# Free Rational Numbers 03 Practice Test - 8th Grade

How many natural numbers are there
between 310  and710?

A.

0

B.

1

C.

2

D.

3

#### SOLUTION

Solution : A

Natural numbers start from 1 and goes on as 2, 3, 4, ...

310=0.3 and  710=0.7

Thus, there are no natural numbers between 0.3 and 0.7.

Between any two given rational numbers, there are infinite rational numbers.

A.

True

B.

False

#### SOLUTION

Solution : A

There are infinite rational numbers between any two rational numbers. Let's consider an example to understand this better.

Rational numbers between 110 and 310:

010, 110, 210 are the obvious rational numbers between them.

But 110 can be written as 10000100000 and 310 = 30000100000

So, rational numbers between 110 and 310 are 9999100000, 9998100000 ,…..29998100000, 29999100000
Thus, we can find infinite rational numbers between any two rational numbers.

Rational numbers can be represented on the number line.

A.

True

B.

False

#### SOLUTION

Solution : A

All real numbers can be represented on a number line and rational numbers are also real numbers. Thus rational numbers can also be represented on the number line.

The additive identity for rational numbers is 0.

A.

True

B.

False

#### SOLUTION

Solution : A

Zero is the additive identity for rational numbers, integers and whole numbers, as adding zero to these numbers does not affect its value.

Eg:a+0=0+a=a.

The number of natural numbers between 15 and 20 is  ___.

#### SOLUTION

Solution :

There are only 4 natural numbers between 15 and 20 which are 16, 17, 18 and 19.

Multiplication of a number with its reciprocal gives ___.

#### SOLUTION

Solution :

Multiplication of any number with its reciprocal results in 1.
For example,25×52=1

Division of whole numbers follows the commutative law.

A.

True

B.

False

#### SOLUTION

Solution : B

An operation is commutative if changing the order of operands does not change the result.

Division of whole numbers is not commutative. abba

For example: a = 2, b = 3; 2332

If we subtract 12 from a number and multiply the result by 12, we get 38. What is the number?

A.

1

B.

2

C.

1.25

D.

1.5

#### SOLUTION

Solution : C

Let the number be y.

(y12)×(12)=(38)

(y12)=(34)

y=34+12=34+24=54=1.25

Raju earns ₹ 34000 per month. He spends 14th of his income on food, 310th of the remainder on house rent and 521th of the remainder on education of children. How much money is still left with him?

A.

₹13100

B.

₹13200

C.

₹13300

D.

₹13600

#### SOLUTION

Solution : D

Raju's total monthly income = ₹ 34000

Raju’s expenses on food = 14×34000

= ₹ 8500

Money left with Raju = 34000 - 8500
= ₹ 25500

House rent = 310×25500
= ₹ 7650

Now, money left with Raju = 255007650
= ₹ 17850

Children's education = 521×17850
= ₹ 4250

Money left with Raju = 17850 – 4250
= ₹13600

After reading 49th of a book, 30 pages are left. How many pages are there in the book?

A.

54

B.

36

C.

24

D.

60

#### SOLUTION

Solution : A

Let the  total number of pages in the book be x.

(49×x) pages are read

Remaining pages=x 4x9
=5x9=305x=30×9
x=54 pages