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Q1: How do you represent a fraction on a number line?
Ans: Fraction represents part of a whole. To represent a fraction on a number line, divide the space between every pair of two consecutive integers on the number line into as many equal parts as the denominator of the fraction. Mark first point of the number line as 0, the next parts on the number line is 1/b, 2/b, 3/b, 4/b, and the last part is b/b = 1 where b is the denominator of the fraction.
Q2: How do we identify equivalent fractions using models?
Ans: Fractions are equivalent if they represent the same amount. To identify equivalent fractions using model, draw both the fractions using the model, if the shaded area represented by both the models is exactly equal irrespective of the number of parts in it, then the fractions are equivalent. For example, 2/3 and 4/6 have different parts but are equivalent as both fraction models have two-third part shaded, i.e both represent the same amount.
Q3: What are the fractions between 0 and 1?
Ans: There can be any number of fractions between 0 and 1 depending on the number of parts 1 is divided into. For example, if you want to divide 1 into 10 equal parts, so there are fractions like 1/10, 2/10, 3/10, 4/10 and so on till 9/10 between 0 and 1. If you choose to have more equal parts of 1, there will be more fractions between 0 and 1.
Q4: How can we compare fractions using models?
Ans: To compare the fractions using models, we closely take a look at the shaded area of each fraction. The model which has bigger shaded area represents a bigger fraction and vice versa.
In initial years of math education, kids deal with numbers and operations. The first glimpse of fraction kids get to see is when their parents buy groceries and vegetable that have fractional weights. Half a pound of apple, quarter pound of spices, etc are some things that they are used in their everyday life. Another example of fractions that they see every day is the amount of gas filled in the fuel tank as full/half/quarter tanks.
So, what is fraction?
Fraction is a representation of a part of a whole. If the fuel tank is divided into two equal compartments, filling one of them is precisely the half. One slice of a pizza that is cut into four equal slices represents a quarter.
Fraction is a totally new concept introduced in 3rd grade curriculum. According to common core mathematics curriculum, this should be done using good math manipulatives and interactive games for kids. Kids should be encouraged to get more involved in problem solving activities.
Fraction chart is one of the most commonly used manipulative for the topic.
Fraction circles can be used for educational math games as well as a manipulative to teach fractions.
They can also be used for adding and subtracting fractions worksheets or games in higher grades. Playdoughs can be made to different fractions to show kids about how they are formed.
There are many math games for 3rd graders. Digital puzzle games for kids are also available in abundant. They use fractional questions as puzzle solvers by unfolding an image by answering them correctly.
Comparing fractions games between two players can be something like rolling a fractional die and comparing the numbers rolled. The one who gets a larger fraction wins that particular roll and wins a point. Whoever reaches 10 points first, wins the game.
Apart from these, there are many math online games for kids that can help them practice the skills that they learned.
SplashLearn is one of the best math websites for students, providing a well-designed kindergarten activities and fun worksheets for kids up to grade 5 as per math common core standards.
Sarah is celebrating her birthday with her friends. She cut her birthday cake into 12 equal pieces and ate one of them. That is, she ate one out of 12 of the cake. This can also be represented using a fractional notation, 
of the cake. Here, 1 is called the numerator, 12 is called the denominator. The line that separates the numerator and the denominator is called a fraction bar.
Suppose there are 8 kids attending the birthday party. When a pizza is distributed equally, each kid would get 
of the pizza.
Miranda is very fond of pizza, so she would like to eat 3 slices. That is, she would eat 3 out of 8 equally cut slices or 
of the pizza.
A fraction is a part of a whole which is equally divided into different parts.
One out of 4 equal parts in the above square is shaded. So, it represents the fraction 
. If there are 3 parts shaded, then it represents 
. That is, there are 3 one-fourths in a three-fourths.
The denominator tells about the number of parts that the whole is equally cut into. Note that it is important to divide the whole into equal parts.
This does not represent the fraction as the parts are not divided equally.
Another way to represent a fraction is using a number line.
Since the fraction 
is same as two one-thirds, this can be plotted on a number line with fractions, starting at 0 and moving one-third for two times to the right.
Thus, fractions definition can be summarized as:
Fraction is a representation of a part of a whole.
They are represented using the fractional notation 
, b ≠ 0 where
.
The line that separates the numerator and the denominator is called a fraction bar.
Like fractions have the same denominator. Unlike fractions have different denominators. The fractions 
and are like fractions whereas and 
are unlike fractions.
The different types of fractions are proper, improper and mixed fractions. Proper fractions have numerators less than the denominators. So, they have a value less than 1. The fractions , etc are proper fractions. Improper fractions have numerators greater than the denominators. So, they have a value greater than 1. The fractions 
, 
etc are improper fractions.
Two fractions are equivalent if they have the exact same size.
How to do equivalent fractions?
Consider the fractional area models below:
In the first strip, one part out of two is colored in red. In the second strip, two parts out of 4 are colored in blue and in the third 4 out of 8 is colored in green. When the number of portions colored is considered, it varies from 1 to 4. But the total area colored in each color as a part of the whole is half. That is, in all the three strips, half of the total area is colored. So, the fractions represented are equivalent.
Thus, = 
= 
.
Plot these fractions on a number line.
To mark the ½ on a number line, the whole part from 0 to 1 can be divided into two equal parts and the midpoint can be marked as ½.
Similarly, to mark , the whole part between 0 and 1 can be divided into four equal parts and the second mark from 0 denotes . The fraction is the fourth mark from 0 when the whole from 0 to 1 is divided into 8 equal parts.
Thus the fractions on number lines show that equivalent fractions are plotted at the exact same place.
Another way of understanding the equivalence is to simplify fractions or to reduce fractions.
A fraction can be doubled, tripled, halved, quartered etc as mental math problems to simplify it.
At the simplifying fractions worksheets available at SplashLearn, children can solve math problems for 3rd graders using equivalent fraction models. Equivalent fractions are widely used to add and subtract fractions and many other operations with fractions.
The 3rd grade fractions skills include generating equivalents for common fractions like and .
Consider the fraction equation, = 
.
How to solve fractions?
Comparing the numerators of the two fractions, the numerator of the first fraction is tripled to get that of the second fraction. That is, 6 = 3 × 2 . Since the two fractions are equivalent the denominator is also multiplied correspondingly. That is, the denominator of the first fraction has to be doubled to get that of the second fraction.
Thus, the denominator of the second fraction is 3 × 3 = 9 .
Using the same technique, children can identify a pair of equivalent fractions among others.
In the 3rd grade worksheets for equivalent fractions in SplashLearn children solve math equations involving fractions.
Each of the circle below represents a whole.
The first circle has only 1 part and 1 part is shaded in red. So, the fraction represented is 
or 1.
The second circle is divided into 2 and both the parts are shaded in blue. So, the fraction represented is 
or 1. Similarly, the other two circles are divided into 3 and 4 parts respectively and all the parts are shaded.
The area covered by the shaded part in each of the circle is the same. Therefore, they are equivalent fractions. That is, = = 
= 
= 1 .
Now, consider 3 whole which is 1 part.
Each of the circles is represented as and there is 3 such whole. Thus, the fraction represented here is 
.
This can also be represented using a number line.
Like normal addition, 3 whole are added one by one by taking leaps to the right on a number line.
Since the skip counting is by 1, each addition takes a leap of one whole to the right and the denominator of the fractional representation is 1. Thus, the whole number 3 represented in fractional form is .
Now, the same representation can be done with skip counting by .
Since the skip counting is by ½, each addition takes a leap of one-half to the right and the denominator of the fractional representation is 2. Thus, the whole number 3 represented in fractional form is 
.
In a similar way, by skip counting by one can re-write the whole number 3 into 
, as a fraction. Since all these fractions represent the same number on the number line, they are equivalent fractions.
Thus, 3 = = = . Note that these equivalent fractions examples are not
fractions in simplest forms.
Note that any whole number can be written as a fraction with a denominator 1. Writing fractions as decimals would make it easier to understand this concept. Turning fractions into decimals are discussed in detail in higher grades.
The result of comparing two fractions can be written using either <,>, or = .
If two fractions have the same denominator, then the two can be compared by simply comparing the numerators.
For example:
Here, both the watermelons are cut into 6 equal slices. To compare fractions of slices left, the child just needs to compare the number of pieces left. That is, in the first watermelon there are two slices left and in the second there is only one. So, the fraction represented in the first watermelon is greater than that of the one in the second. That is, 
> 
.
The third grade worksheets for comparing fractions with the same denominators are available at SplashLearn. Solving word math problems gives a clearer idea of the concept as the kids can connect it to the real-life.
Below are two identical squares one divided into two equal parts and the other into four.
One part of each square is shaded. The shaded region of the first square is more than that of the second one as the second square is divided into 4 equal parts. So, each part of the second square is smaller than that of the first. That is, < . Similar fractions practice problems that compare fractions with the same numerators are available in SplashLearn.
In general, when fractions with same numerators are compared, the fraction with a larger denominator is smaller than that with a smaller one.
Equivalent fractions have exactly the same size. So when compared, the result can be connected using equality symbol. For example, = 
= 
= 
.
In a similar way, multiple fractions can be compared. A clear understanding of this topic will help in comparing and ordering fractions in later stages.
