Free Rational Numbers 01 Practice Test - 7th grade

The sum of the rational numbers 819 and 457 is _____.

A.

2857

B.

1257

C.

4247

D.

3247

SOLUTION

Solution : A

819+457=(8×3)(19×3)+457

=2457+457

=2857

Find the greatest rational  number among the given options.

A.

49

B.

512

C.

718

D.

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.

Which of the following forms a pair of equivalent rational numbers?

A.

2440 and 3550

B.

2535 and 5577

C.

815 and 2448

D.

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)=140200120200
Thus, 2440 and 3550 are not equivalent.
Considering 2535 and 5577, LCM of 35 and 77 is 385.
(25×11)(35×11)=275385
and     (55×5)(77×5)=275385.
Thus,  2535 and 5577 are equivalent rational numbers.

Similarly, on checking the remaining options we find that 2535 and 5577 is the only pair of equivalent rational numbers.

Find the value of
1621÷43.

A.

310

B.

47

C.

721

D.

76

SOLUTION

Solution : B

1621÷43=1621×34

=47

Compare the rational numbers and choose the correct option.

25___34.

A.

>

B.

<

C.

=

D.

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.

Write a rational number equal to 47 with 63 as the denominator.

A.

1263

B.

2063

C.

3663

D.

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.

Which of the following is a rational number that lies between 0 and 1?

A.

3913

B.

2420

C.

1314

D.

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.

Find the result obained by the addition of
23  to the reciprocal of  23.

A.

56

B.

56

C.

67

D.

67

SOLUTION

Solution : B

Reciprocal of  23  is 32.

2332=4696=(49)6=56

[LCM of 2 and 3 is 6]

Simplified form of 10812 is 8.

A.

True

B.

False

Solution : B

12 × 9 = 108

10812=(12×9)12

= 9

43>0

A.

True

B.

False

SOLUTION

Solution : B

Any negative number is less than 0. So, 43<0