#### Solved Examples and Worksheet for Finding the product of Rational and Irrational Numbers

Q1What is the product of 9 and17 ?

A. 917
B. 9
C. 317
D. 179

Step: 1
The product of 9 and 17 is 917.
Q2What is the product of 21 and reciprocal of 7?

A. 3 + 7
B. 37
C. 21 + 7
D. 217

Step: 1
The reciprocal of 7 is 17
Step: 2
Therefore, the product of 21 and 17 is 217 .
Step: 3
217 = 217 × 77
[By rationalizing the denominator.]
Step: 4
= 2177
[Sim[plify.]
Step: 5
= 37
Q3What is the product of 45 and reciprocal of 5 ?

A. 95
B. 455
C. 45 + 5
D. 9 + 5

Step: 1
The reciprocal of 5 is 15.
Step: 2
Therefore, the product of 45 and 15 is 455.
Step: 3
455 = 455 × 55
[By rationalizing the denominator]
Step: 4
= 4555
[Simplify.]
Step: 5
= 95
Step: 6
∴ The product of 45 and reciprocal of 5 is 95.
Q4What is the product of the reciprocal of 3 and 396
A. 311
B. 211
C. 2 + 11
D. 3 + 11

Step: 1
The reciprocal of 3 is 13.
Step: 2
396 = 3 × 3 × 2 × 2 × 11 = 3 × 211 = 611.
[Simplify.]
Step: 3
The product of 13 and 611 = 13 × 611 = 6113 = 2 11.
[Simplify.]
Step: 4
∴ The product of the reciprocal of 3 and 396 is 211.
Q5If x = 12 and y = 29 then find the value of x × y

A. 2912
B. 1229
C. 29 + 12
D. 12 + 29

Step: 1
Given that x = 12 and y = 29.
Step: 2
x × y = 1229
[Substitute x = 12, y = 29 and Simplify]
Step: 3
∴ The value of x × y is 1229.
Q6What is 818 in simplest form?
A. 242
B. 82
C. 918
D. 22

Step: 1
818 = 83 × 3 × 2 = 8 × 32 = 242
Q7What is the product of 13 and 13

A. 1313
B. 13
C. 13
D. 13 + 13

Step: 1
The product of 13 and 13 is 13 × 13 = 1313.
Q8Multiply 50 and 19 ?

A. 50 + 19
B. 50
C. 5019
D. 19

Step: 1
The multiplication of 50 and 19 = 50 × 19 = 5019
Q9Find twice the area of a triangle if its base and height are 10 cm and 11cm respectively.

A. 511 sq.cm
B. 1110 sq.cm
C. 1011 sq.cm
D. 110 sq.cm

Step: 1
Area of a triangle = 12 × base × height
[Formula.]
Step: 2
Twice the area of a triangle = base 7times; height
Step: 3
= 10 × 11
[Substitute base = 10 cm, height = 11]
Step: 4
= 1011
Step: 5
∴ Twice the area of the triangle is 1011 sq.cm
Correct Answer is :   1011 sq.cm
Q10Find the perimeter of a rhombus of side 29 m?
A. 6429m
B. 429m
C. 29m
D. 4629m

Step: 1
Perimeter of a rhombus = 4 × side
[Formula.]
Step: 2
= 4 × 29
[Substitute side = 29 m and simplify.]
Step: 3
= 429
Step: 4
∴ perimeter of the rhombus = 429 m