NCERT Solutions Class 7 Maths Chapter 12 — Rational Numbers

Solution:

Step 1: An equivalent rational number is obtained by multiplying or dividing both the numerator and the denominator by the same non-zero integer.

Step 2: 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:

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

Step 2: 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]

Step 3: And: [-2/3 = (-2 × 4) / (3 × 4) = -8/12]

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

Solution:

Step 1: 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.

Step 2: 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.

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

Solution:

Step 1: The expression is -5/7 - (-2/7).

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

Step 3: Since the denominators are already the same, we can add the numerators directly: [(-5 + 2) / 7]

Step 4: This simplifies to: [-3/7]

Solution:

Step 1: 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.

Step 2: Sugar needed = (3/4) × (2/3)

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

Step 4: 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]