Solved Examples and Worksheet for Finding the product of Rational and Irrational Numbers
Q1
What is the product of 9 and
1
7
?
A
. 9
1
7
B
. 9
C
. 3
1
7
D
. 17
9
Solutions
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Step: 1
The product of 9 and
1
7
is 9
1
7
.
Correct Answer is :
9
1
7
Q2
What is the product of 21 and reciprocal of
7
?
A
. 3 +
7
B
. 3
7
C
. 21 +
7
D
. 21
7
Solutions
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Step: 1
The reciprocal of
7
is
1
7
Step: 2
Therefore, the product of 21 and
1
7
is
2
1
7
.
Step: 3
⇒
2
1
7
=
2
1
7
×
7
7
[By rationalizing the denominator.]
Step: 4
=
2
1
7
7
[Sim[plify.]
Step: 5
= 3
7
Correct Answer is :
3
7
Q3
What is the product of 45 and reciprocal of
5
?
A
. 9
5
B
. 45
5
C
. 45 +
5
D
. 9 +
5
Solutions
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Step: 1
The reciprocal of
5
is
1
5
.
Step: 2
Therefore, the product of 45 and
1
5
is
4
5
5
.
Step: 3
⇒
4
5
5
=
4
5
5
×
5
5
[By rationalizing the denominator]
Step: 4
=
4
5
5
5
[Simplify.]
Step: 5
= 9
5
Step: 6
∴ The product of 45 and reciprocal of
5
is 9
5
.
Correct Answer is :
9
5
Q4
What is the product of the reciprocal of 3 and
3
9
6
A
. 3
1
1
B
. 2
1
1
C
. 2 +
1
1
D
. 3 +
1
1
Solutions
Share
Step: 1
The reciprocal of 3 is
1
3
.
Step: 2
3
9
6
=
3
×
3
×
2
×
2
×
1
1
= 3 × 2
1
1
= 6
1
1
.
[Simplify.]
Step: 3
The product of
1
3
and 6
1
1
=
1
3
× 6
1
1
=
6
1
1
3
= 2
1
1
.
[Simplify.]
Step: 4
∴ The product of the reciprocal of 3 and
3
9
6
is 2
1
1
.
Correct Answer is :
2
1
1
Q5
If
x
= 12 and
y
= 29 then find the value of
x
×
y
A
. 29
1
2
B
. 12
2
9
C
. 29 +
1
2
D
. 12 +
2
9
Solutions
Share
Step: 1
Given that
x
= 12 and
y
= 29.
Step: 2
x
×
y
= 12
2
9
[Substitute
x
= 12,
y
= 29 and Simplify]
Step: 3
∴ The value of
x
×
y
is 12
2
9
.
Correct Answer is :
12
2
9
Q6
What is 8
1
8
in simplest form?
A
. 24
2
B
. 8
2
C
. 9
1
8
D
. 2
2
Solutions
Share
Step: 1
8
1
8
= 8
3
×
3
×
2
= 8 × 3
2
= 24
2
Correct Answer is :
24
2
Q7
What is the product of
1
3
and 13
A
. 13
1
3
B
. 13
C
.
1
3
D
. 13 +
1
3
Solutions
Share
Step: 1
The product of
1
3
and 13 is
1
3
× 13 = 13
1
3
.
Correct Answer is :
13
1
3
Q8
Multiply 50 and
1
9
?
A
. 50 +
1
9
B
. 50
C
. 50
1
9
D
.
1
9
Solutions
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Step: 1
The multiplication of 50 and
1
9
= 50 ×
1
9
= 50
1
9
Correct Answer is :
50
1
9
Q9
Find twice the area of a triangle if its base and height are 10 cm and
1
1
cm respectively.
A
. 5
1
1
sq.cm
B
. 11
1
0
sq.cm
C
. 10
1
1
sq.cm
D
.
1
1
0
sq.cm
Solutions
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Step: 1
Area of a triangle =
1
2
× base × height
[Formula.]
Step: 2
Twice the area of a triangle = base 7times; height
Step: 3
= 10 ×
1
1
[Substitute base = 10 cm, height =
1
1
]
Step: 4
= 10
1
1
Step: 5
∴ Twice the area of the triangle is 10
1
1
sq.cm
Correct Answer is :
10
1
1
sq.cm
Q10
Find the perimeter of a rhombus of side
2
9
m?
A
. 64
2
9
m
B
. 4
2
9
m
C
.
2
9
m
D
. 46
2
9
m
Solutions
Share
Step: 1
Perimeter of a rhombus = 4 × side
[Formula.]
Step: 2
= 4 ×
2
9
[Substitute side =
2
9
m and simplify.]
Step: 3
= 4
2
9
Step: 4
∴ perimeter of the rhombus = 4
2
9
m
Correct Answer is :
4
2
9
m
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