RD Sharma Class 7 Solutions Chapter 4 Exercise 4.4
FAQs on RD Sharma Class 7 Solutions Chapter 4 - Rational Numbers (Ex 4.4) Exercise 4.4
1. What is the correct step-by-step method to multiply two rational numbers, as required in RD Sharma Solutions for Exercise 4.4?
To multiply two rational numbers, such as (a/b) and (c/d), you should follow this simple procedure:
- Step 1: Multiply the numerators of the two rational numbers (a × c).
- Step 2: Multiply the denominators of the two rational numbers (b × d).
- Step 3: Write the result as a new fraction: (a × c) / (b × d).
- Step 4: Simplify the resulting fraction to its standard form by dividing the numerator and denominator by their greatest common divisor (GCD).
2. What is the standard form of a rational number and why is it important for the final answer?
The standard form of a rational number requires two conditions to be met:
1. The denominator must be a positive integer.
2. The numerator and the denominator must be co-prime, meaning their only common factor is 1.
It is crucial to express the final answer in standard form because it provides a unique and simplified representation of the value, which is essential for accurate marking as per CBSE guidelines for the 2025-26 session.
3. How is the concept of a multiplicative inverse (or reciprocal) used in Chapter 4, Rational Numbers?
The multiplicative inverse, or reciprocal, of a non-zero rational number p/q is q/p. Its main property is that when a number is multiplied by its reciprocal, the result is always 1. For example, the reciprocal of 5/7 is 7/5, and (5/7) × (7/5) = 1. While this concept is foundational in Exercise 4.4, it becomes critically important when solving division problems, as dividing by a rational number is the same as multiplying by its reciprocal.
4. What is a common mistake students make when multiplying rational numbers with different signs?
A very common mistake is incorrectly determining the sign of the final product. Students should remember these rules:
- Multiplying a positive rational number by a negative one results in a negative product.
- Multiplying two negative rational numbers results in a positive product.
5. Why is finding a common denominator (LCM) essential for adding rational numbers but not for multiplying them?
Finding a common denominator is necessary for addition and subtraction because these operations require combining or comparing parts of a whole. The fractions must be expressed in terms of the same-sized 'units' (the denominator) before they can be added or subtracted. In contrast, multiplication is about finding a 'fraction of a fraction'. The operation itself does not require the 'units' to be the same size, as you directly multiply the numerators and denominators to find the new part of the new whole.
6. How can you determine if a rational number will result in a terminating or a non-terminating repeating decimal?
To determine this, first, ensure the rational number is in its simplest form. Then, examine the prime factors of its denominator.
- If the prime factorisation of the denominator contains only powers of 2, powers of 5, or both, the decimal will be terminating.
- If the denominator has any other prime factor (such as 3, 7, 11, etc.), the decimal will be non-terminating and repeating.
7. In what real-world situations would a Class 7 student apply the concept of rational numbers?
Rational numbers are used constantly in daily life. Some common applications include:
- Recipes and Cooking: Adjusting a recipe by using 1/2 or 3/4 of the ingredients.
- Finance: Calculating discounts (e.g., a 1/3 off sale), interest rates, or splitting a bill among friends.
- Measurements: Using fractions of an inch, a kilometre, or a kilogram in crafts, construction, or shopping.
- Time: Describing time, such as a quarter (1/4) of an hour or half (1/2) an hour.
