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. $\frac{8}{11}$ b. $\frac{7}{10}$ c. $\frac{4}{5}$ 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.

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. $\frac{10}{24}$ and $\frac{15}{36}$ b. $\frac{15}{36}$ and $\frac{10}{36}$ c. $\frac{10}{36}$ and $\frac{15}{24}$ 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.

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.

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.

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.

56.
Which pair of fractions is equivalent to the fraction modeled by the figure shown?

 a. $\frac{10}{16}$ and $\frac{12}{15}$ b. $\frac{8}{10}$ and $\frac{12}{15}$ c. $\frac{9}{15}$ and $\frac{15}{24}$ d. $\frac{8}{18}$ and $\frac{12}{27}$

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.

57.
Write two equivalent fractions for the fraction modeled by the figure.

 a. $\frac{6}{24}$ and $\frac{12}{32}$ b. $\frac{10}{16}$ and $\frac{5}{8}$ c. $\frac{3}{8}$ and $\frac{12}{32}$ 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.

58.
Choose two equivalent fractions for the fraction represented by the figure.

 a. $\frac{10}{16}$ and $\frac{15}{24}$ b. $\frac{6}{10}$ and $\frac{9}{15}$ c. $\frac{6}{16}$ and $\frac{9}{24}$ 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.

59.
Write the fraction represented by the model in its simplest form.

 a. $\frac{4}{5}$ b. $\frac{2}{5}$ c. $\frac{3}{5}$ 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.

60.
Find the value of $n$, if $\frac{3}{n}$ and $\frac{12}{20}$ 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.