RBSE Solutions Class 6 Maths Chapter 12 Algebra Exercise 12.1

Algebra Ex 12.1

Question 1. Make the matchstick pattern of the letters given below. Draw the figures of the patterns in your note book. Create rules to find out number of matchsticks required for each pattern. (You can use literals like a, b, x, y e.t.c. to create rules).
(i) T pattern of T, T, TT
(ii) N pattern of N, N, NN,
(iii) W pattern of W, W, WW,
Answer:
(i) Pattern of T
For the letter 'T', two matchsticks are needed to form one pattern. If we need to make 'n' patterns of 'T', the total number of matchsticks required will be given by the rule: \( 2 \times n = 2n \). For example, for two 'T' patterns, \( 2 \times 2 = 4 \) matchsticks are needed.
(ii) Pattern of N
For the letter 'N', three matchsticks are needed to form one pattern. If we need to make 'n' patterns of 'N', the total number of matchsticks required will be given by the rule: \( n \times 3 = 3n \). This pattern uses diagonal matchsticks to connect the vertical ones.
(iii) Pattern of W
For the letter 'W', four matchsticks are needed to form one pattern. If we need to make 'n' patterns of 'W', the total number of matchsticks required will be given by the rule: \( n \times 4 = 4n \). The 'W' shape is formed by two 'V' shapes joined together.
In simple words: First, count how many matchsticks are needed for just one letter shape (like T, N, W). Then, to find the total matchsticks for 'n' of those shapes, multiply that number by 'n'.

🎯 Exam Tip: When forming patterns with matchsticks, always start by clearly counting the number of sticks for a single unit of the pattern. This base number is crucial for creating the correct algebraic rule.

Question 2. Tree plantation program was held in a school. 4 Trees were planted in each row. Write the number of trees planted in terms of the number of rows.
Answer: In this tree plantation program, 4 trees were planted in every single row. Let \( x \) represent the total number of rows where trees were planted. To find the total number of trees, we multiply the number of trees in one row by the total number of rows. So, the total number of trees planted will be \( 4 \times x = 4x \). This algebraic expression helps us calculate trees for any number of rows.
In simple words: If 4 trees are in each row and there are 'x' rows, you just multiply 4 by 'x' to find all the trees.

🎯 Exam Tip: Always clearly define what your variable (like 'x' or 'n') stands for in your answer to avoid confusion and make your algebraic expression meaningful.

Question 3. Ranu is 5 years younger than Leela.
(i) Let Leela's age be years. Write the age of Ranu in terms of
(ii) Let Ranu's age of be P years. Write the age of Leela in terms of P.
Answer:
(i) If Leela's age is \( x \) years, and Ranu is 5 years younger than Leela, then Ranu's age can be written as \( (x - 5) \) years. This shows how Ranu's age relates to Leela's age with a simple subtraction.
(ii) If Ranu's age is \( P \) years, and Leela is 5 years older than Ranu (since Ranu is younger), then Leela's age can be written as \( (P + 5) \) years. This expresses Leela's age in terms of Ranu's age.
In simple words: If someone is younger, you subtract from the older person's age. If someone is older, you add to the younger person's age.

🎯 Exam Tip: Pay close attention to keywords like "younger than" (means subtract) and "older than" (means add) when forming algebraic expressions for age problems.

Question 4. Cost of a Pen is Rs.5 Madan has some money with him. He pays all of that money to buy those pens. Write the number of pens purchased in terms of the money he had.
Answer: The cost of one pen is Rs. 5. Let's say Madan has \( x \) rupees in total. He spends all his money to buy pens. If \( n \) is the number of pens Madan bought, then the total money spent must be equal to the cost of one pen multiplied by the number of pens. So, we can write this as \( x = 5 \times n \).
\( \implies \) To find the number of pens \( n \), we divide the total money \( x \) by the cost of one pen, which is Rs. 5.
\( \implies n = \frac{x}{5} \). This formula helps determine how many pens can be bought with any amount of money.
In simple words: To find out how many pens Madan bought, divide the total money he had by the price of one pen.

🎯 Exam Tip: When dealing with cost and quantity problems, remember that the total cost is always the unit price multiplied by the quantity. To find the quantity, you'll usually divide the total cost by the unit price.