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Equivalent Fractions Worksheet - Page 11

Equivalent Fractions Worksheet
  • Page 11
 101.  
Choose the number sentence that is true about the figure shown.


a.
1 2 > 2 4
b.
1 2 = 2 4
c.
1 2 < 2 4
d.
1 2 = 4 2


Solution:

The fraction represented by the first square is 1 / 2 .
[1 out of 2 parts is shaded.]

The fraction represented by the second square is 2 / 4 .
[2 out of 4 parts are shaded.]

Also, we notice that the squares are of the same size and the same amount is shaded in both the squares.

So the number sentence '1 / 2 = 2 / 4' is true about the figure shown.


Correct answer : (2)
 102.  
Identify the figure that shows a pair of equivalent fractions.

a.
Figure 1
b.
Figure 4
c.
Figure 2
d.
Figure 3


Solution:

Among the four figures shown, only the pair in Figure 1 have the same amount shaded.

So, Figure 1 shows a pair of equivalent fractions.


Correct answer : (1)
 103.  
Which model is shaded to show a fraction equivalent to 5 15?

a.
Model 2
b.
Model 3
c.
Model 1
d.
Model 4


Solution:

Model 1 represents the fraction 1 / 3.
[1 out of 3 parts is shaded.]

Model 2 represents the fraction 5 / 8.
[5 out of 8 parts are shaded.]

Model 3 represents the fraction 3 / 4.
[3 out of 4 parts are shaded.]

Model 4 represents the fraction 5 / 10.
[5 out of 10 parts are shaded.]

The given fraction 5 / 15 reduces to 1 / 3.
[Divide both the top and the bottom numbers by 5, because they both are multiples of 5.]

So, among the models shown, only Model 1 is shaded to show a fraction equivalent to 5 / 15.
[Because, 5 / 15 = 1 / 3.]


Correct answer : (3)
 104.  
Identify the two figures that have an equivalent fraction shaded.

a.
Figure 2 and Figure 3
b.
Figure 2 and Figure 4
c.
Figure 1 and Figure 2
d.
Figure 3 and Figure 4


Solution:

Figure 1 represents the fraction 6 / 8.
[6 out of 8 parts are shaded.]

Figure 2 represents the fraction 3 / 4.
[3 out of 4 parts are shaded.]

Figure 3 represents the fraction 1 / 4.
[1 out of 4 parts is shaded.]

Figure 4 represents the fraction 1 / 2.
[1 out of 2 parts is shaded.]

Make all the denominators (bottom numbers) the same, preferably 8. Figure 1 already shows a fraction with 8 in the denominator.

Consider 3 / 4. It becomes 6 / 8.
[Multiply the top and the bottom numbers by 2.]

Consider 1 / 4. It becomes 2 / 8.
[Multiply the top and the bottom numbers by 2.]

Consider 1 / 2. It becomes 4 / 8.
[Multiply the top and the bottom numbers by 4.]

So, Figure 1 and Figure 2 have an equivalent fraction shaded.


Correct answer : (3)
 105.  
John and Amy are arranging books in shelves. They have completed 3 5 of the job so far. Identify the fraction that is equivalent to 3 5.
a.
6 10
b.
3 10
c.
6 5
d.
9 8


Solution:

Let us use skip counting to find a fraction equivalent to 3 / 5.

Skip count the top number by 3′s and the bottom number by 5′s.

3 / 5 , 6 / 10 , 9 / 15 , 12 / 20, and so on.
[All these fractions are equivalent to each other, because we added as many 5′s as 3′s to each fraction.]

So, among the fractions listed, 6 / 10 is the right answer.


Correct answer : (1)
 106.  
Use the figure shown to choose the number that replaces the ? to make the fractions equivalent.

a.
6
b.
3
c.
12


Solution:

In the first rectangle, 6 out of 12 parts are shaded.

In the second rectangle, 3 out of 6 parts are shaded.

So, 6 / 12 = 3 / 6.
[Because, both the rectangles shown are the same size and the same amount is shaded in both the rectangles.]

So, 3 replaces the ? to make the fractions equivalent.


Correct answer : (3)
 107.  
Are the pair of fractions 2 5 and 3 10 equivalent ?
a.
Yes
b.
No


Solution:

Fractions that represent the same amount are called equivalent fractions.


Represent 2 / 5 using two 1 / 5 strips and represent 3 / 10 using three 1 / 10 strips and line up three 1 / 10 strips below the two 1 / 5 strips as below.

From the above figure, 2 / 5 and 3 / 10 does not represent same amount.

So, the fractions 2 / 5 and 3 / 10 are not equivalent fractions.


Correct answer : (2)
 108.  
Compare the two figures. Are the fractions equivalent?


a.
No
b.
Yes


Solution:

The fraction represented by the first circle is 1 / 2 and the fraction represented by the second circle is 3 / 8.

Fractions that represent same amount are called equivalent fractions.

In fraction 1 / 2, multiplying the numerator and the denominator by 3 gives 3 / 6.

As 3 / 6 is not equal to 3 / 8, the fractions 1 / 2 and 3 / 8 are not equivalent fractions.

So, the fractions represented by the figures are not equivalent.


Correct answer : (1)
 109.  
Find an equivalent fraction of 6 8 .
a.
1 2
b.
3 4
c.
3 2
d.
8 6


Solution:

Fractions that represent same amount are called equivalent fractions.


Represent the fraction 6 / 8 by using six 1 / 8 strips as below.

Line up 1 / 4 strips below 1 / 8 strips.

As three 1 / 4 strips form the same amount as six 1 / 8 strips, 6 / 8 and 3 / 4 are equivalent fractions.

So, the equivalent fraction of 6 / 8 is 3 / 4 .


Correct answer : (2)
 110.  
Find the fraction equivalent to 2 3 .
a.
4 6
b.
1 3
c.
13 6
d.
2 4


Solution:

Fractions that represent same amount are called equivalent fractions.


Represent the fraction 2 / 3 using two 1 / 3 strips as below.

Line up 1 / 6 strips below 1 / 3 strips.

As four 1 / 6 strips form the same amount as two 1 / 3 strips, 2 / 3 and 4 / 6 are equivalent fractions.

So, the equivalent fraction of 2 / 3 is 4 / 6 .


Correct answer : (1)

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