# Free Rational Numbers 03 Practice Test - 7th grade

The sum of three rational numbers is 15.If two numbers are 25 and 310, then find the third number.

A.

810

B.

110

C.

110

D.

210

#### SOLUTION

Solution : C

Let the unknown number be x.

15=310+25+xx=15310+25

Taking LCM, we get,x=210310+410x=110

What is the quotient, when a non-zero rational number is divided by its additive inverse?

A.

0

B.

-1

C.

1

D.

2

#### SOLUTION

Solution : B

Let pq be a non-zero rational number. Then p, q0.

That is, pq+pq=pq+pq=0

On dividing pq by pq, we get -1.

Which of the following is obtained by the subtraction of 1/2 from its reciprocal

A. 1
B. 3/2
C. 1/2
D. 2/3

#### SOLUTION

Solution : B

From a rope of length 40.50 m, some
pieces are cut each measuring 94 m.
Find the number of pieces cut.

A.

15

B.

18

C.

22

D.

9

#### SOLUTION

Solution : B

Converting all the lengths into centimetre.

Total length of the rope = 4050 cm,
Length of each piece
=94×100=9004

Number of Pieces
=Total lengthLength of each piece

Number Of  Pieces Cut
=4050(9×100)4=18

=4050×4(9×100)=18

Number of pieces cut = 18.

What number must be subtracted from
14  to get 12?

A.

12

B.

14

C.

1

D.

-1

#### SOLUTION

Solution : B

Let the number be x.

14x=12

x=1412=14

Find the value of x such that 11x is not a rational number.

A.

1

B.

2

C.

-1

D.

0

#### SOLUTION

Solution : D

A number which can be written in the form pq , where p and q are integers and q ≠ 0 is called a rational number.

By the above definition, pq can be a rational number only when q ≠ 0.

So, for the given fraction to be not a rational number, x should be zero.

For all the other given values of x, we will obtain a rational number.

For example, when x = 1,
11x=111=11

when x = 2,
11x=112=5.5

when x = -1,
11x=111=11

What should be added to 34 to get 516?

A.

1216

B.

1316

C.

1116

D.

1716

#### SOLUTION

Solution : D

Let the number to be added be x.

34+x=516

x=516+34=516+1216=1716.

Write a rational number equivalent to 23 whose numerator is 8.

A.

821

B.

812

C.

815

D.

820

#### SOLUTION

Solution : B

Consider 23.

To make the numerator 8, we have to multiply the numerator by 4.

Therefore, multiplying both numerator and denominator by 4 gives the required number.

2×43×4=812

Therefore, required rational number is 812.

4422 in simplified form is __.

#### SOLUTION

Solution :

4422=21    [Dividing both numerator and denominator by 22]

21=2

State whether the following is true or false.

-1413<16

A.

True

B.

False

#### SOLUTION

Solution : A

By using the number line, we know that the statement is true. 