games and if education becomes a part of those interactive games, all kids would love to be a part of it. One big advantage of learning through math games is that children need not be pressurized to study as they themselves would freely choose to participate in these math games. These math games provide opportunities for building self-concepts about different topics in maths such as number sequences, fractions, decimals, operations, basic algebra, etc, and lead them towards developing a positive problem-solving attitude, thereby making them math solvers. Playing math games encourages strategic mathematical thinking as children find different strategies for solving problems and deepen their understanding of numbers. These games make the children love the subject and its concepts, and give them a fair bit of idea how those concepts are used in the real-world. Learning through math games keep the children stress-free, and they learn from their mistakes and errors, rather than fearing them.

Another very important thing is that when children learn by traditional methods, there are high chances of them forgetting concepts, but if they solve those problems as levels in games, then that would last much longer as they have solved the problem by themselves, and that too in a game, so the chances of him forgetting those concepts become less.

Children often learn from one another as they interact more with each other. Learning concepts through math games not only boost their academic performance but also enhances their overall personality. Concepts of the number system, operations, fractions, place value system, time, etc can be beautifully explained with the help of math games.

It is generally seen that most children of grade 3 find FRACTIONS difficult to understand. The reason is that FRACTIONS is a completely new topic for them, so it takes some time for them to grab things. But learning with the help of FRACTION GAMES will give a better understanding of the fraction concepts.

Let us take an example:

The image shown below interrogates the user, whether he wants to eat the 1/4th part of the 1/8th part.

It can be clearly seen that the first pizza is divided into eight small parts, and the second pizza is divided into four small parts.

Now, suppose each part has to be distributed among children, then a pizza lover will definitely choose the part from the second pizza as it is bigger.

This illustrates the fact that when the numerators are same, then two fractions can be compared by seeing their denominators. The one with a larger denominator will be the smaller fraction. The reason is that it is divided into more no of parts, so each part will be smaller as compared to the one which is divided into less no of parts.

Learning through these interactive means would mark a strong impression of that concept on the children` memory.

In this way, FRACTIONS, a complicated topic can be easily learned through math games.

SplashLearn has been a great platform for children who want to learn mathematical concepts in an effective way. SplashLearn believes that learning through math games make the concepts crystal clear along with its real-world applications. SplashLearn has various learning tools along with a structured gamified content for K-5 that is aligned with CCS that aims for building a deeper understanding of the subject and making the children love mathematics.

OVERVIEW OF FRACTION TOPICS

Children should develop an understanding of fractions as numbers:
What is a fraction?
A fraction is a quantity that represents a part of a whole. In other words, it is a quantity that is formed by a part when a whole is partitioned into b equal parts. It can either be the form , where one whole quantity is partitioned equally into b parts or be of the form a/b, where there are "an" equal parts of size " " each.

Consider the first circle to be a whole. Since the whole portion is shaded, so it can be represented as 1.

Now, if it is divided into two equal parts, the shaded portion represents half of the whole portion, that is . In other words, only one out of two part is shaded and hence it is represented as .

Now in the third circle, only one out of four parts are shaded and hence, it is represented as .

In the last circle, three out of four parts are shaded, and hence it is represented as 3 out of 4 or .

The "total number of parts that the figure is divided into" is determined by the denominator and "the total number of parts that are shaded" is determined by the numerator.

Two fractions are said to be like fractions if they have the same denominators. For instance, and are like fractions. Now, and are unlike fractions as they have different denominators.

SplashLearn provides a set of interactive exercises on identifying fractions. Children are recommended to solve all these worksheets which are carefully structured.

Some more interactive worksheets have been prepared for modeling fractions to familiarize children with the concept. You may practice model fractions

Equivalent fractions:

Fractions which appear different but have the exact same value are known as equivalent fractions.

Multiplying the numerator and denominator with the same number does not change the value of the fraction but creates an equivalent fraction.

For instance,

Similarly, and , on reducing becomes .

=

Hence, these are equivalent fractions.

Consider an example of equivalent fractions:

There are several worksheets available on SplashLearn on equivalent fractions.

One such example is:

=

Find the missing number.

The two fractions are given to be equivalent. That is, the numerator and the denominator of are multiplied by a number to get . Which number do we need to multiply 2 with to get 6? It is 3. So, both the numerator and denominator of is multiplied by 3 to get the new fraction.

Answer: 21

Fractions with like denominators:

While comparing fractions with like denominators, children need to consider the numerators and compare them. In such a case, the greater the numerator, the greater the value of the fraction and vice-versa.

For example:

and : which is greater?

Since the denominators are same, we will compare the numerators. 7 > 3, so > .

Fractions with same numerators:

When the numerators of two fractions are same, then children need to compare their denominators and accordingly decide. In such a case, the greater the denominator, the lesser the value of the fraction and vice-versa.

Identify the fraction which is smaller in value: & ?

Since the numerators are same, we will compare the denominators. 8 > 5, the greater the denominator, the lesser is the value. So, is smaller than .

Comparing unlike fractions: Till grade 3, children learned about like fractions, identifying them, comparing them with either same numerators or same denominators. In grade 4, children will learn about comparing unlike fractions.

The first step in comparing two unlike fractions is to rewrite the fractions with a common denominator. Once the denominators are the same, they can be compared by simply comparing the numerators.

Consider the fractions and .

Rewrite such that the denominator is 10. For that multiply the numerator and the denominator of by 2.

Now the two fractions have the same denominator, compare the numerators.

6 < 7

Thus, .

Proper and improper fractions:

Fractions with their numerators less than the denominators are called proper fractions. The ones which have their numerators greater than their denominators are called improper fractions.

For instance, is a proper fraction, whereas is an improper fraction.

Improper fractions can be written as mixed numbers. Mixed numbers contain a natural number along with a fraction. For instance, can be written as 2.

To convert an improper fraction into a mixed number, first, we need to divide the numerator by the denominator. The quotient is written as a whole number, and the remainder divided by the denominator (divisor) is written as the fraction.

Similarly, to convert a mixed number into a fraction, we need to multiply the denominator of the fraction with the natural number and then add the numerator, while the denominator remains the same as that of the denominator of the fraction.

For example, 8 ¾ can be written as . So 8¾ can be written as .

Adding and Subtracting Fractions with Like Denominators:

Two like fractions are added by simply adding the numerators.

Adding and Subtracting Fractions with Unlike Denominators:

Like comparing unlike fractions, for adding unlike fractions, the step is to write them with a common denominator. Then, add them by adding the numerators.

For example, to add and , multiply the numerator and denominator of by 2 and that of by 5.

Now, add.

The procedures for subtraction are similar.

Multiplying fractions with whole numbers:

Multiplication is introduced as an extended addition using fraction strips. Initially, unit fractions are added with the help of visual models. Eventually, children advance to non-unit fractions without any models.

To multiply a fraction by a whole number, children are first expected to rewrite the whole number as a fraction and then multiply it by the fraction. That is, numerator multiplied with the numerator, and the denominator multiplied with the denominator.

Let us take an example:

= = .

Practice problems by playing games on Multiply unit fractions by a whole number and multiply fraction by whole number

Further, children learn to multiply more complex fractions.

Multiplying Fractions:

The multiplication of two fractions can be modeled by fractional strips as shown:

Algebraically they do it as below:

You can play games on multiply fractions

Operations on Mixed Numbers:

Adding mixed fractions or mixed numbers can be done in two ways.

1. Add the integral parts and fractional parts separately

2. Convert the mixed numbers into improper fractions and add them

Subtraction follows similar rules.

In grade 5, the children are introduced to multiplying mixed fractions. The first step is converting mixed numbers to improper fractions and then multiplying improper fractions.

Tenths and hundredths:

Tenths are special fractions with denominator 10 and hundredths are the ones with 100. Since 100 is obtained by multiplying 10 by 10, an equivalence between tenths and hundredths can be defined by rewriting the fractions.

If you want to rewrite with a denominator of 100, then how will you convert it?

You can solve this visually. Consider a square divided into 10 parts of which 7 parts are shaded. Now, what we have is another square divided into 100 parts, so we need to find out what fraction of it should be shaded so that its fraction turns out to be .

Out of 100 parts, if 70 parts get shaded, then that will be , which is nothing but .

So, the answer is 70.

Consider adding fractions and .

Try to express with a denominator 100, so that it becomes easy for you to add. So multiplying and dividing by 10, we get .

So, now adding , we get 53 hundredths or .

Convert fraction to decimal

= 0.53

Subtraction follows the similar procedure.

Dividing Fractions:

Dividing a whole number by a unit fraction:

This concept can be understood by a simple example:

2 = ?

This can be evaluated as =

This can also be solved visually.

If 2 is divided into pieces that are each of a whole, then how many pieces will be required?

5 piece will cover up to , and the other 5 pieces will cover up to 2, so a total of 10 pieces are required to cover a list of 2 units.

Multiplying and dividing fractions worksheets are available in SplashLearn.

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Fraction Games for Kids Online - SplashLearn

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Q1: How do you explain fraction to a child? Ans: Fraction represents part of a whole and usually refers to quantities which are less than 1. It is written in the form a/b where 'a' is called the numerator and 'b' is called the denominator.

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Find Math games to practice every skill.

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Browse Fraction Online Games | Education.com

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Browse Fraction Online Games. Award winning educational materials designed to help kids succeed. Start for free now!