Expressions using Letter-Numbers - Chapter 4 Class 7 (Ganita Prakash)
Master Expressions using Letter-Numbers - Chapter 4 Class 7 (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
NCERT Solutions
Expressions using Letter-Numbers - Chapter 4 Class 7 (Ganita Prakash) – NCERT Solutions
Each question below opens its complete step-by-step Teachoo solution.
Figure it out - Page 84, 85
9 questionsQuestion 1 (a)
Write formulas for the perimeter of: (a) triangle with all sides equal.Let
Side of equilateral triangle = a
Question 1 (b)
Write formulas for the perimeter of: (b) a regular pentagon (as we have learnt last year, we use the word ‘regular’ to say that all sidelengths and angle measures are equal) We know that
Pentagon has 5 sides
Question 1 (c)
Write formulas for the perimeter of: (c) a regular hexagonWe know that
Hexagon has 6 sides
Question 2
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 expression for the combined length of the pipe. Use the letter-number ‘k’ to denote the length in meters of the other pipe.
View solutionQuestion 3
What is the total amount Krithika has, if she has the following numbers of notes of ₹100, ₹20 and ₹5? Complete the following table:Alright,
Let’s fill in the table
Question 4
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 grind into powder. Which of the expressions below describes the time taken to complete 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 + 8Given that
Time taken to start running = 10 seconds
Time taken to grind 1 kg of grain = 8 seconds
Question 5
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 numberLet the required number = n
View solutionQuestion 6
Describe situations corresponding to the following algebraic expressions: (a) 8 × x + 3 × y (b) 15 × j – 2 × k(a) 8x+3y:
This expression can represent the total cost of two different sets of items. For example, the total cost of buying 'x' pens at ₹8 each and 'y' pencils at ₹3 each.
Question 7
In a calendar month, if any 2 × 3 grid full of dates is chosen as shown in the picture, write expressions for the dates in the blank cells if the bottom middle cell has date ‘w’.For a 2 × 3 grid of dates where the bottom middle cell is 'w', the expressions for the other dates are based on the calendar layout where
a date to the right is 1 more,
to the left is 1 less,
and directly above is 7 less.
Figure it out - Page 93, 94
2 questionsQuestion 1
Add the numbers in each picture below. Write their corresponding expressions and simplify them. Try adding the numbers in each picture in a couple different ways and see that you get the same thing.Okay let’s answer one by one
Image 1
Question 2
(a) Simplify each of the following expressions: (a) p + p + p + p, p + p + p + q, p + q + p – q, Let’s do it one by one
p + p + p + p = 4p
p + p + p + q = 3p + q
p + q + p – q = p + p + q – q = 2p + 0 = 2p
Figure it out - Page 102 to 105
15 questionsQuestion 1
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 – 20yGiven
Cost of one plate Jowar roti = ₹ 30
Cost of one plate pulao. ₹ 20
And,
Number of plates of Jowar roti = x
Number of plates of pulao = y
Now,
Total amount earned
= Number of plates of Jowar roti × Cost of one plate Jowar roti
+ Number of plates of pulao × Cost of one plate pulao
= x × 30 + y × 20
= 30x + 20y
Question 2
Pushpita sells two types of flowers on Independence day: champak and marigold. ‘p’ customers only bought champak, ‘q’ customers only bought marigold, and ‘r’ customers bought both. On the same day, she gave away a tiny national flag to every customer. How many flags did she give away that day? (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)We can do it by an example also
Say 2 customers bought champak, 3 customers bought marigold, 5 customers bought both
Now, every customer got a national flag
Thus, total flags = 2 + 3 + 5
Similarly, Total flags = p + q + r
Thus,
‘p’ customers that bought champak also got a national flag
∴ Number of flags = p
‘a’ customers that bought marigold got a national flag
∴ Number of flags = q
‘r’ customers that bought flowers got a national flag
∴ Number of flags = r
Question 3
(a) A snail is trying to climb along the wall of a deep well. During the day it climbs up ‘u’ cm and during the night it slowly slips down ‘d’ cm. This happens for 10 days and 10 nights (a) Write an expression describing how far away the snail is from its starting positionIn one day and one night, the snail's net movement is
climbing up 'u' cm and
slipping down 'd' cm.
So, the net progress per day-night cycle is (u−d) cm.
Question 4
Radha is preparing for a cycling race and practices daily. The first week she cycles 5 km every day. Every week she increases the daily distance cycled by ‘z’ km. How many kilometers would Radha have cycled after 3 weeks?Now, we do it week wise
View solutionQuestion 5
In the following figure, observe how the expression w + 2 becomes 4w + 20 along one path. Fill in the missing blanks on the remaining paths. The ovals contain expressions and the boxes contain operations.Let’s fill it
Here are the missing expressions in the ovals, based on the operations in the boxes.
Question 6
(b) A local train from Yahapur to Vahapur stops at three stations at equal distances along the way. The time taken in minutes to travel from one station to the next station is the same and is denoted by t. The train stops for 2 minutes at each of the three stations. (b) What is the algebraic expression for the time taken to travel from Yahapur to Vahapur? [Hint: Draw a rough diagram to visualise the situation]We found this out in part (a)
Total journey time = 4t + 6
Question 7
(a) Simplify the following expressions: (a) 3a + 9b – 6 + 8a – 4b – 7a + 16 Now,
3a + 9b – 6 + 8a – 4b – 7a + 16
= (3a + 8a – 7a) + (9b – 4b) + (16 – 6)
= (11a – 7a) + 5b + 10
= 4a + 5b + 10
Question 8
(a) Add the expressions given below: (a) 4d – 7c + 9 and 8c – 11 + 9dNow,
(4d – 7c + 9) + (8c – 11 + 9d)
= 4d – 7c + 9 + 8c – 11 + 9d
= 4d + 9d + 8c – 7c + 9 – 11
= 4d + 9d + 8c – 7c – 11 + 9
= (4d + 9d) + (8c – 7c) – (11 – 9)
= 13d + c – 2
Question 9
(a) Subtract the expressions given below: (a) 9a – 6b + 14 from 6a + 9b – 18 Now, our expression is
(6a + 9b – 18) – (9a – 6b + 14)
= 6a + 9b – 18 – 9a + 6b – 14
= – 9a + 6a + 9b + 6b – 18 – 14
= –(9a – 6a) + (9b + 6b) – (18 + 14)
= – 3a + 15b – 32
Question 10
Describe situations corresponding to the following algebraic expressions: (a) 8x + 3y (b) 15x – 2x8x + 3y:
This expression can describe a situation where two different items are being tallied. For example, it could be the total cost of buying 'x' books at ₹8 each and 'y' pens at ₹3 each.
Question 11
Imagine a straight rope. If it is cut once as shown in the picture, we get 2 pieces. If the rope is folded once and then cut as shown, 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?From images, we note that
When a straight rope (0 folds) is cut once, you get 2 pieces
When the rope is folded once (1) and then cut, you get 3 pieces
When the rope is folded twice (2) and then cut, you get 4 pieces
Question 12
Look at the matchstick pattern below. Observe and identify the pattern. How many matchsticks are required to make 10 such squares. How many are required to make w squares?From image we note that
To make 1 square, you need 4 matchsticks.
To make 2 squares, you add 3 more matchsticks, for a total of 7.
To make 3 squares, you add another 3 matchsticks, for a total of 10.
We observe that the pattern is that you start with 1 matchstick and add 3 matchsticks for every square you want to make.
Question 13
Now, we also have to find expressions for each color
View solutionQuestion 14
Observe the pattern below. How many squares will be there in Step 4, Step 10, Step 50? Write a general formula. How would the formula change if we want to count the number of vertices of all the squares?Number of Squares
Step 1 has 5 squares.
Step 2 has 9 squares.
Step 3 has 13 squares.
Question 15
(a) Numbers are written in a particular sequence in this endless 4-column grid. (a) Give expressions to generate all the numbers in a given column (1, 2, 3, 4).Let’s look at the pattern
Column 1:
Contains numbers 1, 5, 9, ...
The expression is 4n + 1
Why Learn This With Teachoo?
Expressions Using Letter-Numbers is Chapter 4 of NCERT Class 7 Ganita Prakash Part 1. It is the chapter where arithmetic ideas begin to take a clearly algebraic form. Students use letters to represent numbers that may vary or may not yet be known, build expressions from patterns and situations, simplify those expressions and examine the relationships they reveal. Teachoo explains the notation and reasoning in a learner-friendly sequence, with detailed support for the chapter’s Figure it out activities.
What are letter-numbers?
A letter-number is a letter used to stand for a number. The value might be specified later, change from one case to another or remain unknown while a general rule is being expressed. If a pattern has a fixed feature and a changing feature, a letter can represent the changing quantity. This allows one expression to describe every stage of the pattern instead of listing many separate calculations.
The chapter introduces algebraic notation, including omission of the multiplication symbol. A product such as 5 × n is normally written as 5n, and a product of letters may be written by placing them together. This notation is compact, but students must still understand that multiplication is taking place.
Simplification of algebraic expressions involves identifying compatible terms and combining them correctly. A number multiplying a letter forms part of the term, and terms involving different letters or different structures cannot automatically be added as though they were identical. Substitution can be used to check whether two expressions give the same value for selected letter-numbers, but students also learn to justify a relationship generally.
Pick Patterns and Reveal Relationships asks students to observe numerical or geometric patterns and express what remains true. This develops generalisation, one of the central habits of algebra. Mind the Mistake, Mend the Mistake helps learners diagnose incorrect reasoning and repair it, making error analysis part of learning.
The Figure it out sets on pages 84–85, 93–94 and 102–105 combine notation, simplification, pattern recognition and explanation.
Topics covered on Teachoo
Students can study:
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meaning and use of letter-numbers;
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introductory algebraic expressions;
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omission of the multiplication symbol;
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simplification of algebraic expressions;
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identifying and correcting mistakes;
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using patterns to reveal mathematical relationships; and
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solutions for all listed Figure it out pages.
Learning outcomes
Students should be able to define the quantity represented by a letter, write algebraic products in standard notation and simplify expressions by combining compatible terms. They should form a general expression from a pattern, test it for chosen values and explain why the rule continues. They should also locate a mistake in algebraic working and correct it with a clear reason—an important competency-based skill.
Why is this chapter important?
Letter-numbers allow mathematics to describe a rule that works in many cases. Formulas for perimeter, area, distance and other quantities all depend on this idea. The chapter therefore lays the foundation for equations, identities, coordinate relationships and advanced algebra.
It also changes the kind of question a student asks. Arithmetic often asks, “What is the answer in this case?” Algebra asks, “What rule describes every case?” Learning to move between these viewpoints is essential for mathematical reasoning.
How Teachoo supports learning
Teachoo organises concepts so that students can progress from the meaning of a letter to notation, simplification and generalisation. Worked solutions make implicit steps visible: what a letter represents, how a term is formed, why terms may or may not combine and how a pattern becomes an expression.
While studying, define every letter in words. If n represents the number of stages, objects or units, write that meaning before forming an expression. Draw the first few cases of a pattern, record the numerical relationship and then replace the changing number with n. Test the expression for small values to catch errors, but also explain why the rule continues.
Common mistakes to avoid
A letter is not a label or unit; it represents a number. The expression 3a means 3 × a, not the two-digit object “3a.” Do not combine unlike terms. Also avoid assuming that adjacent letters are being added: ab conventionally means a × b.
Students sometimes discover a pattern that fits the first two cases but fails later. Check at least three cases and relate the expression to the construction of the pattern. During simplification, preserve operation signs and brackets.
Deeper reasoning and concept connections
Study Expressions Using Letter-Numbers (Ganita Prakash) through comparison and justification. Place two related examples side by side, identify the decisive difference and explain why one method works in each case. Then create a new example and a deliberate non-example. This forces the definition to do real work and exposes gaps that passive reading hides.
Students should also practise reversing questions. After solving for an answer, ask what question could have produced it, whether more than one answer is possible and which extra condition would make the result unique. Reverse reasoning develops flexibility and is especially useful for missing-value, assertion–reason and error-analysis questions. The goal is to understand the network of ideas, not merely the order of a textbook solution.
How to solve unfamiliar and competency-based questions
Begin by separating facts from conclusions. Facts are given by the question or a known property; conclusions must be derived. Draw or rewrite the problem so each fact has a visible place. If several methods are possible, prefer the one with fewer assumptions and an easy final check. Record intermediate results rather than doing everything mentally.
Competency questions often change context without changing mathematics. Replace names and story details with variables, shapes, sets or data values. After solving, restore the context and check feasibility: counts should be whole where required, lengths and areas should have suitable units, probabilities should lie between 0 and 1, and constructed figures should satisfy every stated condition.
What complete mastery looks like
For Expressions Using Letter-Numbers (Ganita Prakash), a student should be able to define the central ideas in simple language, recognise them in different representations, solve routine questions accurately and explain the method used. They should also be able to correct a flawed solution, create an example satisfying given conditions and combine two ideas from the chapter in one problem. A reliable mastery test is to solve one direct question, one application question and one reasoning question without looking at notes, then explain all three aloud or in writing.
Keep a compact error log with four labels: concept, interpretation, calculation and presentation. Reattempt each error after a gap instead of rereading the answer immediately. Improvement comes from correcting the decision that caused the mistake, not from repeating questions whose method is already known.
Additional frequently asked questions
What should a student know before starting Expressions Using Letter-Numbers (Ganita Prakash)?
Revise the definitions, number operations, diagrams or notation used at the beginning of the chapter. The prerequisite list should be short: if an earlier skill blocks progress, repair that skill with two or three focused questions and return to the chapter.
How can a student check an answer in Expressions Using Letter-Numbers (Ganita Prakash)?
Use an independent check whenever possible: substitute the result, reverse the operation, estimate its size, compare it with the figure, test a simpler case or solve using another representation. A check should examine the mathematical condition, not merely repeat the same arithmetic.
How many questions are enough for strong preparation?
There is no fixed number. Stop counting questions and track coverage: every concept, every standard method, at least one mixed problem, one competency-based problem and every previously incorrect type should be solved independently. Ten varied, analysed questions are more valuable than fifty copied solutions.
How should Teachoo solutions be used without becoming dependent on them?
Attempt the question first and mark the exact step where progress stops. Read only enough of the solution to repair that step, close it and restart the question. Finally, solve a similar problem without help. This turns a solution into feedback rather than a substitute for thinking.
Frequently asked questions
Is Expressions Using Letter-Numbers an algebra chapter?
Yes. It introduces core algebraic ideas through letters, expressions, simplification and patterns.
Why is the multiplication sign omitted?
Algebra uses compact notation. A numerical coefficient placed beside a letter indicates multiplication, so 6x means 6 × x.
How can I check an expression formed from a pattern?
Substitute the stage numbers for the letter and verify that the expression gives the correct result in several cases. Then explain how each part of the expression matches the pattern.
Use Teachoo to build the concept before memorising notation. When every symbol has a clear meaning, algebra becomes a language for expressing patterns rather than a collection of mysterious rules.