Constructing Models of Equivalent Fractions-Gr 3-Solved Examples

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

Solutions

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

Solutions

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

Solutions

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

Solutions

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

Solutions

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

Solutions

Step: 1

In Figure 1, three out of five equal parts are shaded (35^th part).

Step: 2

In Figure 2, one out of three equal parts is shaded (13^rd part).

Step: 3

In Figure3, two out of five equal parts is shaded (25^th part).

Step: 4

In Figure 4, three out of six equal parts are shaded (36^th part).

Step: 5

So, among the given figures, Figure 2 is 13^rd 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

Solutions

Step: 1

In Figure 1, one out of four parts is shaded (14^th part).

Step: 2

In Figure 2, one out of ten parts is shaded (110^th part).

Step: 3

In Figure 3, one out of eight parts is shaded (18^th part).

Step: 4

In Figure 4, one out of six parts is shaded (16^th part).

Step: 5

So, Figure 3 is 18^th 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

Solutions

Step: 1

In Figure 1, one out of eight parts is shaded (18^th part).

Step: 2

In Figure 2, two out of eight parts is shaded (28^rd part).

Step: 3

In Figure 3, three out of eight parts is shaded (38^th part).

Step: 4

In Figure 4, four out of eight parts is shaded (48^th part).

Step: 5

So, Figure 2 is 28^th 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

Solutions

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

Solutions

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

Solutions

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

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

Solutions

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

Step: 6

So, fractions represented by the pair in Figure 2 are equivalent.

[48 = 2×24×2 = 24 .]

Correct Answer is : Figure 2

Solved Examples and Worksheet for Constructing Models of Equivalent Fractions

Related Worksheet

Related Topic

HighSchool Math