Raju

Do you want to cover the Addition and Subtraction of Rational Numbers in one go? Then, you have come the right way where you will get a Worksheet on Addition and Subtraction of Rational Numbers. We tried covering everything like Addition and Subtraction of Rational Numbers with both Same as well as Different Denominators. You can always look up to our Rational Numbers Worksheets to clear all your queries.

Assess your preparation levels using the Worksheets for Addition and Subtraction of Rational Numbers. To help you we have listed numerous questions that can aid your preparation. Practice them on a regular basis and get the step by step solution listed here.

1. Add the following rational numbers

(i) 2/24+12/24 (ii)10/4+13/4

Solution:

(i) 2/24+12/24

= (2+12)/24

= 14/24

(ii) 10/4+13/4

= (10+13)/4

= 23/4

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2. Add the following rational numbers

(i) 3/4 and -5/3 (ii) -5 and -4/3

Solution:

Find the LCM of 4, 3 since the denominators aren’t the same.

LCM(4, 3) = 12

3/4 = 3*3/4*3 = 9/12

-5/3 = -5*4/3*4 = -20/12

= 9/12-20/12

= -11/12

(ii) -5 and -4/3

Find the LCM of 1, 3 since the denominators aren’t the same.

LCM(1, 3) = 3

-5/1 = -5*3/1*3 = -15/3

-4/3 = -4*1/3*1 = -4/3

= -15/3-4/3

= -19/3

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3. Find the Sum of 0+4/3?

Solution:

= 0+4/3

= (0+4)/3

= 4/3

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4. What number should be added to -2 to get the Rational Number 4/7?

Solution:

-2 +x = 4/7

x = 4/7-(-2)

= 4/7+2

= 18/7

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5. Simplify the following and write the result as a whole number, improper fraction, or mixed fraction.

3/4+2/4

Solution:

Since Denominators aren’t the same we have

= (3+2)/4

= 5/4

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6. Simplify the following and write the result as a whole number, improper fraction, or mixed fraction.

12/10 – 4/10

Solution:

= (12-4)/10

= 8/10

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7. Simplify the following and write the result as a whole number, improper fraction, or mixed fraction

5/4 – 2/5

Solution:

Since the Denominators aren’t the same we need to find the LCM

LCM(4, 5) = 20

5/4 = 5*5/4*5 = 25/20

2/5 = 2*4/5*4 = 8/20

= 25/20 – 8/20

= 17/20

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8. Simplify 2/5+4/8?

Solution:

Find the LCM of 5, 8 i.e. 40

2/5 = 2*8/5*8 = 16/40

4/8 = 4*5/8*5 = 20/40

= 16/40+20/40

= 36/40

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Those looking for help on the Subtraction of Rational Numbers can make the most out of the Worksheet on Subtracting Rational Numbers. Use the Subtraction of Rational Numbers Worksheet and try to answer the questions on your own. Identify the Knowledge Gap and work on the areas you are lagging accordingly. For complete information on Rational Numbers check out our Rational Numbers Worksheets and clarify your concerns.

To help you out we have covered every minute detail in the Worksheet for Subtraction of Rational Numbers and you can get a good hold of the concepts. The Questions over here include Subtracting Rational Numbers with both the Same and Different Denominators.

1. Evaluate each of the following

(i) 2/4 – 3/2

(ii) -4/5 – 2/(-3)

(iii) 7/3 – (-5)/(-7)

Solution:

(i) 2/4 – 3/2

Since the Denominators aren’t the same firstly find the LCM to rewrite them into Equivalent Rational Numbers

LCM(4, 2) = 4

Rewriting the Rational Numbers as Equivalent Rational Numbers using the LCM obtained.

2/4 = 2*1/4*1 = 2/4

3/2 =3*2/2*2 = 6/4

2/4-6/4 = (2-6)/4

= -4/4

= -1/1

(ii) -4/5 – 2/(-3)

Rearrange the Rational Numbers to obtain the positive denominator.

2/-3 = 2*(-1)/-3*(-1) = -2/3

Since the Denominators aren’t the same firstly find the LCM to rewrite them into Equivalent Rational Numbers.

LCM(5,3) = 15

-4/5 = -4*3/5*3 = -12/15

(-2/3) = -2*5/3*5 = -10/15

= -12/15-(-10/15)

= 2/15

(iii) 7/3 – (-5)/(-7)

(-5)/(-7) = 5/7

LCM(3, 7) = 21

7/3 = 7*7/3*7 = 49/ 21

5/7 = 5*3/7*3 = 35/21

= 49/21-35/21

= 14/21

= 2/3

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2. Subtract the first rational number from the second one in the following

(i) 3/8, 6/8

(ii) -5/9, 3/9

(iii) -2/10, -9/10

(iv) 11/15, -4/15

Solution:

(i) 6/8 – 3/8 = 3/8

(ii) 3/9 -(-5/9) = 8/9

(iii) -9/10-(-2/10) = -7/10

(iv) -4/15-11/15 = -15/15 = -1

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3. The Sum of Two Numbers is 4/9. If one of it is 1/3 find the other.

Solution:

Let the number to be found as x

From the given data we get the equation as follows

x+1/3 = 4/9

x = 4/9 – 1/3

= (4-3)/9

= 1/9

1/9 should be added to 1/3 to get the resultant sum 4/9.

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4. What number should be subtracted from 4/7 to get 5/4?

Solution:

From the given at we have

4/7 – x = 5/4

x= 4/7-5/4

= (16-35)/28

= -19/28

-19/28 should be subtracted from 4/7 to get 5/4.

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5. Simplify (8/5 -1/5) – 2/5?

Solution:

Given (8/5 -1/5) – 2/5

= 7/5 – 2/5

= 5/5

= 1

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6. Simplify the following and write your answer as a proper fraction or as a whole or mixed number?

12/5 – 4/5

Solution:

Since the Denominators are the Same we can write the expression with a common denominator and then combine the numerators

= (12-4)/5

= 8/5

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7. Simplify the following and write your answer as a proper fraction or as a whole or mixed number?

5/4 – 3/5

Solution:

Since the Denominators aren’t the same find the LCM of Denominators of given rational numbers.

LCM(4, 5) = 20

Writing the given Rational Numbers as Equivalent Rational Numbers

5/4 = 5*5/4*5 = 25/20

3/5 = 3*4/5*4 = 12/20

= 25/20 -12/20

= 13/20

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8. Fill in the Blanks

(i) -3/11 – (-4)/11 = ……

(ii) (-7)/13 + …… = -1

Solution:

(i) -3/11 – (-4)/11

=  -3/11 – (-4)/11

= -3/11+4/11

= 1/11

(ii) (-7)/13 + …… = -1

Consider the number to be found as x

-7/13+x = -1

x = -1-(-7/13)

= -1+7/13

= (-13+7)/13

= -6/13

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Students who want to get a grip on the concept Properties of Addition of Rational Numbers can make the most out of the Worksheet on Properties of Addition of Rational Numbers available. Practice the Questions in the Addition of Rational Numbers Properties Worksheet on a regular basis. There are certain properties when it comes to Adding Rational Numbers and to more about them check our Rational Numbers Worksheets.

The Questions covered in the Worksheet for Properties of Addition of Rational Numbers include Closure Property, Commutative Property, Associative, Existence of Additive Identity Property, Existence of Additive Inverse Property, etc.

1. Verify the following:

(i) -12/7 + 2/5 = 2/5 + -12/7

(ii) -5/4 + -9/12 = -9/12 + -5 /4

Solution:

-12/7 + 2/5

Since Denominators are not the same express them as Equivalent Rational Numbers using the LCM.

= (-12*5+2*7)/35

= (-60+14)/35

= -46/35

2/5 + -12/7

Since Denominators are not the same express them as Equivalent Rational Numbers using the LCM.

= (2*7-12*5)/35

= (14-60)/35

= -46/35

Therefore, -12/7 + 2/5 = 2/5 + -12/7

(ii) -5/4 + -9/12

= (-5*3-9*1)/12

= (-15-9)/12

= -24/12

= -2

-9/12 + -5 /4

= (-9*1-5*3)/12

= -24/12 = -2

Therefore, -5/4 + -9/12 = -9/12 + -5 /4

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2. Fill in the Blanks

(i) (-3/16) + (-12/7) = (-12/7) + (_____ )

(ii) (-8/11 + 3/7) + (-13/2) = (_____ ) + [3/7 + (-13/2)]

(iii) -11 + (7/13 + -9/10) = (-11 + 7/13) + (_____ )

(iv) -16/3 + _____ = _____ + -16/3 = -16/3

Solution:

(i) (-3/16)

(ii)(-8/11)

(iii)(-9/10)

(iv) 0, 0

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3. Find the Additive Inverse for the following Rational Numbers

(i) 1/5

(ii) 24/9

(iii) -15

(iv) -17/3

(v) 15/-2

(vi) 0

Solution:

(i) -1/5

(ii) -24/9

(iii) 15

(iv) 17/3

(v) 15/2

(vi) 0

Additive Inverse of a number is nothing but the number to be added to the given number to make it equal to 0.

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4. Which of the following is the sum of 12 1/3 +(-12 1/3)?

a) Positive Number

b) Negative Number

c) Zero

Solution:

c) Zero

Whenever you add a number to its additive inverse the result is 0.

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5. State Whether the following statements are True or False?

(i) Which Rational Number has its own Additive Inverse?

(ii) Is the Addition of Rational Numbers Commutative?

(iii) Is the Addition of Rational Numbers Associative?

(iv) Is Subtraction of Rational Numbers Commutative?

(v) Is Subtraction of Rational Numbers Associative?

Solution:

(i) Zero

(ii) True

(iii) True

(iv) False

(v) False

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Assess your knowledge on Rational Numbers Addition using the Worksheet on Adding Rational Numbers. Bridge the knowledge gap and prepare accordingly. Practice the Questions in the Adding Rational Numbers Worksheets and ace up your preparation level. Questions are based on the Adding Rational Numbers with the Same Denominator and Different Denominator. Make use of Rational Numbers Worksheets to get a complete idea of the concept.

1.  Add the following Rational Numbers -2/3 and 4/3

Solution:

Since the Given Rational Numbers are having the Same Denominator

Just add the Numerators and Keep the Denominator Unchanged.

-2/3 + 4/3 = (-2+4)/3

= 2/3

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2. Add the Rational Numbers 11/8 and -5/8

Solution:

Since the Given Rational Numbers are having the Same Denominator

Just add the Numerators and Keep the Denominator Unchanged.

11/8+(-5/8) = (11-5)/8

= 6/8

= 3/4

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3. Add the Rational Numbers 1/-10 and 2/-15?

Solution:

Given Rational Numbers are 1/-10 and 2/-15

Rearranging the Denominators to Change them to positive

1/-10 = 1*(-1)/-10*(-1) = -1/10

2/-15 = 2*(-1)/-15*(-1) = -2/15

Find the LCM of Denominators and then express them as Equivalent Rational Numbers.

LCM(10, 15) = 30

-1/10 = -1*3/10*3 = -3/30

-2/15= -2*2/15*2 = -4/30

Adding the Equivalent Rational Numbers

= -3/30-4/30

= -7/30

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4. Simplify the Expression 8/7 + -10/6?

Solution:

Since the Denominators aren’t the same change them to Equivalent Rational Numbers.

Find the LCM of 7,6

LCM(7, 6) = 42

Changing the Given Rational Numbers to Equivalent Rational Numbers using the LCM obtained.

8/7 = 8*6/7*6 = 48/42

10/6 = 10*7/6*7 = 70/42

Adding them we get

= 48/42 -70/42

= -22/42

= -11/21

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5. Simplify 7/8 + 3/-2?

Solution:

Since the Denominators aren’t the same change them to Equivalent Rational Numbers.

Rearrange the denominator to positive i.e. 3/-2 = 3*(-1)/-2*(-1) = -3/2

Find the LCM of 8, 2

LCM(8, 2) = 8

Changing the Given Rational Numbers to Equivalent Rational Numbers using the LCM obtained.

7/8 = 7*1/8*1 = 7/8

– 3/2 = -3*4/2*4

= -12/8

Adding the Equivalent Rational Numbers we have

= 7/8 -12/8

= -5/8

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6. Add and Express the Sum of 24/5 + -11/3 as a Mixed Fraction?

Solution:

Given Rational Numbers are 24/5 and -11/3

Since the Denominators aren’t the same simply find the LCM and change them as Equivalent Rational Numbers

LCM(5, 3) =15

24/5 = 24*3/5*3 = 72/15

-11/3 = -11*5/3*5 = -55/15

Adding the Rational Numbers we get

= 72/15-55/15

= 17/15

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Have you ever felt the topic Representation of Rational Numbers on a Number Line difficult? Not anymore! with our Worksheet on Representation of Rational Numbers on a Number Line and you can use them during your practice sessions. Clear all your queries by going through the solved examples on how to Plot Rational Numbers on a Number Line. For complete guidance on the Chapter Rational Numbers, you can use our Rational Numbers Worksheets.

The Questions covered in Placing Rational Numbers on the Number Line Worksheet include representing both positive and negative rational numbers on the number line. In general, any rational number is represented on the number line by a point. However, Positive Rational Numbers lie to the right of 0 and Negative Rational Numbers lie to the left of 0.

1. Between which two numbers does the Rational Number 8/3 lie?

Solution:

Given Rational Number is an Improper Fraction

Firstly change it to Mixed Fraction i.e. 2 2/3

The Whole Number is 2 therefore the rational number 8/3 lies between 2 and 3.

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2. Between which two numbers the Rational Number -11/3 lie?

Solution:

Given Rational Number is an Improper Fraction

Firstly change it to Mixed Fraction i.e. -3 2/3

Therefore the given rational number lies between -3 and -4.

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3. Which of the following statements is true or false

(i) -1/5 lies to the left of 0 on the number line.

(ii) The Rational Number 19/23 lies to the left of 0 on the number line.

(iii) -12/5 lies to the right of 0 on the number line.

(iv) The rational numbers 1/4 and -5/2 are on the opposite sides of 0 on the number line.

(v) The rational numbers (-11)/(-5) and (-4)/17 are on the opposite sides of 0 on the number line.

Solution:

(i) True

(ii) False

(iii) False

(iv) True

(v) True

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4. Represent 4/3 on the Number Line?

Solution:

a) Firstly draw a number line

b) since the number is positive it will lie on the right side of 0. Since 4/3 can be written as mixed fraction 1 1/3 the number lie between 1 and 2.

c) Therefore, to the right side of zero mark 1/3, 2/3, 3/3, 4/3, 5/3, 6/3, and so on.

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5. Draw a Number Line and Represent the Following Positive Rational Numbers on the Number Line?

(i) 5/3

(ii) 1/3

(iii) 2/4

(iv) 3/7

(vi) 7/8

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6. Represent each of the Negative Rational Numbers on the Number Line?

(i) (-5)/8

(ii) (-3)/14

(iii) (-2)/3

(iv) -3/4

(v) (-7)/3

(vi) 22/(-6)

(vii) (-13)/3

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Students who would like to practice Questions on Comparison of Rational Numbers can make use of the Worksheet on Comparison of Rational Numbers. Solve numerous questions on the concept of Comparing Rational Numbers and get a good grip on the concept. For more information, refer to Rational Numbers Worksheets and clear all your queries easily.

Questions include finding the greater and smaller rational number among the given pair of rational numbers, arranging rational numbers in descending, ascending order, etc. Assess your preparation standards and concentrate on the areas you are lagging and improvise on them.

1. Which rational numbers in each of the following pairs of rational numbers is greater?

(i) 2/8 or 0

(ii) (-5)/8 or 0

(iii) (-2)/7 or 0

(iv) 2/3 or 0

(v) (-3)/4 or 2/4

(vi) (-4)/10 or 3/11

(vii) (-5)/7 or (-2)/7

Solution:

(i) 2/8 or 0

Between 2/8 and 0 2/8 is greater than 0

(ii) (-5)/8 or 0

Negative Numbers are Small when compared to 0.

0 is greater than -5/8

(iii) (-2)/7 or 0

Negative Numbers are Small when compared to 0.

0 is greater than -2/7

(v) (-3)/4 or 2/4

Between Negative and Positive Number, Positive Number is Greater

2/4 is greater than -3/4

(vi) (-4)/10 or 3/11

Between Negative and Positive Number, Positive Number is Greater

3/11 is greater than -4/10

(vii) (-5)/7 or (-2)/7

Between Negative Numbers, Smaller Number is Greater

-2/7 is greater than -5/7

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2. Which of the rational numbers in each of the following pairs of rational numbers is smaller?

(i) -4/2 or -8/2

(ii) (-4)/(-13) or 7/13

(iii) 7/8 or -5/8

(iv) 16/(-4) or 3

Solution:

(i) -4/2 or -8/2

-4/2 < -8/2

(ii) (-4)/(-13) or 7/13

-4/-13<7/13

(iii) 7/8 or -5/8

-5/8<7/8

(iv) 16/(-4) or 3

16/-4 <3

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3. Fill in the blanks with the symbol among >, = and <

(i) (-6)/4 ____ 7/13

(ii) (-3)/4 ____ (-5)/6

(iii)(-8)/3 ____ (-9)/10

(iv) 0 ____ (-4)/(-5)

(v) -2 ____ (-12)/5

Solution:

(i) (-6)/4 __<__ 7/13

(ii) (-3)/4 _>___ (-5)/6

(iii)(-8)/3 _<___ (-9)/10

(iv) 0 __>__ (-4)/(-5)

(v) -2 _>___ (-12)/5

The above symbols are given after checking the given rational numbers. The Logic is quite simple in the case of negative numbers the one with less value is greater.

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4. Compare the fractions, and write >, < or = in the blank.

4/8 …… 7/10

Solution:

In order to compare the above rational numbers we need to find the LCM since the Denominators are not the same

LCM(8, 10) = 40

To make the denominator common use the LCM Obtained and express the rational numbers accordingly

4/8 = 4*5/8*5 = 20/40

7/10 = 7*4/10*4 = 28/40

Since Numerator 28 is greater the Rational Number 7/10 is greater

4/8 < 7/10.

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5. Compare the fractions, and write >, < or = in the blank.

7/14 …..1/4

Solution:

In order to compare the above rational numbers we need to find the LCM since the Denominators are not the same

LCM(14, 4) = 28

To make the denominator common use the LCM Obtained and express the rational numbers accordingly

7/14 = 7*2/14*2 = 14/28

1/4 = 1*7/4*7 = 7/28

Since Numerator 14 is greater the Rational Number 7/14 is greater.

7/14 < 1/4

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6. Arrange the following rational numbers in ascending order

2/3, 5/4, (-4)/(-8), 1/3

Solution:

Firstly check whether all the rational numbers given have a positive denominator or not

If not rearrange them to make them positive.

-4/-8 = -4*-1/-8*-1 = 4/8

Thus, Rational become 2/3, 5/4, 4/8, 1/3

LCM of(3, 4, 8, 3) = 24

2/3 = 2*8/3*8 = 16/24

5/4 =5*6/4*6 = 30/24

4/8 = 4*3/8*3 = 12/24

1/3 = 1*8/3*8 = 8/24

Therefore Rational Numbers arranged in Ascending Order is 1/3 < 4/8< 2/3< 5/4

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7. Arrange the following rational numbers in descending order

(-3)/(-2), 17/30, (-8)/15, 7/(-10)

Solution:

Firstly check whether all the rational numbers given have a positive denominator or not

If not rearrange them to make them positive.

-3/-2 = -3*(-1)/-2*(-1) = 3/2

7/-10 = 7*(-1)/-10*(-1) = -7/10

Therefore, Rational Numbers are 3/2, 17/30, 8/15, -7/10

Find the LCM of denominators i.e. 2, 30, 15, 10

LCM(2, 30, 15, 10) =30

3/2 = 3*15/2*15 = 45/30

17/30 = 17*1/30*1 = 17/30

8/15 = 8*2/15*2 = 16/30

-7/10 = -7*3/10*3 = -21/30

Therefore Rational Numbers in Descending Order is 3/2> 17/30> 8/15> -7/10.

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If you want guidance on the concept of Equality of Rational Numbers then check out our Worksheet on Equality of Rational Numbers. Practice as much as you can using our Equality of Rational Numbers Worksheet and get a good grip on the topic. For a complete idea on the Chapter Rational Numbers, use Rational Numbers Worksheets prevailing and test your subject knowledge. Enhance your problem-solving skills by solving Worksheet for Equality of Rational Numbers frequently and assess your preparation standards.

A Rational Number can be written in several equivalent forms. The Questions are framed by subject experts cover whether given rational numbers are equal or not, equality of rational numbers using the standard form, cross multiplication, common denominator, etc.

1. If each of the following pairs represents a pair of equivalent rational numbers, find the values of x.

(i) 3/5 and 6/x

(ii) -5/4 and x/3

(iii) 8/7 and x/-2

Solution:

(i) 3/5 and 6/x

Since they are equivalent rational numbers

3/5 = 6/x

Cross multiplying them to obtain the value of x we have

3x=30

x= 10

(ii) -5/4 and x/3

Since they are equivalent rational numbers

-5/4=x/3

Cross multiplying them to obtain the value of x we have

4x= -15

x = -15/4

(iii) 8/7 and x/-2

Since they are equivalent rational numbers

8/7 = x/-2

Cross multiplying them to obtain the value of x we have

7x= -16

x= -16/7

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2. A Number which can be expressed in the form of p/q where p, q are integers and q is not equal to 0 is called …….

Solution:

Rational Number.

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3. Two Rational are said to be equal if they have the same ……. Form

Solution:

Standard Form

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4. Standard Form of -2 is ……..

Solution:

Standard Form is -2/1 and the Rational Number doesn’t have any common factors other than 1.

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5. Which of the following Rational Numbers are Equal?

(i) -15/27 and 6/-18

(ii) -18/24 and 15/-20

(iii) -8/32 and 24/-96

(iv) -6/-18 and 11/19

Solution:

(iii) -8/24 and 24/-96

The Given Set of Rational Numbers are Equal as they have the same standard form

-8/32 = -1/4

24/-96 = 1/-4 = -1/4

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6. Is the Statement True or False

Two Rational Numbers with Different Numerators cannot be Equal.

Solution:

False

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7. Are the Rational Numbers -7/3 and -5/3 equal?

Solution:

No, the Rational Numbers -7/3 and -5/3 are not equal. They might have a common denominator but the numerators are not equal.

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8. Determine whether the Rational Numbers 3/-9 and -15/45 are equal or not using a standard form?

Solution:

Standard Form of 3/-9 = 1/-3 = -1/3

Standard Form of -15/45 = -1/3

Since the Standard Forms of both the Rational Numbers 3/-9 and -15/45 are Equal the given Rational Numbers are Equal.

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Looking for help on the Rational Number Standard Form Concept? You have reached the right destination as you can make use of the Worksheet on Standard Form of a Rational Number free of cost. To help you ace up your preparation level we have provided the Example Questions in Rational Numbers Standard Form Worksheet. Practice the Rational Numbers Worksheets so that you don’t miss out on any concept.

A Rational Number is said to be in Standard Form if the HCF of numerator and denominator is 1 and denominator is positive. You will better understand how to convert Rational Numbers to Standard Form with the example problems listed as you will get step by step solution.

1.  Find the Standard Form of Rational Number -18/27?

Solution:

To find the Standard Form of a Rational Number -18/27

Simply Divide the Rational Number with the HCF of absolute values of Numerator and Denominator.

HCF(18, 27) = 9

-18/27 = (-18÷9)/(27÷9)

= -2/3

Standard Form of a Rational Number -18/27 is -2/3.

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2. Express the Rational Number 4/21in Standard Form?

Solution:

Rational Number 4/21 itself is in Standard Form as it has no common factors other than 1.

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3. Which of the following Rational Numbers is in Standard Form?

a) 1/5 b) -2/8 c) 6/4 d) 5/10

Solution:

a)

Rational Number 1/5 in its Standard Form as the HCF(1, 5) = 1 and the denominator is positive. The rest of the options have common factors other than 1 and need to be simplified in order to make them in Standard Form.

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4. Fill in the Blank

5/45 = …../9

Solution:

Given Rational Number 5/45

To make it to standard form simply divide the numerator and denominator with HCF

HCF(5, 45) = 5

5/45 = (5÷5)/(45÷5) = 1/9

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5. Write each of the following Rational Numbers to Standard Form?

Write each of the following rational numbers in the standard form:

(i) 3/18 (ii) 20/-44

Solution:

(i) Given Rational Number is 3/18

HCF(3, 18) = 3

Divide 3/18 with the HCF

3/18 = (3÷3)/(18÷3)

= 1/6

(ii) Given Rational Number is 20/-44

Rearrange the Denominator to make it positive

20/-44 = 20*(-1)/-44*(-1)

=-20/44

Find the HCF of absolute values of Numerator and Denominator

HCF(20, 44) = 4

-20/44 = (-20÷4)/(44÷4)

= -5/11

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Feeling difficult on how to reduce rational numbers to their lowest form? Don’t Fret as we have got a Worksheet on Lowest Form of a Rational Number for your practice. Try solving the Questions in the Reducing Rational Numbers to Lowest Form Worksheet and understand your preparation standards. A Rational Number is said to be in its lowest form if its numerator and denominator have no other common factors other than 1.

Use the Reducing Rational Numbers to Simplest Form Worksheet as a part of your study and estimate the kind of questions to be asked in exams regarding the topic. Have a look at the Rational Numbers Worksheets if you want to get a grip on the entire chapter and not just this concept.

1. Convert the Rational Number -15/30 to its lowest form?

Solution:

-15/30 is not in its Lowest Form Since it has common factors other than 1

Find the GCF(15, 30) = 15 and then divide the numerator and denominator of the Rational Number with GCF to obtain the lowest form

-15/30 = (-15÷15)/(30÷15)

= -1/2

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2. Determine whether the following Rational Numbers are in its Lowest Form or Not?

a) 1/3 b) -7/2 c) 14/16 d) 17/5

Solution:

Rational Numbers 1/3, -7/2, 17/5 are in their Lowest Form as all of them have no other common factors other than 1. Whereas, Rational Number 14/16 is not in its Lowest Form as it has common factors other than 1 and can be simplified.

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3. Reduce Rational Number 35/40 to its Lowest Form?

Solution:

Given Rational Number is 35/40

In Order to find the Lowest Form of the Rational Number find the GCF of numerator and denominator

GCF(35, 40) = 5

Divide the Numerator and Denominator of Rational Number with the GCF Obtained.

35/40 = (35÷5)/(40÷5) = 7/8

Therefore, 35/40 Reduced to its Simplest or Lowest Form is 7/8.

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4. A Rational Number a/b is said to be in its lowest form if a and b has no …….

Solution: 

Rational Number a/b is in its lowest form if a, b has no other common factors other than 1.

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5. Express each of the following Rational Numbers to their Simplest Form

(i)5/45 (ii) -30/18

Solution:

Given Rational Number is 5/45

GCF(5, 45) = 5

Divide the Rational Number with the GCF

5/45 = (5÷5)/(45÷5)

= 1/9

Therefore, 5/45 in its Lowest Form is 1/9

Given Rational Number is -30/18

GCF(30, 18) = 6

Divide the Rational Number with the GCF

-30/18 = (-30÷6)/(18÷6)

= -5/3

Therefore, -30/18 in its Lowest Form is -5/3.

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6. Which of the following Rational Numbers are in its Lowest Form?

a) -32/-56 b) 6/-13 c) -17/37 d) 24/-64

Solution:

b) & c)

Options B and C are in the Lowest Form as they can’t be simplified further and they have no other common factors other than 1.

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7. Convert Rational Number -14/49 to its Lowest Form?

Solution:

Given Rational Number is -14/49

GCF(14, 49) = 7

Divide the Rational Number with the GCF obtained

-14/49 = (-14÷7)/(49÷7) = -2/7

Therefore, -14/49 reduced to its lowest form is -2/7.

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8. Fill in the Blanks

-4/6 = …./30

Solution:

Consider the number to be found as x

Cross multiplying we have

6x= -4*30

6x = -120

x = -20

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