Free Rational Numbers 02 Practice Test - 8th Grade
Question 1
The ___ property states that we can add rational numbers in any order.
commutative
SOLUTION
Solution : A
The addition of rational numbers can be done in any order and the result remains the same. This is called commutative property.
E.g: 2 + 3 = 3 + 2
Question 2
Choose the rational numbers whose numerator is (−5)×6, and the denominator is (34−23)×(7−5).
2011
4022
−1511
−3022
SOLUTION
Solution : C and D
Rational numbers are the numbers which can be expressed in the form of pq, given q≠0, p and q are integers.
pq=−5×6(34−23)×(7−5)
=−3011×2
=−3022
=−1511
Question 3
Write down the rational number whose numerator is the smallest four digit number and denominator is the largest five digit number.
100099999
100099900
999999999
100010000
SOLUTION
Solution : A
The smallest four digit number is 1000 and largest five digit number is 99999.
Therefore, the required rational number is smallest four digit numberlargest five digit number=100099999 .
Question 4
Which of the following pair of rational numbers are smaller than -5?
−122 & −202
−105 & −324
−273 & −183
−1005 & −2005
SOLUTION
Solution : A, C, and D
a) −122=−6 & −202=−10
-6 and -10 are smaller than -5.
b) −105=−2 & −324=−8
-2 is greater than -5.
c) −273=−9 & −183=−6
-9 and -6 are smaller than -5.
d) −1005=−20 &−2005=−40
-20 and -40 are smaller than -5.
Question 5
Arrange the following rational numbers in the ascending order
54,23,68,85,92.
23<68<54<85<92
54<68<23<85<92
92<85<54<68 < 23
92<23<54<85<68
SOLUTION
Solution : A
To compare the rational numbers, we first make the denominators equal.
L.C.M of the denominators 4, 3, 8, 5, 2 is 120.Equivalent fractions with the denominator 120 are
54×3030=150120
23×4040=80120
68×1515=90120
85×2424=192120
92×6060=540120
Since the denominator is same in the above equivalent fractions, we can decide the ascending order based on the numerator values.Ascending order :
23<68<54<85<92
Question 6
Product of 76 and reciprocal of 1166 is __________.
16
76
7
711
SOLUTION
Solution : C
Reciprocal of 1166=6611
⇒76×6611=7×1111=7
Question 7
−1551 is a multiplicative inverse of −175.
True
False
SOLUTION
Solution : A
Multiplicative inverse of ab is cd if ab×cd=1.
Now, −1551×−175=33=1
Question 8
Which of the following rational numbers are equivalent to 94?
123
8125
6328
3616
SOLUTION
Solution : C and D
When we multiply and divide a rational number by the same number, the value of rational number remains unchanged. Therefore,
94×77=632894×44=3616
Question 9
Which of the following statements is incorrect?
Every whole number is a rational number
Every integer is a rational number
Zero is a whole number and it is rational number too
Every rational number is not an integer
SOLUTION
Solution : C
Zero is a whole number as well as the rational number. Zero can be expressed in the form of pq as 01. Hence zero is a rational number since it satisfies the definition of rational number where p = 0 and q ≠ 0.
Question 10
Which of the following rational numbers lie betwen 37 and 48 ?
92
2656
-2
1328
SOLUTION
Solution : B and D
L.C.M of 7 and 8 is 56.
37 and 48 can be written as 2456 and 2856.
Check for numbers which lie between 2456 and 2856.
Now, 1328 = 2656 lies between 37 and 48.