Question 1

Q1: Write formulas for the perimeter of: (a) triangle with all sides equal. (b) a regular pentagon (as we have learnt last year, we use the word 'regular'...

Accepted Answer

To Find: Formulas for the perimeter of given regular polygons. Let: The length of one side of the regular polygon be denoted by the letter-number '$s$'. (a) Triangle with all sides equal (Equilateral Triangle): An equilateral triangle has 3 equal sides. Perimeter = Sum of all sides $$P = s + s + s =...

Question 2

Q2: Munirathna has a 20 m long pipe. However, he wants a longer watering pipe for his garden. He joins another pipe of some length to this one. Give the e...

Accepted Answer

Given: Length of the first pipe = 20 m Length of the second pipe = $k$ m To Find: An expression for the combined length of the pipe. Solution: The combined length is the sum of the lengths of the two pipes. Combined length = (Length of first pipe) + (Length of second pipe) Expression = $20 + k$ Fina...

Question 3

Q3: What is the total amount Krithika has, if she has the following numbers of notes of ₹100, ₹20 and ₹5? Complete the following table: | No. of ₹100 note...

Accepted Answer

To Find: Complete the given table by finding the expression and total amount for each row. Solution: Row 1: - No. of ₹100 notes = 3 - No. of ₹20 notes = 5 - No. of ₹5 notes = 6 Expression: $(3 	imes 100) + (5 	imes 20) + (6 	imes 5)$ Total amount = $300 + 100 + 30 = 	ext{₹}430$ Row 2: The expres...

Question 4

Q4: Venkatalakshmi owns a flour mill. It takes 10 seconds for the roller mill to start running. Once it is running, each kg of grain takes 8 seconds to gr...

Accepted Answer

Given: Fixed start-up time for the mill = 10 seconds Time to grind 1 kg of grain = 8 seconds Amount of grain to grind = $y$ kg To Find: The expression for the total time taken. Solution: The total time is the sum of the fixed start-up time and the variable grinding time. 1.  Fixed Time: The machine...

Question 5

Q5: Write algebraic expressions using letters of your choice. (a) 5 more than a number (b) 4 less than a number (c) 2 less than 13 times a number (d) 13 l...

Accepted Answer

Let: The number be represented by the letter-number '$x$'. (a) 5 more than a number This means we add 5 to the number. Expression: $x + 5$ (b) 4 less than a number This means we subtract 4 from the number. Expression: $x - 4$ (c) 2 less than 13 times a number First, find '13 times a number': $13 	i...

Question 6

Q6: Describe situations corresponding to the following algebraic expressions: (a) $8 	imes x+3 	imes y$ (b) $15 	imes j-2 	imes k$

Accepted Answer

(a) Situation for $8 	imes x+3 	imes y$ (or $8x + 3y$) This expression represents a total value calculated from two different items with different quantities and prices. Example Situation: A person buys $x$ notebooks costing ₹8 each and $y$ pens costing ₹3 each. The total amount of money spent is...

Question 7

Q7: In a calendar month, if any $2 	imes 3$ grid full of dates is chosen as shown in the picture, write expressions for the dates in the blank cells if t...

Accepted Answer

Given: A $2 	imes 3$ grid of dates from a calendar. The date in the bottom middle cell is '$w$'. To Find: Expressions for the dates in the blank cells. Understanding a Calendar Grid: - A date in a cell to the right is 1 more than the date to its left. - A date in a cell below is 7 more than the dat...

Question 8

Q1: If a=3, then 3a = 33.

Accepted Answer

Mistake Identification: The expression 3a was interpreted as concatenating the digit '3' with the value of 'a' (which is 3) to form the number 33. Explanation of Error: The notation 3a in algebra means '3 multiplied by a' or 3 	imes a. Correction: Given $a=3$. $$3a = 3 	imes a$$  $$= 3 	imes 3$$...

Question 9

Q2: If b=4, then 5b+2 = 56.

Accepted Answer

Mistake Identification: The expression 5b was interpreted as concatenating the digit '5' with the value of 'b' (which is 4) to form the number 54. Then 2 was added: $54+2=56$. Explanation of Error: The notation 5b means '5 multiplied by b' or 5 	imes b. Correction: Given $b=4$. $$5b+2 = (5 	imes b...

Question 10

Q3: If c=5, then c-5 = 5.

Accepted Answer

Mistake Identification: A simple subtraction error was made. $5-5$ was incorrectly calculated as 5. Explanation of Error: Subtracting a number from itself results in 0. Correction: Given $c=5$. $$c-5 = 5 - 5$$  $$= 0$$ Correct Value: 0

Question 11

Q4: If d=2, e=3, then d+e = 23.

Accepted Answer

Mistake Identification: The expression d+e was evaluated by concatenating the values of d (2) and e (3) to form the number 23, instead of performing addition. Explanation of Error: The '+' symbol represents the operation of addition. Correction: Given $d=2$ and $e=3$. $$d+e = 2 + 3$$  $$= 5$$ Correc...

Question 12

Q5: If x=6, y=2, then x-y = 62.

Accepted Answer

Mistake Identification: The expression x-y was evaluated by concatenating the values of x (6) and y (2) to form the number 62, instead of performing subtraction. Explanation of Error: The '-' symbol represents the operation of subtraction. Correction: Given $x=6$ and $y=2$. $$x-y = 6 - 2$$  $$= 4$$...

Question 13

Q6: If k=3, m=4, then km = 34.

Accepted Answer

Mistake Identification: The expression km was interpreted as concatenating the values of k (3) and m (4) to form the number 34. Explanation of Error: When two letter-numbers are written together like km, it implies multiplication: k 	imes m. Correction: Given $k=3$ and $m=4$. $$km = k 	imes m$$  $...

Question 14

Q1: $23-10 	imes 2$

Accepted Answer

To Find: The value of the expression $23-10 	imes 2$. Solution: According to the order of operations (BODMAS/PEMDAS), multiplication is performed before subtraction. First, calculate the multiplication part: $$10 	imes 2 = 20$$ Now, perform the subtraction: $$23 - 20 = 3$$ Final Answer: The value...

Question 15

Q2: $83+28-13+32$

Accepted Answer

To Find: The value of the expression $83+28-13+32$. Solution: We can rearrange the terms to make the calculation easier (using commutative and associative properties of addition). Group the numbers that are easy to add or subtract. $$83+28-13+32 = (83 - 13) + (28 + 32)$$ First, calculate the values...

Question 16

Q3: $34-14+20$

Accepted Answer

To Find: The value of the expression $34-14+20$. Solution: Performing the operations from left to right: First, perform the subtraction: $$34 - 14 = 20$$ Now, perform the addition: $$20 + 20 = 40$$ Final Answer: The value of the expression is 40.

Question 17

Q4: $42+15-(8-7)$

Accepted Answer

To Find: The value of the expression $42+15-(8-7)$. Solution: According to the order of operations, we solve the expression inside the brackets first. $$(8-7) = 1$$ Now the expression becomes: $$42 + 15 - 1$$ Performing the operations from left to right: $$42 + 15 = 57$$ $$57 - 1 = 56$$ Final Answer...

Question 18

Q5: $68-(18+13)$

Accepted Answer

To Find: The value of the expression $68-(18+13)$. Solution: According to the order of operations, we solve the expression inside the brackets first. $$(18+13) = 31$$ Now the expression becomes: $$68 - 31$$ Performing the subtraction: $$68 - 31 = 37$$ Final Answer: The value of the expression is 37.

Question 19

Q6: $7 	imes 4+9 	imes 6$

Accepted Answer

To Find: The value of the expression $7 	imes 4+9 	imes 6$. Solution: According to the order of operations, multiplication is performed before addition. First, calculate the multiplication parts: $$7 	imes 4 = 28$$ $$9 	imes 6 = 54$$ Now, perform the addition: $$28 + 54 = 82$$ Final Answer: The...

Question 20

Q7: $20+8 	imes (16-6)$

Accepted Answer

To Find: The value of the expression $20+8 	imes (16-6)$. Solution: According to the order of operations, we solve the expression inside the brackets first. $$(16 - 6) = 10$$ Now the expression becomes: $$20 + 8 	imes 10$$ Next, perform the multiplication before addition: $$8 	imes 10 = 80$$ Fina...

No. of ₹100 notes	No. of ₹20 notes	No. of ₹5 notes	Expression and total amount
3	5	6
			$\begin{gathered} 6 \times 100+4 \times 20+3 \times 5 \ =695 \end{gathered}$
8	4	Z
X	y	Z

NCERT Solutions