Free Rational Numbers 01 Practice Test - 8th Grade
Question 1
A number which can be represented in the form of pq, q≠0 where p and q are integers is called a
SOLUTION
Solution :A number which can be represented in the form of pq, q≠0 where p and q are integers is called a rational number.
For example, 23,5, −4 etc are all rational numbers as they can be expressed in pq form with p and q as integers and q≠0.
Question 2
The product of two whole numbers is always a whole number.
True
False
SOLUTION
Solution : A
If 'a' and 'b' are any two whole numbers, their product will also be a whole number. We know that the multiplication of any two numbers can be expressed as repeated addition of one number. So, if we are adding any whole number to itself again and again, then we will surely get a whole number.
Let's assume a=2,b=3.
a×b=2×3 which is same as adding '2' three times to itself, which will result in a whole number.
Question 3
Which of the following lies between 254 and 223?
SOLUTION
Solution : A
Rational numbers can be compared by making their denominators equal.
Here, we need to compare all given rational numbers 254,223,132,152,172 and 81.
We know LCM of 1, 2, 3 and 4, i.e., the denominators of the above fractions, is 12.
Converting all the above fractions into like fractions, we get
254=25×34×3=7512
223=22×43×4=8812
132=13×62×6=7812
152=15×62×6=9012
172=17×62×6=10212
8=81=8×121×12=9612
Arranging these fractions in an ascending order, we have
7512,7812,8812,9012,9612,10212
Thus, 132 lies between 254 and 223.
Question 4
Which operations on whole numbers are commutative?
Addition
Multiplication
Division
Subtraction
SOLUTION
Solution : A and B
An operation is commutative if changing the order of operands does not change the result.
Addition and multiplication are commutative for whole numbers.
For example, 2+3=5, 3+2=5.
Also, 3×4=12, 4×3=12
Question 5
The reciprocal of -10 is
0.1
- 0.1
0.01
- 0.01
SOLUTION
Solution : B
The reciprocal of any non-zero number 'a' is 1a.
The reciprocal of '-10' = 1(−10)=−0.1
Question 6
Division of the reciprocal of 511 by −5518 results in −1825.
True
False
SOLUTION
Solution : A
Reciprocal of 511 is 115.
115÷−5518
=11×185×(−55)=−1825
Question 7
By what rational number should we divide 227 so as to get the number −1114?
- 2
57
127
-4
SOLUTION
Solution : D
Let the rational number be x.
227÷x = −1114 (given)
⇒227=x×−1114
⇒227÷−1114=x
⇒227×14−11=x⇒x=−4
Therefore, 227 should be divided by -4 to get −1114.
Question 8
For what value of x, −12x is equal to 3?
−4
4
3
SOLUTION
Solution : A
−12x=3
⇒−123=x
Or
x=−4
Question 9
Which of the following is a rational number between 13 and 53 ?
73
43
SOLUTION
Solution : B
In the fractions 13 and 53, the denominators are same.
So, considering numerator values, we can find the required rational number.
4 lies between 1 and 5.
So, keep 4 in the numerator and keep the same denominator as it is.
The required rational number is 43.
Question 10
(59÷13)÷52=59÷(13÷52).
True
False
SOLUTION
Solution : B
Let's first evaluate LHS.
(5913)×152=59676
Now, RHS
59×(5213)=306813
We see that both LHS and RHS are not equal.