RBSE Solutions Class 6 Maths Chapter 12 Algebra Exercise 12.2

Question 1. With the numbers 3, 7 and 4, form arithmetic expressions using
(i) Only addition and subtraction operations.
(ii) Only multiplication and addition operations.
Answer:
(i) Using only addition and subtraction operations:
\( 3 + 7 + 4 \)
\( 3 - 7 + 4 \)
\( 3 + 7 - 4 \)
\( - 3 + 7 + 4 \)
\( - 3 + 7 - 4 \)
\( - 3 - 7 + 4 \)
\( - 3 - 7 - 4 \)
(ii) Using only multiplication and addition operations:
\( 3 \times 7 + 4 \)
\( 3 \times 7 \times 4 \)
\( 3 + 7 \times 4 \)
\( 3 + 4 \times 7 \)
\( 3 \times 4 + 7 \) When forming expressions, consider different orders and placements of numbers and operations to create unique combinations.
In simple words: For part (i), we can combine 3, 7, and 4 using plus and minus signs in many ways. For part (ii), we use multiply and plus signs in different orders.

🎯 Exam Tip: Remember to explore all possible combinations and permutations of numbers and operations to ensure no valid expression is missed. Order matters for subtraction and multiplication.

Question 2. For each of the below expressions, mention whether it is an arithmetic expression or algebraic expression?
(i) \( (3x + 5) \)
(ii) \( 5 \times 4 + 7 \)
(iii) \( 3 + 4 \times 3 + 5 \)
(iv) \( 2x + 1 \)
(v) \( \frac {x}{2}+5-x \)
(vi) \( 3x \)
Answer:
(i) \( (3x + 5) \) is an algebraic expression because it contains a variable \( x \).
(ii) \( 5 \times 4 + 7 \) is an arithmetic expression because it contains only numbers and arithmetic operations.
(iii) \( 3 + 4 \times 3 + 5 \) is an arithmetic expression because it contains only numbers and arithmetic operations.
(iv) \( 2x + 1 \) is an algebraic expression because it contains a variable \( x \).
(v) \( \frac {x}{2}+5-x \) is an algebraic expression because it contains a variable \( x \).
(vi) \( 3x \) is an algebraic expression because it contains a variable \( x \). An expression is algebraic if it involves variables, otherwise it's arithmetic.
In simple words: If an expression has letters (like 'x' or 'y') mixed with numbers, it's called an algebraic expression. If it only has numbers, it's an arithmetic expression.

🎯 Exam Tip: The key difference between arithmetic and algebraic expressions is the presence of variables (letters representing unknown values) in algebraic expressions. If no variables are present, it's arithmetic.

Question 3. Observe the expressions in the table carefully. Mention, what all operations are used to form that expression by putting the sign of right/wrong in the table.
Answer:

The table shows which mathematical operations (addition, subtraction, multiplication, division) are used in each given expression. Each checkmark means the operation is present, while an 'x' means it's not. For example, in \( 7m + 3 \), both multiplication (between 7 and m) and addition are used.
In simple words: This table tells us what kind of math is happening in each expression. A check mark means that math operation is being used, and an 'x' means it is not.
🎯 Exam Tip: Carefully examine each expression to identify all operations present. Remember that terms like \( 7m \) imply multiplication, and fractions like \( \frac{y}{17} \) imply division.

Question 4. Write algebraic expression for the following situations:
(i) 7 added to a
(ii) 10 subtracted from b
(iii) y multiplied by 4
(iv) x divided by 4
(v) x subtracted from 7
(vi) 10 divided by q
Answer:

These expressions translate common English phrases into mathematical notation using variables and operations. For instance, "7 added to a" means `a + 7`, while "x subtracted from 7" means `7 - x`.
In simple words: We write these word problems as math sentences. We use letters for unknown numbers and symbols like +,-,×,÷.
🎯 Exam Tip: Pay close attention to the order of operations, especially for subtraction and division. "A subtracted from B" is \( B - A \), not \( A - B \).

Question 5. Give expressions for the following cases:
(i) 15 added to 2n
(ii) 15 subtracted from 2x
(iii) 3 added to twice of p
(iv) 3 subtracted from twice of q
(v) 11 subtracted from the product of y and 5
(vi) 11 added to the product of z and - 3
Answer:

Translating word descriptions into algebraic expressions requires careful attention to the order of operations and the meaning of terms like "twice" or "product". For example, "twice of p" means \( 2 \times p \), or \( 2p \).
In simple words: We turn these sentences into math problems. "Added to" means plus, "subtracted from" means minus, "product" means multiply, and "twice" means multiply by two.
🎯 Exam Tip: Be careful with phrases like "subtracted from". The number *being subtracted* comes second in the expression. For example, "A subtracted from B" is written as \( B - A \).

Question 6. Form algebraic expressions using q, 5 and – 3.
Answer:
(i) \( q + 5 - 3 \)
(ii) \( q - 5 - 3 \) We can combine the numbers 5 and -3 with the variable q using different arithmetic operations to form various expressions. For instance, \( q + (5) + (-3) \) can be simplified to \( q + 2 \), and \( q - (5) - (-3) \) simplifies to \( q - 2 \).
In simple words: We can make math sentences using the letter 'q' and the numbers 5 and -3. We can add or subtract them in different orders.

🎯 Exam Tip: When forming expressions with multiple numbers, remember that the order of operations (like addition and subtraction) can change the outcome, so explore various arrangements.

Question 7. Nathu has Rs. x with him Then,
(i) How much money do Bina have if she owns twice as much as Nathu does?
(ii) How much money is Nathu left with after buying books worth Rs. 150?
(iii) How much money do Seema have if she owns half as much as Nathu has initially?
(iv) How much money do Milli have if she owns thrice as much as Nathu does?
Answer:
(i) Nathu has Rs. \( x \). Bina has twice as much as Nathu.
\( \implies \) Bina's money = \( 2 \times x = \text{Rs. } 2x \)
(ii) Nathu bought books worth Rs. 150.
\( \implies \) Money remaining with Nathu = \( \text{Rs. } (x - 150) \)
(iii) Nathu initially had Rs. \( x \). Seema has half as much as Nathu.
\( \implies \) Seema's money = \( \frac { x }{ 2 } \text{ Rs.} \)
(iv) Nathu has Rs. \( x \). Milli has thrice as much as Nathu.
\( \implies \) Milli's money = \( 3 \times x = \text{Rs. } 3x \) Using variables like 'x' helps us represent unknown amounts and easily perform calculations based on given conditions.
In simple words: If Nathu has Rs. 'x', then Bina has double that (2x), Nathu has 'x - 150' left after buying books, Seema has half of 'x' (x/2), and Milli has three times 'x' (3x).

🎯 Exam Tip: Carefully read keywords like "twice," "half," "thrice," and "subtracted from" to correctly translate them into mathematical operations and build the expressions.

Question 8. The height of a triangle is 5 more than twice of its base. What is its height if base is b?
Answer:
Given base of triangle = \( b \) unit.
Height of triangle is 5 more than twice of base.
\( \implies \) Height = \( 2 \times b + 5 \)
\( \implies \) Height = \( (2b + 5) \) unit. This algebraic expression lets us find the height for any given base 'b'.
In simple words: If the base of a triangle is 'b', its height is found by multiplying the base by 2, and then adding 5 to that result.

🎯 Exam Tip: Break down word problems into smaller parts. "Twice of its base" translates to \( 2b \), and "5 more than" means adding 5 to that result.

Question. Age of Vimal's mother is 5 years less than twice of Vimal's age. How old is his mother?
Answer:
Let Vimal's present age be \( P \) years.
(i) His age 10 years ago = \( (P - 10) \) years.
(ii) Vimal's age after 5 years from now = \( (P + 5) \) years.
(iii) Vimal's aunt's age = \( 3 \times P = 3P \) years.
(iv) Vimal's mother's age = 5 years less than twice of Vimal's age
\( \implies \) Vimal's mother's age = \( 2 \times P - 5 = (2P - 5) \) years. We use 'P' to represent Vimal's current age, and then create expressions for his age at different points in time or the ages of his relatives based on the given conditions.
In simple words: If Vimal's age is 'P', then his age 10 years ago was \( P-10 \), in 5 years it will be \( P+5 \), his aunt is \( 3P \) years old, and his mother is \( (2P-5) \) years old.

🎯 Exam Tip: Define a variable for the unknown quantity (like Vimal's present age) first. Then, translate each piece of information into a mathematical expression based on that variable.