Finding the product of Rational and Irrational Numbers-Algebra1-Solved Examples

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

Q1What is the product of 9 and

$17$ ?

A. 9

$17$
B. 9
C. 3

$17$
D. 17

$9$

Solutions

Step: 1

The product of 9 and

$17$ is 9

$17$ .

Correct Answer is : 9

$17$

Q2What is the product of 21 and reciprocal of

$7$ ?

A. 3 +

$7$
B. 3

$7$
C. 21 +

$7$
D. 21

$7$

Solutions

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

= 3

$7$

Correct Answer is : 3

$7$

Q3What is the product of 45 and reciprocal of

$5$ ?

A. 9

$5$
B. 45

$5$
C. 45 +

$5$
D. 9 +

$5$

Solutions

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

= 9

$5$

Step: 6

∴ The product of 45 and reciprocal of

$5$ is 9

$5$ .

Correct Answer is : 9

$5$

Q4What is the product of the reciprocal of 3 and

$396$
A. 3

$11$
B. 2

$11$
C. 2 +

$11$
D. 3 +

$11$

Solutions

Step: 1

The reciprocal of 3 is

$13$ .

Step: 2

$396$ =

$3 × 3 × 2 × 2 × 11$ = 3 × 2

$11$ = 6

$11$ .

[Simplify.]

Step: 3

The product of

$13$ and 6

$11$ =

$13$ × 6

$11$ =

$6113$ = 2

$11$ .

[Simplify.]

Step: 4

∴ The product of the reciprocal of 3 and

$396$ is 2

$11$ .

Correct Answer is : 2

$11$

Q5If

$x$ = 12 and

$y$ = 29 then find the value of

$x$ ×

$y$

A. 29

$12$
B. 12

$29$
C. 29 +

$12$
D. 12 +

$29$

Solutions

Step: 1

Given that

$x$ = 12 and

$y$ = 29.

Step: 2

$x$ ×

$y$ = 12

$29$

[Substitute

$x$ = 12,

$y$ = 29 and Simplify]

Step: 3

∴ The value of

$x$ ×

$y$ is 12

$29$ .

Correct Answer is : 12

$29$

Q6What is 8

$18$ in simplest form?
A. 24

$2$
B. 8

$2$
C. 9

$18$
D. 2

$2$

Solutions

Step: 1

$18$ = 8

$3 × 3 × 2$ = 8 × 3

$2$ = 24

$2$

Correct Answer is : 24

$2$

Q7What is the product of

$13$ and 13

A. 13

$13$
B. 13
C.

$13$
D. 13 +

$13$

Solutions

Step: 1

The product of

$13$ and 13 is

$13$ × 13 = 13

$13$ .

Correct Answer is : 13

$13$

Q8Multiply 50 and

$19$ ?

A. 50 +

$19$
B. 50
C. 50

$19$
D.

$19$

Solutions

Step: 1

The multiplication of 50 and

$19$ = 50 ×

$19$ = 50

$19$

Correct Answer is : 50

$19$

Q9Find twice the area of a triangle if its base and height are 10 cm and

$11$ cm respectively.

A. 5

$11$ sq.cm
B. 11

$10$ sq.cm
C. 10

$11$ sq.cm
D.

$110$ sq.cm

Solutions

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

= 10

$11$

Step: 5

∴ Twice the area of the triangle is 10

$11$ sq.cm

Correct Answer is : 10

$11$ sq.cm

Q10Find the perimeter of a rhombus of side

$29$ m?
A. 64

$29$ m
B. 4

$29$ m
C.

$29$ m
D. 46

$29$ m

Solutions

Step: 1

Perimeter of a rhombus = 4 × side

[Formula.]

Step: 2

= 4 ×

$29$

[Substitute side =

$29$ m and simplify.]

Step: 3

= 4

$29$

Step: 4

∴ perimeter of the rhombus = 4

$29$ m

Correct Answer is : 4

$29$ m

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

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Related Topic

HighSchool Math