#### Solved Examples and Worksheet for Equivalent Fraction for a given Model or Fractions

Q1Find a fraction equivalent to 34.

A. 68
B. 69
C. 78
D. 58

Step: 1
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 and so on.
[Write the multiples of the numerator.]
Step: 2
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 and so on.
[Write the multiples of the denominator.]
Step: 3
The equivalent fraction of 34 is 68.
Q2Fill in the missing numerator in the given equivalent fractions.
1012 = ?6

A. 10
B. 5
C. 6
D. none of these

Step: 1
Given, the fractions in the problem are equivalent.
Step: 2
An equivalent of a fraction is obtained by multiplying or dividing the numerator and the denominator of a given fraction with a common number.
Step: 3
The denominator in the first fraction is a multiple of the denominator in the resultant fraction. So, the denominator should be divided by some number to get the resultant denominator.
Step: 4
122 = 6
Step: 5
The numerator of the fraction should be divided by 2 to get the missing numerator. The missing numerator = 10 ÷ 2.
Step: 6
The missing numerator = 5.
Q3Which fraction is equivalent to 34?
A. 1012
B. 98
C. 12
D. 68

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).]
Q4Which of the following fractions is equivalent to 13?
A. 59
B. 29
C. 49
D. 39

Step: 1
13
[Given fraction.]
Step: 2
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: 3
Multiply the numerator and the denominator of the fraction by 1, 2, 3, . . .
Step: 4
13 = 26 = 39 = 412 = . . .
Step: 5
So, 13 = 39 .
Q5Find the fraction equivalent to 35.
A. 610
B. 56
C. 410
D. 310

Step: 1
Fractions that represent same amount are called equivalent fractions.
Step: 2
Represent the fraction 35 by using three 15 strips as below.
Step: 3
Line up 6 strips of 110 below the three15strips.
Step: 4
As six 110 strips form the same amount as three 15 strips, 35 and 610are equivalent fractions.
Step: 5
So, the equivalent fraction of 35 is 610.
Q6Identify a fraction equivalent to 29.
A. 92
B. 78
C. 836
D. 39

Step: 1
To find an equivalent fraction, we have to multiply or divide the numerator and denominator by the same number.
Step: 2
Multiples of 2 are 2, 4, 6, 8, 10, and so on.
[Write the multiples of the numerator.]
Step: 3
Multiples of 9 are 9, 18, 27, 36, 45, and so on.
[Write the multiples of the denominator.]
Step: 4
Therefore, among the choices, 836 is the equivalent fraction of 29.
Q7Which set of numbers completes the pattern shown?
13 , 26 , 39 , ?12 , ?15 , ?18

A. 3, 4, and 5
B. 5, 6, and 7
C. 4, 5, and 6

Step: 1
Let us use skip counting to find the set of numbers.
Step: 2
We observe from the pattern shown that the top numbers are counted by 1′s and the bottom numbers are skip counted by 3′s.
Step: 3
13 , 26 , 39 , 412 , 515 , 618
[The bottom numbers are skip counted by 3′s in order, so, count the top numbers in order, we get 4, 5, and 6.]
Step: 4
4, 5, and 6 is the set of numbers that completes the pattern shown.
Correct Answer is :   4, 5, and 6
Q8Find an equivalent fraction for the point marked on the number line.

A. 515
B. 410
C. 45

Step: 1
From the number line, the point represented is 810.
Step: 2
Fractions that represent the same amount are called equivalent fractions.
Step: 3
810 = 8÷210÷2 = 45
[Divide both the numerator and the denominator by the common factor 2.]
Step: 4
So, the fraction equivalent to the point given on the number line is 45.
Q9Find an equivalent fraction of 912 .
A. 34
B. 23
C. 12
D. 46

Step: 1
Equivalent fractions are formed by multiplying or dividing the numerator and the denominator by the same number.
Step: 2
Divide the numerator and the denominator of 912 by 3.
Step: 3
912 = 9÷312÷3
= 34
Step: 4
So, the fraction equivalent to 912 is 34 .
Q10Which pair of fractions is equivalent to the fraction modeled by shaded parts of the figure shown?

A. 810 and 1215
B. 1016 and 1215
C. 818 and 1227
D. 915 and 1524

Step: 1
In the figure shown, 4 divisions are shaded out of 9 divisions.
Step: 2
The figure represents the fraction 49.
Step: 3
49 = 4×29×2 = 818
[Multiply numerator and denominator by the same nonzero number.]
Step: 4
49 = 4×39×3 = 1227
[Multiply numerator and denominator by the same nonzero number.]
Step: 5
The pair of fractions equivalent to the fraction modeled by shaded parts of the figure is 818 and 1227.
Correct Answer is :   818 and 1227