#### Solved Examples and Worksheet for Equivalent Fraction for a given Fraction

Q1Name the fraction equivalent to 919.

A. 3818
B. 1738
C. 1839
D. 1838

Step: 1
9×219×2
= 1838
[Multiply the numerator and denominator by the same non-zero number.]
Step: 2
The equivalent fraction of 919 is 1838
Q2Choose a model which is not equivalent to the other models.

A. Figure 4
B. Figure 2
C. Figure 3
D. Figure 1

Step: 1
Figure 1 represents the fraction 48.
Step: 2
Factors of 4 are 1, 2 and 4.
Step: 3
Factors of 8 are 1, 2, 4 and 8.
Step: 4
The common factors of 4 and 8 are 1, 2 and 4.
Step: 5
48 = 4÷28÷2 = 24
[Divide numerator and denominator by the common factor, 2 and simplify.]
Step: 6
48 = 4÷48÷4 = 12
[Divide numerator and denominator by the common factor, 4 and simplify.]
Step: 7
The two fractions equivalent to 48 are 24 and 12.
Step: 8
Figures 2 and 3 represent the fractions 24 and 12 respectively.
Step: 9
Figures 1, 2 and 3 model the equivalent fractions.
Step: 10
Figure 4 models the fraction 34, which is not equivalent to the fractions modeled by other figures.
Step: 11
Figure 4 is the model, which is not equivalent to the other models.
Correct Answer is :   Figure 4
Q3Find a fraction equivalent to 56.

A. 1012
B. 1112
C. 1013
D. 912

Step: 1
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45.
[Write the multiples of the numerator.]
Step: 2
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54.
[Write the multiples of the denominator.]
Step: 3
The equivalent fraction of 56 is 1012.
Q4Pick the fractions equivalent to 23.
 A B C D 4/9 6/9 12/3 8/12

A. B and D
B. A and C
C. B, C, and D
D. None of the above

Step: 1
An equivalent of the fraction is obtained by multiplying or dividing the numerator and the denominator of the fraction with a common number.
Step: 2
We cannot get A by multiplying the numerator and the denominator of 23 by any number.
Step: 3
So, A is not an equivalent fraction of the fraction.
Step: 4
We get B by multiplying the numerator and the denominator of 23 by 3
Step: 5
= 2×33×3 = 69
Step: 6
We cannot get C by multiplying the numerator and the denominator of 23 by any number.
Step: 7
So, C is not an equivalent fraction of the fraction.
Step: 8
We get D by multiplying the numerator and the denominator of 23 by 4
Step: 9
= 2×43×4 = 812
Step: 10
The fractions equivalent to 23 are 69 and 812
Correct Answer is :   B and D
Q5In a game of 9 matches, Francis won 3 matches. What fraction of the matches did Francis win? Identify equivalent fractions of this fraction.
A. 39, 118 and 36
B. 39, 918 and 36
C. 39, 618 and 13
D. None of the above

Step: 1
The fraction of matches Francis won = Number of matches wonTotal number of matches = 39
Step: 2
The equivalent fractions for this is, 3×29×2 = 618
[Multiply numerator and denominator by the same nonzero number.]
Step: 3
3÷39÷3 = 13
[Divide numerator and denominator by GCF 3.]
Step: 4
The two equivalent fractions of 39 are 618 and 13
Correct Answer is :   39, 618 and 13
Q6Which fraction is equivalent to 34?
A. 1012
B. 68
C. 12

Step: 1
Consider the following fractions strips.
[Because, the question and choices contain half (12), fourths (14), eighths (18), and twelfths (112).]

Step: 2
We need to find the fraction from the choices that is equivalent to the fraction 34. We will use the fraction strips shown above.
Step: 3
The figure below shows 34 .
[Three 14 strips make one 34.]

Step: 4
Consider each fraction listed one-by-one.
Step: 5
Line up the 12 fraction strip directly below the 34 fraction strip as shown. They don't match exactly, we observe some extra space, which means that 12 is less than 34.
Step: 6
Line up ten 112 fraction strip directly below the 34 fraction strip as shown. They don't match exactly, we observe some extra space, which means that 1012 is greater than 34.
[Ten 112 fraction strips make one 1012 fraction strip.]

Step: 7
Line up six 18 fraction strip directly below the 34 fraction strip as shown. They match exactly, which means that 68 is equivalent to 34.
[Six 18 fraction strips make one 68 fraction strip.]

Step: 8
98 need not be considered.
[Because, when 68 is equivalent to 34 , 98 will obviously be greater than 34. (9 > 6).]
Q7Which of the given fractions is equivalent to 34?

A. 912
B. 32
C. 412

Step: 1
To find an equivalent fraction, we have to multiply or divide the numerator and denominator by the same number.
Step: 2
To compare 34 and 412, we would multiply 34 by 33 to produce 912.
[3 × 34 × 3 = 912]
Step: 3
412 and 912 are not equivalent fractions. Since, 412 is not the same as 912.
Step: 4
34 is not same as 32. Since 34 and 32 are not equivalent fractions .
Step: 5
To compare 34 and 912, we would multiply 34 by 33 to produce 912.
[3 × 34 × 3 = 912]
Step: 6
34 and 912 are equivalent fractions.
Q8Which fraction is equivalent to 45 ?

A. 610
B. 210
C. 410
D. 810

Step: 1
Fractions that represent same amount are called Equivalent fractions.
Step: 2
45 = 4 × 25 × 2 = 810
[Multiply numerator and denominator by 2.]
Step: 3
So, the fraction 810 equivalent to the fraction 45 .
Q9Name the fraction equivalent to 511.
A. 1023
B. 1022
C. 922
D. 2210

Step: 1
511 = 5×211×2 = 1022
[Multiply the numerator and denominator by the same non-zero number.]
Step: 2
The equivalent fraction of 511 is 1022.
Q10Which of the following is an equivalent fraction to 49 ?

A. 188
B. 819
C. 818
D. 718

Step: 1
49 = 4×29×2 = 818
[Multiply the numerator and denominator by the same non-zero number.]
Step: 2
The equivalent fraction of 49 is 818.
Q11Which of the following fractions is equivalent to 12 and 48 ?

A. 37
B. 614
C. 25
D. 510

Step: 1
An equivalent of a fraction is obtained, by multiplying or dividing the numerator and the denominator of a given fraction, by a common number.
Step: 2
Multiply the numerator and the denominator of the fraction by 1, 2, 3, . . .
Step: 3
12 = 24 = 36 = 48 = 510 = 612.....
Step: 4
So, 12 = 48 = 510.