# 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