#### Solved Examples and Worksheet for Constructing Models of Equivalent Fractions

Q1Which two figures represent equivalent fractions? A. Figure 1 and Figure 3
B. Figure 2 and Figure 4
C. Figure 1 and Figure 4
D. Figure 1 and Figure 2

Step: 1
Figure 1 represents 24.
Step: 2
Figure 2 represents 24.
Step: 3
Figure 3 represents 34.
Step: 4
Figure 4 represents 14.
Step: 5
So, Figures 1 and 2 are equivalent fractions.
Correct Answer is :   Figure 1 and Figure 2
Q2Which model is shaded to show a fraction equivalent to 36? A. Figure 4
B. Figure 3
C. Figure 2
D. Figure 1

Step: 1
Figure 1 represents the fraction 14.
[1 out of 4 parts is shaded]
Step: 2
Figure 2 represents the fraction 38.
[3 out of 8 parts are shaded]
Step: 3
Figure 3 represents the fraction 35.
[3 out of 5 parts is shaded]
Step: 4
Figure 4 represents the fraction 12.
[1 out 2 parts is shaded]
Step: 5
The given fraction 36reduces to 12.
[Divide both the top and the bottom numbers by 3, because they both are multiples of 3.]
Step: 6
So, among the figures shown, only Figure 4 is shaded to show a fraction equivalent to 36.
[Because, 36= 12.]
Correct Answer is :   Figure 4
Q3The rectangle shows 15 shaded. Which fractional part of a rectangle is equal to 15? A. Fraction 1
B. Fraction 3
C. Fraction 4
D. Fraction 2

Step: 1
In each of the choices, there are ten equal parts.
Step: 2
Each part represents 110.
Step: 3
In Fraction 1, only two parts are shaded. It represents 210.
Step: 4
210is the same as 15.
[Because, when we divide the top and the bottom numbers of 210by the number, 2, we get a fraction 15that is equivalent to 210.]
Step: 5
So, Fraction 1 is equal to 15.
Correct Answer is :   Fraction 1
Q4The square shows 14 shaded. Which fractional part of a square is equal to 14? A. Fraction 1
B. Fraction 4
C. Fraction 2
D. Fraction 3

Step: 1
The given figure represents 14.
Step: 2
Among the fractions listed, look for the one that reduces to 14on dividing both its top and bottom numbers by the same number.
Step: 3
Among the fractions listed, only the fraction 28reduces to 14.
[Divide both its top and the bottom numbers by 2.]
Step: 4
So, Fraction 1 represents the equivalent fraction for the figure shown.
Correct Answer is :   Fraction 1
Q5Alice jogged for 13 of an hour in the morning. Which picture shows a fraction equivalent to 13? A. Figure 3
B. Figure 4
C. Figure 1
D. Figure 2

Step: 1
Figure 1 shows two out of four parts shaded.
Step: 2
Figure 2 shows three out of eight parts shaded.
Step: 3
Figure 3 shows one out of three parts shaded.
Step: 4
Figure 4 shows three out of six parts shaded.
Step: 5
So, Figure 3 shows a fraction equivalent to 13.
Correct Answer is :   Figure 3
Q6Which of the figures is 13 shaded? A. Figure 2
B. Figure 3
C. Figure 4
D. Figure 1

Step: 1
In Figure 1, three out of five equal parts are shaded (35th part).
Step: 2
In Figure 2, one out of three equal parts is shaded (13rd part).
Step: 3
In Figure3, two out of five equal parts is shaded (25th part).
Step: 4
In Figure 4, three out of six equal parts are shaded (36th part).
Step: 5
So, among the given figures, Figure 2 is 13rd shaded.
Correct Answer is :   Figure 2
Q7Which among the following figures is 18 shaded? A. Figure 4
B. Figure 1
C. Figure 2
D. Figure 3

Step: 1
In Figure 1, one out of four parts is shaded (14th part).
Step: 2
In Figure 2, one out of ten parts is shaded (110th part).
Step: 3
In Figure 3, one out of eight parts is shaded (18th part).
Step: 4
In Figure 4, one out of six parts is shaded (16th part).
Step: 5
So, Figure 3 is 18th part shaded.
Correct Answer is :   Figure 3
Q8Which among the following figures is 28 shaded? A. Figure 3
B. Figure 2
C. Figure 4
D. Figure 1

Step: 1
In Figure 1, one out of eight parts is shaded (18th part).
Step: 2
In Figure 2, two out of eight parts is shaded (28rd part).
Step: 3
In Figure 3, three out of eight parts is shaded (38th part).
Step: 4
In Figure 4, four out of eight parts is shaded (48th part).
Step: 5
So, Figure 2 is 28th part shaded.
Correct Answer is :   Figure 2
Q9Which of the figures represents equivalent fractions? A. Figure 1 and Figure 2
B. Figure 1 and Figure 3
C. Figure 2 and Figure 3

Step: 1
Figure 1 represents the fraction 34.
[3 out of 4 parts is shaded]
Step: 2
Figure 2 represents the fraction 912.
[9 out of 12 parts is shaded]
Step: 3
And 912 is equivalent to 34
[Dividing both numerator and denominator of 912 by 3.]
Step: 4
Figure 3 represents the fraction 812.
[8 out of 12 parts is shaded.]
Step: 5
So, Figure 1 and Figure 2 have an equivalent fraction shaded.
[From steps 1 and 3.]
Correct Answer is :   Figure 1 and Figure 2
Q10Which of the figures represent equivalent fractions? A. all the three
B. Figure 1 and Figure 3
C. Figure 2 and Figure 3
D. Figure 1 and Figure 2

Step: 1
In Figure 1, 1 out of 4 parts are shaded. So, the fraction represented by it is 14.
Step: 2
In Figure 2, 1 out of 8 parts are shaded. So, the fraction represented by it is 18.
Step: 3
In Figure 3, 3 out of 12 parts are shaded. So it represents 312.
Step: 4
An equivalent fraction is a fraction whose numerator and denominator are a multiple of the numerator and denominator of the original fraction.
For example, 23 is a fraction. 46 is a fraction equivalent to 23 ; 4 is a multiple of 2 and 6 is a multiple of 3.
Step: 5
So, Figure 1 and Figure 3 represent equivalent fractions.
[Figure 1 represents 14 and Figure 3 represents 312 = 1×34×3 = 14 .]
Correct Answer is :   Figure 1 and Figure 3
Q11Which figure shows a fraction equivalent to the fraction represented by Figure A? A. Figure 1
B. Figure 3
C. Figure 2
D. All three figures

Step: 1
Figure A represents the fraction 14.
[1 out of 4 parts is shaded.]
Step: 2
Figure 1 represents the fraction 12.
[1 out of 2 parts is shaded.]
Step: 3
Figure 2 represents the fraction 48.
[4 out of 8 parts are shaded.]
Step: 4
Figure 3 represents the fraction 28.
[2 out of 8 parts are shaded.]
Step: 5
An equivalent fraction is a fraction whose numerator and denominator are a multiple of the numerator and denominator of the original fraction.
For example, 23 is a fraction. 46 is a fraction equivalent to 23 ; 4 is a multiple of 2 and 6 is a multiple of 3.
Step: 6
So, Figure 3 shows a fraction equivalent to the fraction represented by Figure A.
[Figure 3 respresents the fraction 28 = 1×24×2 = 14 which is the fraction represented by Figure A.]
Correct Answer is :   Figure 3
Q12Identify the figure that shows a pair of equivalent fractions. A. Figure 3
B. Figure 4
C. Figure 1
D. Figure 2

Step: 1
The fractions represented by the pair in Figure 1 are 28 and 24.
Step: 2
The fractions represented by the pair in Figure 2 are 48 and 24.
Step: 3
The fractions represented by the pair in Figure 3 are 58 and 34.
Step: 4
The fractions represented by the pair in Figure 4 are 48 and 34.
Step: 5
An equivalent fraction is a fraction whose numerator and denominator are a multiple of the numerator and denominator of the original fraction.
For example, 23 is a fraction. 46 is a fraction equivalent to 23 ; 4 is a multiple of 2 and 6 is a multiple of 3.
Step: 6
So, fractions represented by the pair in Figure 2 are equivalent.
[48 = 2×24×2 = 24 .]
Correct Answer is :   Figure 2