Raju

Do you feel difficulty understanding the concept of Equivalent Rational Numbers? Not anymore as you can take the help of our Worksheet on Equivalent Rational Number covering numerous examples. Practice the questions in the Class 8 Worksheet for Equivalent Rational Numbers and learn how to solve problems on your own. You can find Numerous Questions asked in the Rational Numbers Worksheets and learn various topics effectively.

Try Solving the Example Questions on your own and cross-check the solutions to understand where you lag and prepare accordingly. Detailed Explanation is provided for a better understanding of the concept.

1. Are 4/8 and 6/12 Equivalent Rational Numbers?

Solution:

If Two Numbers are Equivalent Rational Numbers then the product obtained by cross multiplying them would be equal

4*12 = 48

8*6 = 48

Therefore, 4/8 and 6/12 are Equivalent Rational Numbers.

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2. Express Rational Number 8/5 with a Numerator 56?

Solution:

In Order to Express Rational Number 8/5 with a Numerator 56

Numerator = 56

To make the rational number 8/5 with a numerator 56 firstly we need to divide the 56 by 8 i.e. 7

Multiply with 7 both the numerator and denominator of rational number 8/5

= 8/5*7/7

= 56/35

Thus, Rational Number 8/5 can be expressed as 56/35 with a numerator 56.

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3. Are 3/7 and 4/5 Equivalent Rational Numbers?

Solution:

If Two Numbers are Equivalent Rational Numbers then the product obtained by cross multiplying them would be equal.

3*5 = 15

7*4 = 28

Thus 15 ≠ 28

Therefore, 3/7 and 4/5 are Not Equivalent Rational Numbers.

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4. Express Rational Number 3/7 with a Denominator 49?

Solution:

To write the rational number 3/7 with a denominator 49

we need to find the number that when multiplied results in denominator 49

49/7 = 7

Multiply with 7 both the numerator and denominator of the rational number 3/7

= 3/7*7/7

= 3*7/7*7

= 21/49

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5. If p/q = m/n then which of the following is true is always true?

a)n/m = p/q b)p*q=m*n c)p/n = m/q d)p*n = m*q

Solution: 

d)p*n=m*q

If Two Numbers are Equivalent Rational Numbers then the product obtained by cross multiplying them would be equal.

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6. A Rational Number Equivalent to 2/1 is

a)10/-5 b)10/5 c)-10/5 d) None of the above

Solution:

b) 10/5

2/1 = 2*5/1*5

= 10/5

Therefore Rational Number Equivalent to 2/1 is 10/5

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7. What is the Rational Number Equivalent to 5/8

a)25/40 b) 25/-40 c)-25/40 d)None of the above

Solution:

a) 25/40

5/8 = 5*5/8*5

= 25/40

Rational Number Equivalent to 5/8 is 25/40

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8. Fill in the blank to make Two Rational Numbers Equivalent

a) 4/7 = …./56

Solution:

32

In order to make the Rational Number 4/7 with denominator 56 we have

4/7 *8/8 = 32/56

Therefore, 4/7 is Equivalent to the Rational Number 32/56.

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9. If 1/x = -x/1 then x is ……..

a) Whole Number b) Natural Number c) Rational Number d) Not a Rational Number

Solution:

d) Not a Rational Number

1/x= -x/1

-x² = 1
x² = -1
x= √ -1

Therefore, x is not a Rational Number.

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10. Select the rational numbers which can be written as a rational number with denominator 4 from the following

7/3, 64/11, 30/(-12), (-16)/17, 5/(-4), 140/28

Solution:

30/(-12), 5/(-4), 140/28

Since all the above options can be rearranged to get a Rational Number with the Denominator 4.

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If you ever have trouble understanding the concepts of Rational Numbers then take the help of the Worksheet on Rational Numbers. Practice using Rational Numbers Worksheets and be familiar with various questions in the Chapter. Worksheets for Rational Numbers available are as per the latest syllabus guidelines. Assess your preparation level and bridge the knowledge gap in the concept accordingly. Use the Questions in the Practice Sheets as a quick reference during your preparation and stand out from the crowd.

1. Write down the numerator of the following rational numbers

(i) (-4)/5

(ii) 5/(-4)

(iii) (-17)/(-12)

(iv) 7/9

(v) 3

Solution:

(i) -4

(ii) 5

(iii) (-17)

(iv) 7

(v) 3

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2. Write down the denominators of the following Rational Numbers?

(i) (-6)/5

(ii) 11/(-30)

(iii) (-15)/(-18)

(iv) 12

(v) 0

Solution:

(i) 5

(ii) (-30)

(iii) (-18)

(iv) 1

(v) Any Non Zero Integer

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3. Subtract the Sum of -4/5 and 1/3 from 1?

Solution:

= 1-(-4/5+1/3)

=1-(-12+5)/15

= 1-(-7/15)

=22/15

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4. Which of the following are positive rational numbers?

(i) (-4)/7 (ii) 5/8 (iii) (-12)/(-13) (iv) (-20)/13

Solution:

(ii) 5/8 (iii) (-12)/(-13)

The above two options are positive since both the numerator and denominator have the same sign.

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5. Which of the following are negative rational numbers?

(i) (-2)/7 (ii) (-6)/-8 (iii) 9/(-8) (iv) (-112)/-197

Solution:

(i) (-2)/7 (iii) 9/(-8)

The above two options are negative since numerator and denominator have the opposite sign.

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6. Write the following rational numbers as integers:

7/1, (-20)/1, 32/1, (-17)/1, 90/1

Solution: 

7, -20, 32, -17, 90

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7. Express the following Integers as Rational Numbers.

-10, 22, 75, -104

Solution:

In Order to Express Integers as Rational Numbers you just need to place the given value over the denominator 1.

-10/1, 22/1, 75/1, -104/1

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8. What is the Rational Number if its denominator is the smallest three-digit number and the denominator is the largest three-digit number?

Solution:

As per the given information Numerator = Smallest Three-Digit Number = 100

Denominator = Largest Three-Digit Number = 999

Rational Number = Numerator/Denominator = 100/999

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9. Which of the following statement is true about the Rational Number?

a) Every Integer is a Rational Number

b) Rational Number is expressed in the form of p/q where p, q are integers and q is non zero integer.

c) 0 is a Rational Number.

Solution:

All three Statements are True regarding the Rational Number.

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10. Write down the Rational Number with Numerator 2*(-5) and Denominator is 5*4?

Solution: 

As per given data Numerator = 2*(-5) = -10

Denominator = 5*4 = 20

Rational Number = -10/20

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