Important Questions: Rational Numbers - Class 7 MCQ

Let us consider a fraction 3/5 and a rational number = 14/7
By definition, 3/5 is a rational number. So, p is true. By definition, -4/7 is not a fraction, since, −4 is not a natural number. So, q is false.

All fractions can be termed as rational numbers; however, all rational numbers cannot be termed as fractions. Only those rational numbers in which 'p' and 'q' are positive integers are termed as fractions.

√2/3 is not a rational number.

because √2 doesn't have an exact value, and on further division by 3, it goes more unstable. 

Since, every integer having a denominator 1 can be expressed in P/q form, p is true. Since, a rational number with denominator other than 1 is not an integer (e.g., 3/5), q is false.

Since, denominator is 0, it is not a rational number.

(a)  −20/15 =-4/3   [ dividing numerator and denominator by 5]  [ Remember you have to divide by same number in numerator and denominator ]
(b)  25/-15 =-5/3     [ dividing numerator and denominator by 5]  [ -ve sign can be puted in denominator as well as numerator ]
(c)  25/15 =5/3   [ dividing numerator and denominator by 5]
(d)  15/25 =3/5    [ dividing numerator and denominator by 5]

- The numerator of 0/7 is 0.
- Zero is a special number that is neither positive nor negative.
- Positive numbers are greater than zero, while negative numbers are less than zero.
- Since zero is not greater or less than itself, it doesn't fit into either category.
- Therefore, the correct classification for the numerator 0 is that it is neither positive nor negative.

Thus, the answer is D: Neither positive nor negative.

3/(−8) = (−12)/32

on simplifying (−12)/32 we get 3/(−8) 

(-4)/7 = (-32)/ X

transposing X to L.H.S

(-4)/7 *X = (-32) 

X =  (-32) * 7/(-4)

On simplifying the equation we get, X=56

as all have same numerator 
just focus in denominator , number which has lowest denominator is greatest 
so 5/11 would be greatest but carefully see all number have - ve sign 
so number which is greatest is actually smallest , and which is smallest is biggest
-5/17 would be the answer 

L.C.M. of 5, 4 and 20 is 20. 
4/−5 × 4/4 = 16/−20;3/4 = 3×5/4×5 = 15/20
−2 < 4/−5 < −11/20 < 3/4
or 
3/4 > −11/20 > 4/−5 > −2
is the required descending order.
Rewrite equivalent fractions of the given fractions and then compare then.
Arrange them in descending order.

The ascending order of 4/7,1/3, 2/5 and 5/9 is 1/3<2/5<5/9<4/7. The two middle numbers are 2/5 and 5/9. 

∴  Average = = 43/90

The given numbers can be arranged in ascending order as1/5 < 3/5 < 7/5 < 9/5
The greatest number = 9/5;
The least number = 1/5
We have,  9/5 × x/100 = 1/5 
⇒ x = 100/9 =11 ¹/₉

The ascending order of given numbers is 1/9,5/9,11/9. 
∴  Required difference = 11/9 −1/9 = 10/9

−24/15 is the equivalent rational number of −8/5.
just divide -24/15  by 3 in numerator and denominator

- First, taking LCM denominator of 2, 11/39 and 5/26, which is 78.
- Rewrite the expression with the common denominator: 156/78 -22/78 + 15/78
- Combine the terms: (156 - 22 + 15)/78
- Simplify the numerator: 149/78
Therefore, the result of 2 - 11/39 + 5/26 is 149/78.

- The equation −7/5 + (2/−11 + −13/25) = (−7/5 + 2/−11) + −13/25 demonstrates the Associative Property.
- The associative property states that the way numbers are grouped in multiplication does not change the result.
- Rearranging the parentheses in multiplication expressions does not affect the result, which is exactly what is shown here.

All the given statements are correct. Consider 4/5 

[a] Since 4/5 + 0 = 4/5, 0 is the additive identity of rational numbers. [

b] Since 4/5 × 1= 4/5, is the  multiplicative identity of rational numbers.

[c] Since 0+0=0, therefore 0 is the additive inverse of 0.

Let's assume another number be x

According to question

(-7/5) + x = -3

⇒ x = -3 + 7/5

⇒ x = -3/1 + 7/5

LCM of 1 and 5 is 5.

So,

⇒ x = (-15 + 7)/5

⇒ x =  -8/5 

∴ Second number is - 8/5,

The correct option is - 8/5

7/3  is a rational number because it can be expressed as a ratio of two integers (7 and 3). The other options represent irrational numbers.

A rational number is defined as a number that can be expressed in the form p/q​, where:

Thus, Option A is the correct definition.