Fraction Games for 5th Graders

Frequently Asked Questions:

Q1: How can we multiply fractions?

Ans: To multiply fractions we multiply the numerators of both the fractions to get the new numerator, and multiply the denominators of both the fractions to get the new denominator. We can then simplify the resulting fraction if possible. For example 4/5 X 2/3 = (4X2) / (5X3) = 8/15.

Q2: How do you add proper fractions?

Ans: To add proper 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.

Q3: How do you teach adding and subtracting fractions to kids?

Ans: To add or subtract fractions with same denominators, kids should add or subtract the numerators keeping the denominator the same. To add or subtract fractions with different denominators we first need to convert both fractions into fractions with common denominator and then add or subtract them just as we did before in case of same denominators.

Q4: How do you simplify fractions in math?

Ans: We can simplify the fractions by dividing both the numerator and denominator by their highest common factor. For example, to simplify 12/18 we first find the highest common factor of 12 and 18, which is 6. Now divide both the numerator and the denominator by 6 to get the simplified form of 12/18 which is 2/3.

Q5: In which grade adding and subtracting fractions is taught?

Ans: Adding and subtracting fractions with same denominators is taught in grade 4. But adding and subtracting fractions with different denominators is taught in grade 5 where we first need to convert both fractions into fractions with common denominator and then add or subtract them just as we do with fractions with same denominators.

Q6: How do you solve word problems on dividing fractions?

Ans: The first step is to understand the word problem to identify the numbers or fractions that need to be divided. Then divide the numbers or fractions obtained to get the answer.

Q7: How do you multiply a fraction by a whole number?

Ans: To multiply a fraction by a whole number, we multiply the numerator of the fraction by the whole number and  keep denominator the same. This gives us the product and we can simplify the product if required.

 

Fractions are introduced in grade 3. It is a complicated topic for kids of that age as they are only used to the basic math concepts like counting. So, it is advised to use a lot of math games, manipulatives, and activities. If you directly explain the parts of a fraction to a 3rd grader, it is definitely going to create confusion. Instead, if real-life situations like distributing cakes to the friends or buying a half/quarter pound of vegetables or filling gas in the fuel tank of the car in quarter/half/full etc.

SplashLearn provides an activity based learning program to achieve well-defined learning skill sets. Activities like identifying fractions and modelling fraction give a strong foundation for the children about the topic.

Math Games for Fractions:

In grade 5, children advance from basic fraction concept to adding, subtracting, multiplying and dividing fractions. Using math games is an effective way for relatively advanced topics like these. Some of the math games discussed below can boost the understanding of the math operations on fractions.

Addition using fractional circles: Number of players 2-4

Fractional circles cut into various fractions are mixed together. Each child takes one fractional circle randomly from the lot as his/hers turn comes. Whoever completes the whole first wins the game.

Fractional addition dice game: Number of players 2-4

A die with familiar fractions such as , , ,  etc on the sides can be rolled by each child. The fractions rolled by each child are added each time and whoever reaches a whole first, wins the game. It can be made more interesting by adding negative fractions also so that children apply subtraction properties as well.

Constructing fractional strips for multiplication: Number of players 1

Given a square grid, say of size 10 by 10, constructing fractional strips to represent the fractions given by selecting the and dragging the required arrays can be a learning activity. Further, children should be made to construct the product fraction also in a similar way.

Math Manipulatives for Teaching Fractions

Fractions are introduced in grade 3 using manipulatives like fraction circles, fraction charts, and fraction wall.

Fraction strips: Visual models like fractional strips are of great help in explaining concepts like addition, subtraction, multiplication, and division of fractions.

Addition:

Subtraction:

Multiplication:

Division:

Learning Methodologies for Fraction Games for 5th Graders

Addition and subtraction of unlike fractions:

Children are familiar with adding and subtracting fractions with like denominators in grade 4 itself.

In grade 5, they learn about adding fractions with different denominators.

Consider the example of adding fractions ½ and ¼.

This can be represented as fraction strips as shown.

Since the denominators are not the same, the numerators cannot be simply added to add the two fractions.

Here, the first step is to estimate the first fraction, had the whole has been divided into 4.

When the whole is divided into four equal parts, the first fraction would look like:

That is, two parts out of four is shaded. This is equivalent to shading one part out of two.

Thus,   is equivalent to  .

So, the addition can be represented as:

Algebraically, the addition can be performed as   + .

Children are already familiar with finding equivalent fractions by multiplying the numerator and the denominator by the same number. So, the first rule for adding unlike fractions is to write the addends with the same denominator using equivalent fractions. Then, the fractions are like and can be added by adding the numerators.

For example, add  .

Multiply the numerator and the denominator of the first fraction by 3 and that of the second fraction by 4.

 

 

 

Now, the two fractions are like fractions. So, add:

 + .

Subtracting fractions can be performed using the same rule.

For example, - .

Children also use the concept of adding and subtracting unlike fractions in word problems.

For example, Zeenat has finished  her project with Teena and Teena has done  of it. Together what part of the project is completed?

To find the completed part, one needs to add the two fractions.

 .   So,  of the project is completed.

Children also assess the correctness of the results by benchmarking the size of the addends.

For example, consider the fractions  and . If the sum of the two is written as  by adding the numerators and denominators separately, a grade 5 child can point out that it is incorrect as it is less than half whereas one of the addends is equal to half.

 

Adding and Subtracting Mixed Number Fractions:

Adding mixed fractions with unlike denominators can be modelled by using a fractional strip, a number line or a fraction bar.

Consider the addition .

How to add fractions on a number line shown below.

Algebraically this can be done in two ways. The integral parts and fractional parts and the fractional parts can be added separately. That is,

 

Another method is to re-write the mixed number into an improper fraction. Then, generate equivalent fractions so that the addends have the same denominator. Now, add the two like fractions.

Here, the mixed fraction  can be written as . The addition can be performed as shown:

 

 

The addition of unlike mixed number fractions worksheets in SplashLearn have enough problems to have a thorough practice of the topic. Some problems ask for the exact answer while some others ask the child to round off the answer to the nearest half. This gives practice for the rounding off concept as well.

The next concept is of subtracting mixed fractions. An easier way is to separate the integral and fractional parts and subtract.

It is just that the child needs to be extra careful with subtraction with regrouping. 

For example, a child might make mistake in  if they separate the integral and fractional parts and subtract.

 

 

 

This can be done as shown:

 

 

 

 

 

 

 

Now, subtract.

 

 

=

 

The subtracting unlike mixed fraction calculator problems in SplashLearn not just ask the children to enter the final answers, but prepares children for each and every step in calculations similar to the above one. Also as in the case of addition, children are asked to round off complex fractions to 0, 1 or ½.

The word problems play as a bridge between the theory and application of a topic in mathematics. By solving the word problems on subtracting unlike mixed numbers, children reinforces the basic knowledge and apply them in real life situations.

Fraction as numerator divided by denominator:

Suppose 25 lbs sugar is equally distributed among 6 persons. To find the amount of sugar got by each person, you need to divide 25 by 6. That is, 25 ÷ 6 or . Thus, fraction is another way of representing a division. It is written as the numerator divided by the denominator.

Writing  as a mixed fraction  , each person would get  pounds of sugar.

Multiplication of two fractions:

A multiplication is always a repeated addition. That is, multiplying a fraction by 3 is same as adding the fraction 3 times. In 4th grade fractions, children learned how to multiply a fraction by a whole number using visual models as well as by direct multiplication.

When a fraction  is multiplied by a whole number c, it is basically the number a added c times together and divided by the number c. Imagine three sandwiches are shared by 4 kids. So, each one will get  of a sandwich. Note that, the product is basically the part of the sandwich that each kid got multiplied by the number of kids. Thus, this product adds up to the total number of sandwiches, that is, 3.

In grade 5, children learn how to multiply fractions using fractional strips initially.

Later, they understand that for multiplying fractions, the numerators are multiplied together and so are the denominator.

That is, . Children apply this property for direct multiplication of fractions.

That is, .

Multiplication of Mixed Fractions:

Consider multiplying two fractions with at least one of them being a mixed fraction. First, convert the mixed fraction into an improper fraction. Then, multiply the numerators and the denominators separately.

For example, to multiply  and  , first rewrite  as an improper fraction following the math order of operations.

 

Now, multiply the two fractions.

 

The improper fraction  can be written as a mixed fraction as .

To multiply mixed fractions, the procedure is similar.

 

 

Now, cancel the common factors of the two fractions to be multiplied.

 

SplashLearn provides a well-designed worksheet for the topic multiplying mixed fractions.  There you can practice the skill and expertise the computations.

Word problems like finding the area of a rectangular pool of fractional dimensions give the practical application of the computations learned on the topic. Further, children also solve problems involving more complex fractions like mixed fractions using the similar technique.

Interpretation of Multiplication as Scaling

When there are two fractions to be multiplied and if we compare the size of one of the factors to that of the product, we can actually predict the size of the product depending on the size of the second factor.

For example, consider the fractions  and . The second factor   is greater than 1. So, the product would be a number greater than the first factor. That is, a multiplication by a fraction which is greater than 1, will expand the second fraction.

Similarly, consider the product of  and  . The second factor  . So, the multiplication by  will compress the value of the first factor  . That is, a multiplication by a fraction which is less than 1, will compress the second fraction.

SplashLearn has a wide range of practice problems on this topic by assessing the possible values of the factors as well as the product.

Dividing unit fractions by whole numbers:

Consider a division problem, . Translating it to words, what would be the size of each part when  is divided into 4 equal parts?

This can be represented using fractional strips as shown:

Algebraically, division by a number is equivalent to writing a fraction with the number as the denominator and the dividend as the numerator. That is, the division is equivalent to multiplying by the reciprocal.

Dividing  by 4 is same as multiplying  by .

 

Dividing fractions worksheets for the division of a unit fraction by a whole number

Word problems related to the topic can be solved either by using the fractional strips like above or by solving equations with fractions that represent the problem.

For example, if quarter pound, that is,  lbs cake is equally distributed among 5 persons, then find the weight of the cake that each person gets.

The equation that represents the problem is .

Solving the equation, .

That is, each person would get  lbs of cake.

Dividing a whole number by unit fraction:

Now, how to divide a whole number by a unit fraction?

Apples need to be distributed among kids with each kid having half an apple. If there are six apples, how many kids can the apples be given to?

This can be translated as how many one-halves are there in the whole 6?

Using a division symbol, one can write this as .

Algebraically, dividing 6 by  is same as multiplying 6 by  .

 

Children can practice the visual models as well as the algebraic division for dividing a whole number by a unit fraction at 

Children apply the knowledge of the topic to solve word problems like, how many one-fourth can be served from 3 pizzas?

This is same as