RD Sharma Class 8 Solutions Chapter 6 - Algebraic Expressions and Identities (Ex 6.1) Exercise 6.1 - Free PDF
FAQs on RD Sharma Class 8 Solutions Chapter 6 - Algebraic Expressions and Identities (Ex 6.1) Exercise 6.1
1. What is the correct method to solve addition problems in RD Sharma Class 8 Maths Exercise 6.1?
To solve addition problems for algebraic expressions as per the method used in RD Sharma solutions, you should follow these steps:
- First, arrange the expressions by writing the like terms one below the other in columns.
- Next, add the numerical coefficients of the terms in each column.
- Finally, write the sum below the respective column, followed by the common variable part. This systematic approach ensures accuracy for all problems in Exercise 6.1.
2. How do you identify the terms and coefficients of an algebraic expression in this chapter?
In any algebraic expression, the parts that are separated by addition (+) or subtraction (-) signs are called terms. The numerical factor of a term is called its coefficient. For example, in the expression 7xy - 5x² + 3, the terms are 7xy, -5x², and 3. The coefficient of the term 7xy is 7, and the coefficient of -5x² is -5.
3. What is a common mistake students make when subtracting algebraic expressions and how can it be avoided?
A frequent error is forgetting to change the sign of every term in the expression being subtracted. Students often only change the sign of the first term. To avoid this, always place the expression to be subtracted inside brackets. When you remove the brackets, distribute the negative sign to each term inside, effectively changing all their signs before you proceed with addition.
4. Why is it essential to group 'like terms' before adding or subtracting expressions?
Grouping like terms is essential because algebraic addition and subtraction are based on the principle of combining similar objects. Just as you can add 5 apples and 3 apples to get 8 apples, you can add 5x and 3x to get 8x. However, you cannot combine 5x (apples) and 3y (oranges). Grouping like terms ensures that you are only combining terms that have the exact same variable parts, which is the fundamental rule for simplifying expressions.
5. How does the concept of adding and subtracting expressions in Exercise 6.1 apply in a real-world scenario?
The skills from Exercise 6.1 are foundational for solving practical problems. For example, if you know the cost of a pen is 'p' and a notebook is 'n', your first purchase might be represented by the expression 3p + 2n. If you later buy 2 more pens and 1 more notebook, that's 2p + n. To find your total expenditure, you would add these two expressions: (3p + 2n) + (2p + n) = 5p + 3n. This shows how combining expressions helps in managing quantities and costs.
6. How are the solutions for Exercise 6.1 different for monomials, binomials, and trinomials?
The underlying method for addition and subtraction remains the same regardless of whether you are working with monomials, binomials, or trinomials. The key is always to identify and combine like terms. The only difference is the number of terms you are managing. With binomials (two terms) or trinomials (three terms), you will have more columns of like terms to add or subtract compared to working with simple monomials (one term).
