# Free Rational Numbers 03 Practice Test - 7th grade

### Question 1

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

810

110

−110

−210

#### SOLUTION

Solution :C

Let the unknown number be x.

−15=310+−25+xx=−15−310+25

Taking LCM, we get,x=−210−310+410x=−110

### Question 2

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

0

-1

1

2

#### SOLUTION

Solution :B

Let pq be a non-zero rational number. Then p, q≠0.

Its additive inverse is −pq.

That is, pq+−pq=−pq+pq=0

On dividing pq by −pq, we get -1.

### Question 3

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

#### SOLUTION

Solution :B

### Question 4

From a rope of length 40.50 m, some

pieces are cut each measuring 94 m.

Find the number of pieces cut.

15

18

22

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 pieceNumber Of Pieces Cut

=4050(9×100)4=18

=4050×4(9×100)=18Number of pieces cut = 18.

### Question 5

What number must be subtracted from

14 to get 12?

12

−14

1

-1

#### SOLUTION

Solution :B

Let the number be x.

14−x=12

x=14−12=−14

### Question 6

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

1

2

-1

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=−11−1=11

### Question 7

What should be added to −34 to get 516?

1216

1316

1116

1716

#### SOLUTION

Solution :D

Let the number to be added be x.

−34+x=516

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

### Question 8

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

821

812

815

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=812Therefore, required rational number is 812.

### Question 9

4422 in simplified form is

#### SOLUTION

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

21=2

### Question 10

State whether the following is true or false.

-1413<16

True

False

#### SOLUTION

Solution :A

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