Equivalent Fractions Worksheet - Page 5

Equivalent Fractions Worksheet
• Page 5
41.
Express the fraction $\frac{30}{70}$ in its simplest form.
 a. b. $\frac{7}{3}$ c. $\frac{3}{7}$ d. None of the above

Solution:

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
[Write factors for numerator.]

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
[Write factors for denominator.]

GCF of 30 and 70 is 10.
[Select the greatest common factor.]

30 / 70 = 30 ÷ 1070 ÷ 10 = 3 / 7
[Divide numerator and denominator by GCF 10.]

The simplest form of the fraction 30 / 70 is 3 / 7.

42.
With what number would you multiply the numerator and the denominator of the fraction $\frac{7}{13}$ to get $\frac{77}{143}$ ?
 a. 12 b. 11 c. 10 d. None of the above

Solution:

77 = 7 × 11 and 143 = 13 × 11
[Express 77 as a multiple of 7 and 143 as a multiple of 13.]

The numerator and denominator of 7 / 13 must be multiplied by 11 to get 77 / 143 .

43.
Using common factors, find two fractions equivalent to $\frac{16}{24}$.
 a. $\frac{12}{4}$ , $\frac{8}{6}$ b. $\frac{8}{4}$ , $\frac{12}{6}$ c. $\frac{8}{12}$ , $\frac{4}{6}$ d. None of the above

Solution:

Factors of 16 are 1, 2, 4, 8, 16.
[Write the factors for 16.]

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
[Write the factors for 24.]

The common factors for 16 and 24 are 1, 2, 4, 8.

1624 = 16÷224÷2 = 812
[Divide numerator and denominator by the common factors and then simplify.]

1624 = 16÷424÷4 = 46
[Divide numerator and denominator by the common factors and then simplify.]

The two fractions equivalent to 16 / 24 are 8 / 12 and 4 / 6 .

44.
Find two equivalent fractions of $\frac{10}{40}$.
 a. $\frac{1}{4}$ and $\frac{2}{8}$ b. none of these c. $\frac{1}{4}$ and $\frac{1}{8}$ d. $\frac{1}{4}$ and $\frac{12}{8}$

Solution:

10 / 40 = 10÷1040÷10 = 1 / 4
[Divide numerator and denominator by their GCF 10.]

1 / 4 = 1×24×2 = 2 / 8
[Multiply numerator and denominator of 1 / 4 by same non-zero number.]

The two equivalent fractions of 10 / 40 are 1 / 4 and 2 / 8.

45.
Josh has 16 chocolates and he gave 7 of them to Ashley. Choose a fraction that is equivalent to the fraction of the chocolates left with Josh.
 a. $\frac{19}{33}$ b. $\frac{32}{18}$ c. $\frac{18}{32}$ d. None of the above

Solution:

The number of chocolates left with Josh = 16 - 7 = 9

The fraction of the chocolates left with Josh = Remaining chocolatesTotal chocolates = 9 / 16

The equivalent fraction for this is, 9×216×2 = 18 / 32
[Multiply numerator and denominator by same non-zero number.]

The equivalent fraction is 18 / 32.

46.
Find two equivalent fractions of $\frac{3}{4}$.
 a. $\frac{9}{12}$, $\frac{15}{20}$ b. $\frac{9}{13}$, $\frac{16}{20}$ c. $\frac{10}{12}$, $\frac{15}{21}$ d. None of the above

Solution:

Multiples of 3 are 3 , 6, 9, 12, 15, 18, 21, 24, 27.
[List a few multiples of 3.]

Multiples of 4 are 4 , 8, 12, 16, 20, 24, 28, 32, 36.
[List a few multiples of 4.]

3x34x3 = 912
[Multiply numerator and denominator by the same number and simplify.]

3x54x5= 1520
[Multiply numerator and denominator by the same number and simplify.]

The two equivalent fractions of 3 / 4 are 9 / 12 and 15 / 20.

47.
In a college election the number of votes polled were 500. Francis got 200 votes. Express the votes that Francis got as a fraction in the simplest form.
 a. $\frac{3}{5}$ b. $\frac{1}{2}$ c. $\frac{2}{5}$ d. None of the above

Solution:

The fraction of votes Francis got = Number of votes Francis got Total number of votes = 200 / 500

200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
500 = 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
[Write factors for numerator and denominator.]

G.C.F of 200 and 500 is 100
[Select the greatest common factor.]

200÷100 / 500÷100 = 2 / 5
[Divide numerator and denominator by GCF,100.]

Francis got 2 / 5of the total number of votes polled.

48.
Find the value of $x$, if $\frac{x}{49}$and $\frac{3}{7}$ are equivalent fractions.
 a. 10 b. 49 c. 1 d. 21

Solution:

x49 = 37
[Given expression.]

x49 = (3x7)(7x7)
[Multiply numerator and denominator of 3 / 7 by 7 to make the denominators of the two fractions equal.]

x = 3 x 7
[Take the numerators of the two fractions.]

= 21
[Multiply.]

So, the value of x is 21.

49.
In a game of 35 matches, Josh won 21 matches. What fraction of the matches did Josh win? Choose two equivalent fractions of this fraction.
 a. $\frac{21}{35}$, $\frac{35}{70}$ and $\frac{5}{42}$ b. $\frac{21}{35}$, $\frac{42}{70}$ and $\frac{3}{5}$ c. $\frac{21}{35}$, $\frac{3}{70}$ and $\frac{5}{42}$ d. None of the above

Solution:

The fraction of matches Josh won = Number of matches wonTotal number of matches = 21 / 35

The equivalent fractions for this is, 21 × 235 × 2 = 42 / 70
[Multiply numerator and denominator by the same nonzero number.]

21÷7 / 35÷7 = 3 / 5
[Divide numerator and denominator by GCF 7.]

The two equivalent fractions of 21 / 35 are 42 / 70 and 3 / 5

50.
Write an equivalent fraction for the model.

 a. $\frac{3}{9}$ b. $\frac{6}{4}$ c. $\frac{8}{16}$ d. None of the above

Solution:

In the model, 4 divisions are shaded out of 8 divisions.

The model represents the fraction 4 / 8.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36. . .

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72. . .

The equivalent fractions for 4 / 8 are 8 / 16, 12 / 24, 16 / 32, . . . .

So, the equivalent fraction for the model is 8 / 16.