DEMO
Look around freely · sample student, nothing is saved
Get the app
04
x
2
+y
NCERT Solutions · Maths Ch 4
Expressions using Letter-Numbers
33 questions · 4 exercises
Closed
Open all
Ex 4.1
Ex 4.2
Ex 4.3
Ex 4.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 4.1 · 8 QUESTIONS
Expressions with Letter-Numbers
Q1
Ketaki buys coconuts at ₹35 each and jaggery at ₹60 per kg. How much should she pay if she buys 8 coconuts and 9 kg jaggery?
(3 marks)
Q2
Write formulas for the perimeter of: (a) a triangle with all sides equal (b) a regular pentagon (c) a regular hexagon
(3 marks)
Q3
Munirathna has a 20 m long pipe. He joins another pipe of some length to it. Give the expression for the combined length of the pipe. Use 'k' to denote the length in metres of the other pipe.
(1 mark)
Q4
What is the total amount Krithika has if she has the following numbers of ₹100, ₹20 and ₹5 notes? (i) 3, 5, 6 (ii) 6, 4, 3 (iii) 8, 4, z (iv) x, y, z
(3 marks)
Q5
Venkatalakshmi's roller mill takes 10 seconds to start. Once running, each kg of grain takes 8 seconds to grind. Which expression describes the time taken to grind 'y' kg of grain, assuming the machine is off initially? (a) 10 + 8 + y (b) (10 + 8) × y (c) 10 × 8 × y (d) 10 + 8 × y (e) 10 × y + 8
(2 marks)
Q6
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 less than 2 times a number
(3 marks)
Q7
Describe situations corresponding to the following algebraic expressions: (a) 8 × x + 3 × y (b) 15 × j − 2 × k
(2 marks)
Q8
In a calendar month, any 2 × 3 grid full of dates is chosen. Write expressions for the dates in the blank cells if the bottom middle cell has date 'w' (bottom row: w − 1, w, ___; top row: three blank cells).
(2 marks)
2
EXERCISE 4.2 · 7 QUESTIONS
Simplification of Algebraic Expressions
Q9
The price per pencil is c. A shop sold 5, 3 and 10 pencils on three days. If c = ₹50, find the total amount earned by the sale of pencils.
(2 marks)
Q10
Fill in the diagrams by replacing the letter-numbers by numbers and compare the values of 5u and 5 + u. Also compare 10y − 3 and 10(y − 3).
(3 marks)
Q11
Add the numbers in each picture below. Write the corresponding expressions and simplify them: (i) a picture with 5y, x, x, 5y, −6, 2 (ii) a picture with 2p and 3q appearing four times each, and 3, −2, −2, 3 (iii) a picture with −5g four times and 5k twelve times
(3 marks)
Q12
Simplify each of the following expressions: (a) p + p + p + p; p + p + p + q; p + q + p − q (b) p − q + p − q; p + q − p + q (c) p + q − (p + q); p − q − p − q (d) 2d − d − d − d; 2d − d − d − c (e) 2d − d − (d − c); 2d − (d − d) − c (f) 2d − d − c − c
(5 marks)
Q13
Some simplifications of algebraic expressions are given. Find the mistake, if any, and give the correct simplest form: (1) 3a + 2b → 5 (2) 3b − 2b − b → 0 (3) 6(p + 2) → 6p + 8 (4) (4x + 3y) − (3x + 4y) → x + 5 (5) 5 − (2 − 6z) → 3 − 6z (6) 2 + (x + 3) → 2x − 6 (7) 2y + (3y − 6) → −y + 6 (8) 7p − p + 5q − 2q → 7p + 3q (9) 5(2w + 3x + 4w) → 10w + 15x + 20w (10) 3j + 6k + 9h + 12 → 3(j + 2k + 3h + 4) (11) 4(2r + 3s + 5) → −20 − 8r − 12s
(5 marks)
Q14
Take a look at all the corrected simplest forms. Is there any relation between the number of terms and the number of letter-numbers in these expressions?
(3 marks)
Q15
Find the formulas of the number machines below and write the expression for each set of inputs. (i) Machine with inputs (5, 2) → 5, (8, 1) → 7, … (ii) Machine with inputs (4, 1) → 5, (6, 0)?, … Also generalise with letters a and b.
(3 marks)
3
EXERCISE 4.3 · 3 QUESTIONS
Patterns and Formulas
Q16
A repeating pattern on a saree border has designs A, B, C in order (A at position 1, B at 2, C at 3, then again A at 4, …). Use the positions to find which design appears at positions 99, 122 and 148.
(3 marks)
Q17
Consider the numbers from a calendar forming a plus shape: one number above the centre, one below, one to the left and one to the right. The sum is always 5 times the centre. Will this always happen? How do you show this?
(3 marks)
Q18
Matchstick pattern: Step 1 has 1 horizontal and 2 diagonal sticks, and each step adds 1 more of each. What are the numbers in Step 3 and Step 4? How does the number change in each orientation? Write an expression for the number of matchsticks at Step 'y' in each orientation. Do the two expressions add up to 2y + 1?
(3 marks)
4
15 QUESTIONS
Exercise 4.4
Q19
One plate of Jowar roti costs ₹30 and one plate of Pulao costs ₹20. If x plates of Jowar roti and y plates of pulao were ordered in a day, which expression(s) describe the total amount in rupees earned that day? (a) 30x + 20y (b) (30 + 20) × (x + y) (c) 20x + 30y (d) (30 + 20) × x + y (e) 30x − 20y
(3 marks)
Q20
Pushpita sells champak and marigold flowers. 'p' customers bought only champak, 'q' customers bought only marigold and 'r' customers bought both. She gave a tiny flag to every customer. How many flags did she give away? (a) p + q + r (b) p + q + 2r (c) 2 × (p + q + r) (d) p + q + r + 2 (e) p + q + r + 1 (f) 2 × (p + q)
(2 marks)
Q21
A snail climbs 'u' cm during the day and slips down 'd' cm during the night. This happens for 10 days and 10 nights. (a) Write an expression describing how far the snail is from its starting position. (b) What can we say about the snail's movement if d > u?
(2 marks)
Q22
Radha cycles 5 km every day in the first week. Every week she increases the daily distance by 'z' km. How many kilometres would Radha have cycled after 3 weeks?
(3 marks)
Q23
In the figure, the expression w + 2 becomes 4w + 20 along one path. Fill in the missing blanks on the remaining paths. (Paths from w + 2: [−5] → (w − 3) → [×3] → ( ); [+3] → (w + 5) → [×4] → (4w + 20); [−8] → ( ) → [−4] → ( ); [−4] → ( ) → [×3] → (3w − 6).)
(3 marks)
Q24
A local train from Yahapur to Vahapur stops at three stations at equal distances along the way. The time to travel from one station to the next is t minutes. The train stops for 2 minutes at each of the three stations. (a) If t = 4, what is the time taken to travel from Yahapur to Vahapur? (b) What is the algebraic expression for the time taken?
(2 marks)
Q25
Simplify the following expressions: (a) 3a + 9b − 6 + 8a − 4b − 7a + 16 (b) 3(3a − 3b) − 8a − 4b − 16 (c) 2(2x − 3) + 8x + 12 (d) 8x − (2x − 3) + 12 (e) 8h − (5 + 7h) + 9 (f) 23 + 4(6m − 3n) − 8n − 3m − 18
(3 marks)
Q26
Add the expressions given below: (a) 4d − 7c + 9 and 8c − 11 + 9d (b) −6f + 19 − 8s and −23 + 13f + 12s (c) 8d − 14c + 9 and 16c − (11 + 9d) (d) 6f − 20 + 8s and 23 − 13f − 12s (e) 13m − 12n and 12n − 13m (f) −26m + 24n and 26m − 24n
(5 marks)
Q27
Subtract the expressions: (a) 9a − 6b + 14 from 6a + 9b − 18 (b) −15x + 13 − 9y from 7y − 10 + 3x (c) 17g + 9 − 7h from 11 − 10g + 3h (d) 9a − 6b + 14 from 6a − (9b + 18) (e) 10x + 2 + 10y from −3y + 8 − 3x (f) 8g + 4h − 10 from 7h − 8g + 20
(5 marks)
Q28
Describe situations corresponding to the following algebraic expressions: (a) 8x + 3y (b) 15x − 2x
(2 marks)
Q29
If a straight rope is cut once we get 2 pieces. If the rope is folded once and then cut, we get 3 pieces. Observe the pattern and find the number of pieces if the rope is folded 10 times and cut. What is the expression for the number of pieces when the rope is folded r times and cut?
(2 marks)
Q30
Matchstick pattern of squares in a row (1 square needs 4 sticks; each extra square needs 3 more sticks). How many matchsticks are required to make 10 such squares? How many are required to make w squares?
(3 marks)
Q31
In a traffic signal the colours change in the order Red, Yellow, Green, Yellow, Red, … Find the colour at positions 90, 190 and 343. Write expressions to describe the positions for each colour.
(3 marks)
Q32
In the pattern of squares, find the number of squares in Step 4, Step 10 and Step 50, and give a general formula. How would the formula change to count the vertices of all the squares?
(3 marks)
Q33
Numbers are written in order in an endless 4-column grid (row 1: 1, 2, 3, 4; row 2: 5, 6, 7, 8; …). (a) Give expressions to generate the numbers in each column. (b) In which row and column will (i) 124 (ii) 147 (iii) 201 appear? (c) What number appears in row r and column c? (d) Observe the columns of multiples of 3.
(5 marks)