To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Equivalent Fractions Worksheet - Page 6

Equivalent Fractions Worksheet
  • Page 6
 51.  
In an examination, Frank scored 70 out of 100. What fraction of the points did Frank get? Choose the fraction in its simplest form.
a.
8 11
b.
7 10
c.
4 5
d.
None of the above


Solution:

The fraction of the points Frank got = points secured by Frank Total score = 70 / 100

70 = 1, 2, 5, 7, 10, 14, 35, 70
100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
[Write factors for numerator and the denominator.]

G.C.F of 70 and 100 is 10.
[Select the greatest common factor for 70 and 100.]

70 ÷ 10100 ÷ 10 = 7 / 10
[Divide numerator and denominator by their GCF, 10.]

The fraction of points Frank scored is 7 / 10.


Correct answer : (2)
 52.  
In a family of 12, 5 are females and the remaining are males. Choose two equivalent fractions for the fraction of females in the family.
a.
10 24 and 15 36
b.
15 36 and 10 36
c.
10 36 and 15 24
d.
None of the above


Solution:

Fraction of females = Number of femalesTotal number of persons in the family = 5 / 12

5 / 12 = 5×212×2 = 10 / 24
[Multiply the numerator and the denominator by the same nonzero number.]

5 / 12 = 5×312×3 = 15 / 36
[Multiply the numerator and the denominator by the same nonzero number.]

The two equivalent fractions for the fraction of females in the family are 10 / 24 and 15 / 36.


Correct answer : (1)
 53.  
Are the two models equal?

a.
Not equal
b.
Equal


Solution:

In model 1, 3 divisions are shaded out of 4 divisions.

So, model 1 represents a fraction of 3 / 4.

In model 2, 6 divisions are shaded out of 8 divisions.

So, model 2 represents a fraction of 6 / 8.

6 = 1, 2, 3, 6 and 8 = 1, 2, 4, 8
[Write factors for the numerator and the denominator.]

6 / 8 = 6÷2 / 8÷2 = 3 / 4
[Divide numerator and denominator by their GCF, 2.]

The equivalent fraction of fraction represented by model 2 is 3 / 4.

As the two fractions are equal, the models are equal.


Correct answer : (2)
 54.  
Are the two models equal?

a.
Not equal
b.
Equal


Solution:

In model 1, 3 divisions are shaded out of 4 divisions.

So, it represents a fraction of 3 / 4.

In model 2, 10 divisions are shaded out of 16 divisions.

So, it represents a fraction of 10 / 16.

10 = 1, 2, 5, 10 and 16 = 1, 2, 4, 8,16
[Write factors for numerator and the denominator.]

= 10÷2 / 16÷2 = 5 / 8
[Divide numerator and denominator by their GCF, 2.]

The equivalent fraction of fraction represented by model 2 is 5 / 8.

As the two fractions are not equal, the models are not equal.


Correct answer : (1)
 55.  
Choose the model which is not equivalent to the other models.


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


Solution:

Figure 1 represents the fraction 4 / 8.

Factors of 4 are 1, 2 and 4.

Factors of 8 are 1, 2, 4 and 8.

The common factors of 4 and 8 are 1, 2 and 4.

48 = 4÷28÷2 = 24
[Divide numerator and denominator by the common factor, 2 and simplify.]

48 = 4÷48÷4 = 12
[Divide numerator and denominator by the common factor, 4 and simplify.]

The two fractions equivalent to 4 / 8 are 2 / 4 and 1 / 2.

Figures 2 and 3 represent the fractions 2 / 4 and 1 / 2.

Figures 1, 2 and 3 model the equivalent fractions.

Figure 4 models the fraction 3 / 4, which is not equivalent to the fractions modeled by other figures.

Figure 4 is the model, which is not equivalent to the other models.


Correct answer : (4)
 56.  
Which pair of fractions is equivalent to the fraction modeled by the figure shown?


a.
10 16 and 12 15
b.
8 10 and 12 15
c.
9 15 and 15 24
d.
8 18 and 12 27


Solution:

In the figure shown, 4 divisions are shaded out of 9 divisions.

The figure represents the fraction 4 / 9.

4 / 9 = 4×29×2 = 8 / 18
[Multiply numerator and denominator by the same nonzero number.]

4 / 9 = 4×39×3 = 12 / 27
[Multiply numerator and denominator by the same nonzero number.]

The pair of fractions equivalent to the fraction modeled by the figure shown is 8 / 18 and 12 / 27.


Correct answer : (4)
 57.  
Write two equivalent fractions for the fraction modeled by the figure.


a.
6 24 and 12 32
b.
10 16 and 5 8
c.
3 8 and 12 32
d.
None of the above


Solution:

In the figure, 6 divisions are shaded out of 16 divisions.

The figure represents a fraction of 6 / 16.

6 / 16 = 6÷2 / 16÷2 = 3 / 8
[Divide numerator and denominator by the same nonzero number.]

6 / 16 = 6×216×2 = 12 / 32
[Multiply the numerator and the by the same nonzero number.]

The two equivalent fractions for the fraction modeled by the figure are 3 / 8 and 12 / 32.


Correct answer : (3)
 58.  
Choose two equivalent fractions for the fraction represented by the figure.

a.
10 16 and 15 24
b.
6 10 and 9 15
c.
6 16 and 9 24
d.
None of the above


Solution:

In the figure, 5 stars are shaded out of 8.

The figure represents a fraction of 5 / 8.

5 / 8 = 5×28×2 = 10 / 16
[Multiply the numerator and the denominator by the same nonzero number.]

5 / 8 = 5×38×3 = 15 / 24
[Multiply the numerator and the denominator by the same nonzero number.]

The two equivalent fractions for the fraction represented by the figure are 10 / 16 and 15 / 24.


Correct answer : (1)
 59.  
Write the fraction represented by the model in its simplest form.

a.
4 5
b.
2 5
c.
3 5
d.
None of the above


Solution:

In the model, 15 divisions are shaded out of 25 divisions.

The model represents a fraction of 15 / 25

15 = 1, 3, 5, 15 and 25 = 1, 5, 25
[Write factors for numerator and the denominator.]

15÷5 / 25÷5 = 3 / 5
[Divide numerator and denominator by their GCF, 5.]

The simplest form of the fraction that the model represents is 3 / 5.


Correct answer : (3)
 60.  
Find the value of n, if 3 n and 12 20 are equivalent fractions.
a.
6
b.
7
c.
5
d.
None of the above


Solution:

Factors of 12 are 1, 2, 3, 4, 6, 12.

Factors of 20 are 1, 2, 4, 5, 10, 20.

The common factors are 1, 2, 4.

3n = 1220
[Since both fractions are equivalent.]

3n = 12÷420÷4
[Divide numerator and denominator of 12 / 20 by their common factor 4 to make the numerator 3.]

3n = 35
[Simplify.]

The value of n is 5.


Correct answer : (3)

*AP and SAT are registered trademarks of the College Board.