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Page 1
Rational Numbers
Points to remember
? Rational numbers are the numbers which can be expressed as
?? ?? ,where p and
q are integers and q?0 example,
?? ??
?? ??
-?? ?? etc.
? Number 0 is neither a positive rational number nor negative rational number.
It is only a rational number.
? If two or more rational numbers have equal simplest form, then these are
called equivalent rational numbers.
? All integers and fractions are rational numbers.
? There are infinitely many rational numbers between any two rational
numbers.
Questions:
1. Find the rational number whose numerator is (36-15) and denominator
is 7 × (-4).
2. Find the rational number whose numerator is 3 × (-2) and denominator
is 5 × (-1).
3. Express
-?? ??
as a rational number with denominator 28.
4. Express
-?? ?? as a rational number with numerator 40.
5. Express
-????
????
into simplest form.
6. Express
-????
??????
into simplest form.
7. Find the product of
-?? ?? and its reciprocal.
8. Find the reciprocal of
-?? ?? .
9. Fill in the blanks:
-?? ??
=
????
=
????
Page 2
Rational Numbers
Points to remember
? Rational numbers are the numbers which can be expressed as
?? ?? ,where p and
q are integers and q?0 example,
?? ??
?? ??
-?? ?? etc.
? Number 0 is neither a positive rational number nor negative rational number.
It is only a rational number.
? If two or more rational numbers have equal simplest form, then these are
called equivalent rational numbers.
? All integers and fractions are rational numbers.
? There are infinitely many rational numbers between any two rational
numbers.
Questions:
1. Find the rational number whose numerator is (36-15) and denominator
is 7 × (-4).
2. Find the rational number whose numerator is 3 × (-2) and denominator
is 5 × (-1).
3. Express
-?? ??
as a rational number with denominator 28.
4. Express
-?? ?? as a rational number with numerator 40.
5. Express
-????
????
into simplest form.
6. Express
-????
??????
into simplest form.
7. Find the product of
-?? ?? and its reciprocal.
8. Find the reciprocal of
-?? ?? .
9. Fill in the blanks:
-?? ??
=
????
=
????
10. Fill in the blanks:
?? -????
=
????
=
????
11. Find the sum of the smallest natural number and the largest negative
integer.
12. Find the product of the smallest whole number and the smallest positive
integer.
13. Amongst how many people 21 Kg of ration be distributed so that each
one gets
?? ??
Kg.
14. Express the shaded portion as a rational number:
15. Express the shaded portion as a rational number.
16. Simplify: (
??
??
×
?? ??
) + (
?? ??
×
?? ??
).
17. Simplify: (
??
??
×
????
?? ) + (
?? ??
×
?? ??
).
18. Express the shaded portion as a rational number:
19. Subtract
??
?? from
??
??
.
Page 3
Rational Numbers
Points to remember
? Rational numbers are the numbers which can be expressed as
?? ?? ,where p and
q are integers and q?0 example,
?? ??
?? ??
-?? ?? etc.
? Number 0 is neither a positive rational number nor negative rational number.
It is only a rational number.
? If two or more rational numbers have equal simplest form, then these are
called equivalent rational numbers.
? All integers and fractions are rational numbers.
? There are infinitely many rational numbers between any two rational
numbers.
Questions:
1. Find the rational number whose numerator is (36-15) and denominator
is 7 × (-4).
2. Find the rational number whose numerator is 3 × (-2) and denominator
is 5 × (-1).
3. Express
-?? ??
as a rational number with denominator 28.
4. Express
-?? ?? as a rational number with numerator 40.
5. Express
-????
????
into simplest form.
6. Express
-????
??????
into simplest form.
7. Find the product of
-?? ?? and its reciprocal.
8. Find the reciprocal of
-?? ?? .
9. Fill in the blanks:
-?? ??
=
????
=
????
10. Fill in the blanks:
?? -????
=
????
=
????
11. Find the sum of the smallest natural number and the largest negative
integer.
12. Find the product of the smallest whole number and the smallest positive
integer.
13. Amongst how many people 21 Kg of ration be distributed so that each
one gets
?? ??
Kg.
14. Express the shaded portion as a rational number:
15. Express the shaded portion as a rational number.
16. Simplify: (
??
??
×
?? ??
) + (
?? ??
×
?? ??
).
17. Simplify: (
??
??
×
????
?? ) + (
?? ??
×
?? ??
).
18. Express the shaded portion as a rational number:
19. Subtract
??
?? from
??
??
.
20. Simplify:
??
??
÷ (
??
?? -
??
??
).
21. Express
??
??
+
??
??
into decimal form.
22. Fill in the blanks:
??
-??
=
????
=
-????
23. Divide
-??
??
by
??
??
.
24. A person bought
??
??
Kg potatoes and
??
??
Kg onions from the market.
What is the amount of weight he is carrying?
25. Find the value of x, if
a)
??
??
= -10 b)
-????
?? =
??
-??
26. Find the product of
??
??
with the reciprocal of -2.
27. Find the value of
-??
?? ÷ (-3).
28. Divide the reciprocal of
??
??
by
-??
?? .
29. Simplify
????
??????
-
????
????
.
30. Find the additive inverse of
??
??
+
??
??
.
31. Find the product of
??
??
and (
-??
??
).
32. Simplify:
????
????
÷ (
????
-?? ).
33. Product of two rational numbers is
??
????
. If one of the numbers is
??
??
, then
find the other number?
34. Which number gives
??
?? on multiplying with
-??
?? .
35. Express the shaded portion as a rational number.
Page 4
Rational Numbers
Points to remember
? Rational numbers are the numbers which can be expressed as
?? ?? ,where p and
q are integers and q?0 example,
?? ??
?? ??
-?? ?? etc.
? Number 0 is neither a positive rational number nor negative rational number.
It is only a rational number.
? If two or more rational numbers have equal simplest form, then these are
called equivalent rational numbers.
? All integers and fractions are rational numbers.
? There are infinitely many rational numbers between any two rational
numbers.
Questions:
1. Find the rational number whose numerator is (36-15) and denominator
is 7 × (-4).
2. Find the rational number whose numerator is 3 × (-2) and denominator
is 5 × (-1).
3. Express
-?? ??
as a rational number with denominator 28.
4. Express
-?? ?? as a rational number with numerator 40.
5. Express
-????
????
into simplest form.
6. Express
-????
??????
into simplest form.
7. Find the product of
-?? ?? and its reciprocal.
8. Find the reciprocal of
-?? ?? .
9. Fill in the blanks:
-?? ??
=
????
=
????
10. Fill in the blanks:
?? -????
=
????
=
????
11. Find the sum of the smallest natural number and the largest negative
integer.
12. Find the product of the smallest whole number and the smallest positive
integer.
13. Amongst how many people 21 Kg of ration be distributed so that each
one gets
?? ??
Kg.
14. Express the shaded portion as a rational number:
15. Express the shaded portion as a rational number.
16. Simplify: (
??
??
×
?? ??
) + (
?? ??
×
?? ??
).
17. Simplify: (
??
??
×
????
?? ) + (
?? ??
×
?? ??
).
18. Express the shaded portion as a rational number:
19. Subtract
??
?? from
??
??
.
20. Simplify:
??
??
÷ (
??
?? -
??
??
).
21. Express
??
??
+
??
??
into decimal form.
22. Fill in the blanks:
??
-??
=
????
=
-????
23. Divide
-??
??
by
??
??
.
24. A person bought
??
??
Kg potatoes and
??
??
Kg onions from the market.
What is the amount of weight he is carrying?
25. Find the value of x, if
a)
??
??
= -10 b)
-????
?? =
??
-??
26. Find the product of
??
??
with the reciprocal of -2.
27. Find the value of
-??
?? ÷ (-3).
28. Divide the reciprocal of
??
??
by
-??
?? .
29. Simplify
????
??????
-
????
????
.
30. Find the additive inverse of
??
??
+
??
??
.
31. Find the product of
??
??
and (
-??
??
).
32. Simplify:
????
????
÷ (
????
-?? ).
33. Product of two rational numbers is
??
????
. If one of the numbers is
??
??
, then
find the other number?
34. Which number gives
??
?? on multiplying with
-??
?? .
35. Express the shaded portion as a rational number.
36.
-??
?? should be added to which number to get
????
????
?
37. Ramesh gives
?? ?? ????
of his income to his wife and
?? ?? ????
to his son.
Find what fraction does he have now?
38. Simplify:
-??
????
+
-??
????
39. Simplify:
??
?? +
??
?? +
??
????
40. Find the multiplicative inverse of
??
?? +
??
??
41. Find the multiplicative inverse of
????
??????
+
????
??????
42. Simplify: (
-????
????
) × (-108).
43. Find the rational number that should be subtracted from 5 so as to get
??
?? ?
44. A boy walks
??
????
Km towards north direction and another boy walks
????
????
Km towards south direction. Find the distance between two boys.
45. Find the rational numbers to complete the pattern such that they are
equivalent fractions:
a)
????
????
,
????
????
,_____ b)
??
????
, ______ ,
????
????
46. If p = 2m × r and q = n × 2r, then find
??
??
47. Fill in the blanks: _______×
-??
?? = 1.
48. Simplify: 0 ÷
??
?? ?
49. Which rational number does not have a reciprocal?
50. Which rational number is its own reciprocal?
Page 5
Rational Numbers
Points to remember
? Rational numbers are the numbers which can be expressed as
?? ?? ,where p and
q are integers and q?0 example,
?? ??
?? ??
-?? ?? etc.
? Number 0 is neither a positive rational number nor negative rational number.
It is only a rational number.
? If two or more rational numbers have equal simplest form, then these are
called equivalent rational numbers.
? All integers and fractions are rational numbers.
? There are infinitely many rational numbers between any two rational
numbers.
Questions:
1. Find the rational number whose numerator is (36-15) and denominator
is 7 × (-4).
2. Find the rational number whose numerator is 3 × (-2) and denominator
is 5 × (-1).
3. Express
-?? ??
as a rational number with denominator 28.
4. Express
-?? ?? as a rational number with numerator 40.
5. Express
-????
????
into simplest form.
6. Express
-????
??????
into simplest form.
7. Find the product of
-?? ?? and its reciprocal.
8. Find the reciprocal of
-?? ?? .
9. Fill in the blanks:
-?? ??
=
????
=
????
10. Fill in the blanks:
?? -????
=
????
=
????
11. Find the sum of the smallest natural number and the largest negative
integer.
12. Find the product of the smallest whole number and the smallest positive
integer.
13. Amongst how many people 21 Kg of ration be distributed so that each
one gets
?? ??
Kg.
14. Express the shaded portion as a rational number:
15. Express the shaded portion as a rational number.
16. Simplify: (
??
??
×
?? ??
) + (
?? ??
×
?? ??
).
17. Simplify: (
??
??
×
????
?? ) + (
?? ??
×
?? ??
).
18. Express the shaded portion as a rational number:
19. Subtract
??
?? from
??
??
.
20. Simplify:
??
??
÷ (
??
?? -
??
??
).
21. Express
??
??
+
??
??
into decimal form.
22. Fill in the blanks:
??
-??
=
????
=
-????
23. Divide
-??
??
by
??
??
.
24. A person bought
??
??
Kg potatoes and
??
??
Kg onions from the market.
What is the amount of weight he is carrying?
25. Find the value of x, if
a)
??
??
= -10 b)
-????
?? =
??
-??
26. Find the product of
??
??
with the reciprocal of -2.
27. Find the value of
-??
?? ÷ (-3).
28. Divide the reciprocal of
??
??
by
-??
?? .
29. Simplify
????
??????
-
????
????
.
30. Find the additive inverse of
??
??
+
??
??
.
31. Find the product of
??
??
and (
-??
??
).
32. Simplify:
????
????
÷ (
????
-?? ).
33. Product of two rational numbers is
??
????
. If one of the numbers is
??
??
, then
find the other number?
34. Which number gives
??
?? on multiplying with
-??
?? .
35. Express the shaded portion as a rational number.
36.
-??
?? should be added to which number to get
????
????
?
37. Ramesh gives
?? ?? ????
of his income to his wife and
?? ?? ????
to his son.
Find what fraction does he have now?
38. Simplify:
-??
????
+
-??
????
39. Simplify:
??
?? +
??
?? +
??
????
40. Find the multiplicative inverse of
??
?? +
??
??
41. Find the multiplicative inverse of
????
??????
+
????
??????
42. Simplify: (
-????
????
) × (-108).
43. Find the rational number that should be subtracted from 5 so as to get
??
?? ?
44. A boy walks
??
????
Km towards north direction and another boy walks
????
????
Km towards south direction. Find the distance between two boys.
45. Find the rational numbers to complete the pattern such that they are
equivalent fractions:
a)
????
????
,
????
????
,_____ b)
??
????
, ______ ,
????
????
46. If p = 2m × r and q = n × 2r, then find
??
??
47. Fill in the blanks: _______×
-??
?? = 1.
48. Simplify: 0 ÷
??
?? ?
49. Which rational number does not have a reciprocal?
50. Which rational number is its own reciprocal?
ANSWERS
1.
-?? ??
26.
-?? ??
2.
?? ??
27.
?? ??
3.
-????
????
28.
????
-??
4.
????
-????
29.
?? ??
5.
-?? ????
30.
-????
????
6.
-????
????
31.
-?? ??
7. 1 32.
-?? ??
8.
?? -??
33.
?? ??
9. -8 and -36
34.
-?? ??
10. -6 and -65 35.
?? ?? or
?? ??
11. 0 36.
????
??
12. 0 37.
????
????
13. 9 38.
-????
????
14.
?? ????
39.
????
????
15.
?? ??
40.
????
????
16. 2 41.
??????
??????
????
????
????
17.
????
??
42. 102
18.
?? ?? or
?? ??
43.
????
??
19.
-?? ??
44.
????
????
Km
20.
????
??
45.
(a)
??????
??????
(b)
????
????
21. 0.45 46.
?? ??
22. -30, 63 47.
-?? ??
23. -1 48. 0
24.
?? ?? ????
kg
49. 0
25. (a) -50 (b) 30 50. 1
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