Free Rational Numbers 01 Practice Test - 7th grade
Question 1
The sum of the rational numbers −819 and −457 is _____.
−2857
−1257
−4247
−3247
SOLUTION
Solution : A
−819+−457=(−8×3)(19×3)+−457
=−2457+−457
=−2857
Question 2
Find the greatest rational number among the given options.
−49
−512
−718
−23
SOLUTION
Solution : C
Note that LCM of 9, 12, 18, 3 is 36.
Using LCM to convert each of the given rational numbers to equivalent forms,
−49 = −1636
−512 = −1536
−718 = −1436
−23 = −2436
Since the denominators are equal, we now compare the rational numbers using its numerators.
Thus, −2436<−1636<−1536<−1436
i.e., −23<−49<−512<−718
∴−718 is the greatest among the given options.
Question 3
Which of the following forms a pair of equivalent rational numbers?
2440 and 3550
−2535 and 55−77
−815 and −2448
972 and −321
SOLUTION
Solution : B
When we have to compare two rational numbers, we first make their denominators equal and then compare their numerators.
Consider 2440 and 3550. LCM of 40 and 50 is 200.
⟹(24×5)(40×5)=120200
and (35×4)(50×4)=140200≠120200.
Thus, 2440 and 3550 are not equivalent.
Considering −2535 and 55−77, LCM of 35 and 77 is 385.
⟹(−25×11)(35×11)=−275385
and (55×5)(−77×5)=−275385.
Thus, −2535 and 55−77 are equivalent rational numbers.
Similarly, on checking the remaining options we find that −2535 and 55−77 is the only pair of equivalent rational numbers.
Question 4
Find the value of
−1621÷−43.
−310
47
−721
−76
SOLUTION
Solution : B
−1621÷−43=−1621×−34
=47
Question 5
Compare the rational numbers and choose the correct option.
25___34.
>
<
=
Cannot be determined
SOLUTION
Solution : B
To compare two rational numbers we make their denominators equal and then compare their numerators.
LCM of the denominator 4 and 5 is 20.
2×45×4=820
3×54×5=1520
Comparing 820 and 1520,
we see that 820 <1520
Hence, 25<34.
Question 6
Write a rational number equal to 47 with 63 as the denominator.
1263
2063
3663
6063
SOLUTION
Solution : C
Consider given rational number 47.
To make the denominator as 63, we have to multiply it with 9.Multiplying both numerator and denominator by 9, we get
4×97×9=3663
Therefore, 3663 is an equivalent rational number of 47 with denominator equal to 63.
Question 7
Which of the following is a rational number that lies between 0 and 1?
3913
2420
1314
1513
SOLUTION
Solution : C
1314
is less than 1 as the numerator of the fraction is smaller than the denominator.
While on the other hand, the other fractions are greater than 1 as all the numbers are positive and their numerator is greater than the denominator.
Question 8
Find the result obained by the addition of
23 to the reciprocal of −23.
56
−56
67
−67
SOLUTION
Solution : B
Reciprocal of −23 is −32.
23−32=46−96=(4−9)6=−56
[LCM of 2 and 3 is 6]
Question 9
Simplified form of 10812 is 8.
True
False
SOLUTION
Solution : B
12 × 9 = 108
⇒10812=(12×9)12= 9
Question 10
−43>0
True
False
SOLUTION
Solution : B
Any negative number is less than 0. So, −43<0