Rational Numbers MCQ Test — Class 7 CBSE

Solution:

An equivalent rational number is obtained by multiplying or dividing both the numerator and the denominator by the same non-zero integer.

This ensures that the value of the rational number remains the same, only its representation changes. — (p × k) / (q × k) = p/q, where k ≠ 0

Solution:

First, identify the negative numbers: -3/4 and -2/3. Positive numbers (1/2) and zero are always greater than negative numbers.

To compare -3/4 and -2/3, find a common denominator, which is 12. Convert the fractions: — -3/4 = (-3 × 3) / (4 × 3) = -9/12

And: — -2/3 = (-2 × 4) / (3 × 4) = -8/12

Since -9 is smaller than -8, -9/12 is smaller than -8/12. Therefore, -3/4 is the smallest rational number.

Solution:

To add rational numbers with different denominators, you must first find a common denominator, which is usually the Least Common Multiple (LCM) of the denominators.

For 2/5 and 1/3, the LCM of 5 and 3 is 15. The correct steps would be to convert them to equivalent fractions with denominator 15.

Anil's mistake was directly adding the denominators (5+3) instead of converting the fractions to have a common denominator first.

Solution:

The expression is -5/7 - (-2/7).

Subtracting a negative number is equivalent to adding its positive counterpart: -5/7 + 2/7.

Since the denominators are already the same, we can add the numerators directly: — (-5 + 2) / 7

This simplifies to: — -3/7

Solution:

To find out how much sugar is needed for 2/3 of the recipe, multiply the total sugar required by the fraction of the recipe you want to make.

Sugar needed = (3/4) × (2/3)

Multiply the numerators and the denominators: — (3 × 2) / (4 × 3) = 6/12

Simplify the fraction 6/12 by dividing both the numerator and the denominator by their greatest common divisor, which is 6: — 6/12 = (6 ÷ 6) / (12 ÷ 6) = 1/2

Solution:

Division by a rational number is defined as multiplication by its reciprocal.

The reciprocal of a non-zero rational number c/d is d/c.

So, (a/b) ÷ (c/d) = (a/b) × (d/c).

Solution:

The property of rational numbers states that between any two distinct rational numbers, there exist infinitely many rational numbers.

This is known as the density property of rational numbers. You can always find a midpoint, and then a midpoint between that and one of the original numbers, and so on, indefinitely.

Solution:

The additive inverse of a rational number 'x' is '-x', such that x + (-x) = 0.

For the rational number -11/13, its additive inverse is the number that makes the sum zero.

-11/13 + (11/13) = 0.

Therefore, the additive inverse of -11/13 is 11/13.

Solution:

To find the number midway between two numbers, you can add them and then divide by 2.

Numbers are -1/2 and 0. Sum = -1/2 + 0 = -1/2.

Midpoint = (Sum) / 2 = (-1/2) / 2.

Dividing by 2 is the same as multiplying by 1/2: — (-1/2) × (1/2) = -1/4

Solution:

Let the unknown rational number be 'x'.

According to the problem, when 'x' is subtracted from 5/9, the result is -2/9. So, we can write the equation: — 5/9 - x = -2/9

To solve for 'x', we can rearrange the equation: — 5/9 + 2/9 = x

Now, add the fractions: — (5 + 2) / 9 = 7/9

So, the rational number is 7/9.