1

Add the following rational numbers:

(i) and

(ii) and

(iii) and

(iv) and

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2

Add the following rational numbers:

(i) and

(ii) and

(iii) and

(iv) and

(v) and

(vi) and

(vii) and

(viii) and

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3

Simplify:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

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4

Add and express the sum as a mixed fraction:

(i) and

(ii) and

(iii) and

(iv) and

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1

Verify commutativity of addition of rational numbers for each of the following pairson of rational numbers:

(i) and

(ii) and

(iii) and

(iv) and

(v) 4 and

(vi) -4and

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2

Verify associativity of addition of rational numbers i.e., when:

(i)

(ii)

(iii)

(iv)

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3

Write the additive invese of each of the following rational numbers:

(i)

(ii)

(iii)

(iv)

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4

Write the negative (additive inverse) of each of the following:

(i)

(ii)

(iii)

(iv)

(v) 0

(vi) 1

(vii) -1

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5

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i)

(ii)

(iii)

(iv)

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6

Re-arrange sutably and find the sum in each of the following.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

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1

Subtract the first rational number from the second in each of the following:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

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2

Evalute each of the following:

(i) +

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

(xi) -

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3

The sum of the two numbers is . If one of the numbers is , find the other

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4

The sum of two numbers is . If one of the numbers is , find the other

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5

The sum of two numbers is . If one of the numbers is -5, find the other

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6

The sum of two ratinal numbers is -8. If one of the numbers is , find the other

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7

What should be added to so as to get ?

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8

What number should be added to so as to get ?

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9

What number should be addede to to get?

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10

What number should be subtracted from to get ?

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11

What number should be subtracted from to get?

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12

What should be added to ( + ) to get?

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13

What should be subtracted from ( + + ) to get 3?

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14

What should be subtracted from ( - ) to get ?

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15

Fill in the blanks:

(i) (ii)

(iii) (iv)

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1

Simplify each of the following and write as rational number of the form:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

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2

Express each of the following as a rational number of the form :

(i)

(ii)

(iii)

(iv)

(v)

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3

Simplify:

(i)

(ii)

(iii) - -

(iv)

(v)

(vi)

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1

Multiply:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

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2

Multiply:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

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3

Simplify each of the following and express the result as a rational number in standard from:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

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4

Simplify:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

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5

Simplify:

(i) ( * ) + ( * ) – ( * )

(ii)

(iii)

(iv)

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1

Verify the property: by taking:

(i)

(ii)

(iii)

(iv)

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2

Verify the property: by taking:

(i)

(ii)

(iii)

(iv)

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3

Verify the property: by taking:

(i)

(ii)

(iii)

(iv)

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4

Use the distributivity of multiplication of rational numbers over their addition to simplify:

(i)

(ii)

(iii)

(iv)

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5

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:

(i) 9

(ii) -7

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix) -1

(x)

(xi)1

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6

Name the property of multiplication of rational numbers illustrated by the following statements:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

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7

Fill in the blanks:

(i) The product of two positive rational numbers is always………..

(ii) The product of a positive rational number and a negative rational number is always ……..

(iii) The product of two negative rational numbers is always………..

(iv)The reciprocal of a positive rational numbers is ………..

(v) The reciprocal of a negative rational number is………..

(vi) The product of a rational number and its reciprocal is……..

(vii) Zero has……. reciprocal

(viii) The numbers……. and….. are their own reciprocals.

(ix)If a is reciprocal of b, then the reciprocal of b is ………

(x) The number 0 is ……… the reciprocal of any number.

(xi) Reciprocal of is

(xii)

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8

Fill in the blanks:

(i) (ii)

(iii)

(iv)

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1

Divide:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

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2

Find the value and express as a rational number in standard from:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

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3

The product of two rational numbers is 15. If one of the numbers is -10, find the other.

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4

The product of two rational numbers is . If one of thenumbers is , find the other.

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5

By what number should we multiply so that the product may be?

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6

By what number should we multiply so that the product may be?

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7

By what number should we multiply so theat the product may be 24?

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8

By what number should be multiplied in order to produce ?

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9

Find if

(i)

(ii)

(iii)

(iv)

(v)

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10

The cost of metres of rope is Rs .Find its cost per metre.

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11

The cost of metres of cloth is Rs. Find the cost of cloth per metre

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12

By what number should be divided to get?

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13

Divide the sum of and by the product of and

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14

Divide the sum of and by their difference.

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15

If 24 trousers of equal size can be prepared in 54 metres of cloth. What length of cloth is required for

each trouser?

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1

Find a rational number between -3 and 1

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2

Find any five rational numbers less than 2.

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3

Find two rational numbers between and

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4

Find two rational numbers between and

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5

Find ten rational numbers between and

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6

Find ten rational numbers between and.

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7

Find ten rational numbers between and

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