NCERT Solutions for Class 7 Maths Chapter 9 Exercise 9.2 - Rational Numbers

Adding and Subtracting Rational Numbers

To add or subtract rational numbers, we first look at their denominators. If the denominators are the same, we simply add or subtract the numerators while keeping the denominator unchanged. However, if the denominators are different, we must find their Least Common Multiple (LCM). We then convert each rational number into an equivalent rational number with this LCM as the common denominator. Once the denominators are equalized, we carry out the integer addition or subtraction in the numerator. Remember to pay close attention to negative signs; subtracting a negative rational number is the same as adding its positive counterpart.

Steps to Multiply and Divide Rational Numbers

1. Multiplication of Rational Numbers — Multiply the numerator of the first rational number by the numerator of the second. Then, multiply the denominator of the first by the denominator of the second. Express the final product in its simplest form.
2. Division of Rational Numbers — To divide one rational number by another, multiply the first rational number (dividend) by the reciprocal of the second rational number (divisor). The reciprocal of a/b is b/a.
3. Sign Rule Application — Apply the product and quotient sign rules: multiplying or dividing two numbers of like signs gives a positive result, while unlike signs yield a negative result.

Worked Solutions from Exercise 9.2

• Example 1 (Addition): Find the sum of 5/4 and (-11/4). Since the denominators are both 4, we write: [5 + (-11)] / 4 = -6/4. Simplifying this by dividing both numerator and denominator by 2 gives -3/2.
• Example 2 (Subtraction): Find the value of 5/63 - (-6/21). First, rewrite the subtraction: 5/63 + 6/21. The LCM of 63 and 21 is 63. Convert 6/21 to 18/63. Now, add: (5 + 18)/63 = 23/63.

Avoid Common Mistakes with Negatives

A very common error in Class 7 rational numbers ex 9 2 is handling signs in denominators. If you have a rational number like 3/-5, always standardise it to -3/5 before doing any addition or subtraction. Also, remember that dividing by a rational number is not the same as dividing by its numerator; you must multiply by the complete reciprocal of the divisor.

Practice Questions with Solutions

• Q: Find the sum: 7/24 + (-17/36) A: Step 1: Find the LCM of the denominators 24 and 36. The LCM of 24 and 36 is 72. Step 2: Convert both rational numbers to have denominator 72. 7/24 = (7 3) / (24 3) = 21/72 -17/36 = (-17 2) / (36 2) = -34/72 Step 3: Add the numerators: [21 + (-34)] / 72 = -13/72 Final answer: -13/72
• Q: Find the value of: -6/13 - (-7/15) A: Step 1: Rewrite subtraction of a negative rational as addition: -6/13 + 7/15 Step 2: Find LCM of 13 and 15, which is 195. Step 3: Convert to equivalent fractions: -6/13 = (-6 15) / 195 = -90/195 7/15 = (7 13) / 195 = 91/195 Step 4: Perform addition: (-90 + 91) / 195 = 1/195 Final answer: 1/195
• Q: Find the product: (3/-10) (-9) A: Step 1: Standardise 3/-10 as -3/10 and write -9 as -9/1. Step 2: Multiply the numerators together and denominators together: Numerator = -3 -9 = 27 Denominator = 10 * 1 = 10 Step 3: Combine them: 27/10. Final answer: 27/10 (or 2.7)
• Q: Find the value of: (-4/5) / (-3) A: Step 1: Write -3 as a rational number: -3/1. Step 2: Take the reciprocal of the divisor -3/1, which is -1/3. Step 3: Multiply the first rational number by this reciprocal: (-4/5) (-1/3) = (-4 -1) / (5 * 3) = 4/15 Final answer: 4/15

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