#### Solved Examples and Worksheet for Comparing/Ordering Fractions using Models-Unlike Denominators

Q1Find the right comparison between 15 and 16. A. 15 > 16
B. 15 < 16
C. 15 = 16
D. 16 > 15

Step: 1
Draw two congruent circles. Step: 2
Divide one circle into five equal parts and shade 1 part to represent 15 . Step: 3
Divide the other circle into six equal parts and shade 1 part to represent 16 . Step: 4
From the figures, 15 is greater than 16 . Correct Answer is :   15 > 16
Q2Write fractions for the models and compare them. A. 512 = 38
B. 512 > 38
C. 512 < 38

Step: 1
The first model represents the fraction 512.
Step: 2
The second model represents the fraction 38.
Step: 3
The LCD of the two fractions is 24.
Step: 4
512 = 1024 and 38 = 924
[Write the equivalent fractions of the fractions using the LCD as denominator.]
Step: 5
1024 > 924
[Compare the numerators and arrange the fractions in the decreasing order.]
Step: 6
512 > 38
Correct Answer is :   512 > 38
Q3Choose an appropriate symbol to compare the fractions. A. +
B. >
C. <
D. =

Step: 1
The strip representing 16 covers half of the strip representing 13.
Step: 2
This shows that, one strip representing 13 equals two strips of 16.
Step: 3
13 > 16
Q4Order the fractions from the greatest to the least. A. 12 , 15 , 13
B. 12 , 35 , 15
C. 225 , 215 , 13
D. 12 , 25 , 13

Step: 1
From the figure, 12 > 25 .
[The fraction strip representing 12 is larger than the two fraction strips representing 15 each.]
Step: 2
From the figure, 25 > 13 .
[The strip combining the two fraction strips representing 15 each, is larger than the strip representing 13 .]
Step: 3
As 12 > 25 and 25 > 13 , 12 > 25 > 13 .
Step: 4
So, the fractions ordered from greatest to least are 12 , 25 , 13 .
Correct Answer is :   12 , 25 , 13
Q5Use < , > , or = to compare the two fraction models. A. =
B. I don′t know.
C. >
D. <

Step: 1 Step: 2
We got two fractions from the above model are 13 and 23.
Step: 3
Now we are comparing the fractions.
Step: 4
Here, denominators are common, but numerators are different. So, let us compare the numerators. That is 1 < 2.
Step: 5
So, amongst the choices, "<" fills the box given in the model.
Q6Compare the fractions represented by the models. A. 46 > 68
B. 57 = 68
C. 46< 68
D. 56 = 78

Step: 1
The first model represents 68, the second model represents 46
Step: 2
LCD of 68 and 46 = LCM of denominators 8 and 6 = 24.
Step: 3
68 = 6x38x3 = 1824
[Use LCD to write equivalent fraction of 68.]
Step: 4
46 = 4x46x4 = 1624
[Use LCD to write equivalent fraction of 46.]
Step: 5
16 < 18
[Compare the numerators of 1824 and 1624.]
Step: 6
1624 < 1824
Step: 7
46 < 68
Correct Answer is :   46< 68
Q7Joanna bought 12 peaches. She gave 13 of them to Cris and 12 of them to Hal. Which symbol would go inside the circle to compare the fractions? A. <
B. >
C. ×
D. =

Step: 1
13, 12
[Original fractions.]
Step: 2
Since the numerator for all the fractions is same, compare the denominators.
Step: 3
The fraction with the greatest denominator will have the least value.
Step: 4
As 3 > 2, 13 < 12
Step: 5
So, 13 < 12.
Q8Which number sentence compares the fractions represented by the models? A. 127 > 84
B. 712 > 48
C. 712 < 48
D. 712 = 48

Step: 1
The first model represents the fraction 712 and the second model represents 48 .
[Because, in the first model, 7 out of 12 parts are shaded and in the second model, 4 out of 8 parts are shaded.]
Step: 2
Look at the shaded areas. The shaded area of the first model is larger than the second model. So, 712 > 48.
Correct Answer is :   712 > 48
Q9Choose an appropriate symbol to compare the fractions 110 and 120.

A. >
B. =
C. <

Step: 1
One strip representing 110 equals two strips representing 120 . Step: 2
So, 110 > 120 .
Q10Are the shaded parts of Rectangle A and Rectangle B equal? A. No
B. Yes

Step: 1
The figure shown contains two rectangles of equal size: one rectangle is divided into 6 equal parts with 1 part shaded representing the fraction 16 and the other rectangle is divided into 3 equal parts with 1 part shaded representing the fraction 13.
Step: 2
From the figure shown, it is clear that the area shaded in Rectangle A is less than the area shaded in Rectangle B.
Step: 3
Therefore, the shaded parts of Rectangle A and Rectangle B are not equal.
Q11Are the shaded parts of Circle A and Circle B equal? A. Yes
B. No

Step: 1
The figure shown contains two circles of equal size: one circle divided into 8 equal parts with 6 parts shaded representing the fraction 68 and the other circle is divided into 4 equal parts with 2 parts shaded representing the fraction 24.
Step: 2
From the figure shown, it is clear that the area shaded in Circle A is greater than the area shaded in Circle B.
Step: 3
Therefore, the shaded parts of Circle A and Circle B are not equal.