This MCQ module is based on: Notion of Letter-Numbers
TOPIC 12 OF 31
Notion of Letter-Numbers
🎓 Class 7
Mathematics
CBSE
Theory
Ch 4 — Expressions Using Letter-Numbers
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Notion of Letter-Numbers
Targeting Class 7 level in Algebra, with Basic difficulty.
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4.1 The Notion of Letter-Numbers
In this chapter we look at a neat way of expressing mathematical relations and patterns. We will see how such writing helps us in thinking about these relations and patterns, and in explaining why they really hold.
Example 1: Shabnam is 3 years older than Aftab. When Aftab's age is 10, Shabnam's age is 13. When Aftab is 18, Shabnam is 21. If Aftab is some number of years old, what will Shabnam's age be?
Think: Given Aftab's age, how will you find Shabnam's age?
Answer: Add 3 to Aftab's age. We can also write this as a rule.
Answer: Add 3 to Aftab's age. We can also write this as a rule.
A neat form of the rule: Shabnam's age = Aftab's age + 3. Instead of using words, we can use a letter. Let the letter \(a\) denote Aftab's age. Then Shabnam's age is \(a + 3\).
Fig. 4.1 — Aftab's age and Shabnam's age in rows
Replacing \(a\) by 23 gives \(a+3 = 23+3 = 26\). So, when Aftab is 23, Shabnam is 26. Letters such as \(a\) and \(s\) used to represent numbers are called letter-numbers?. Mathematical expressions containing letter-numbers, like \(a+3\), are called algebraic expressions?.
Key Idea
A letter-number (or variable) stands for "any number at all". An algebraic expression is a rule written using letter-numbers, the four operations, and brackets. Substituting a value for the letter gives a specific number.If \(s\) denotes Shabnam's age, then the algebraic expression telling us Aftab's age is \(s - 3\). When \(s = 23\), Aftab's age is \(23 - 3 = 20\).
Example 2 — Matchstick Patterns
Parthiv is making matchstick patterns. He places 2 matchsticks next to each other for each L. Each L has 2 matchsticks.
Fig. 4.2 — Each L uses 2 matchsticks
How many matchsticks are needed to make 5 L's? \(5 \times 2 = 10\). For 7 L's? \(7 \times 2 = 14\). For 45 L's? \(2 \times 45 = 90\). In general, the number of matchsticks is 2 times the number of L's. If \(n\) is the number of L's, total matchsticks = \(2n\).
Try this: How many matchsticks are needed for 100 L's? Answer: \(2 \times 100 = 200\).
Example 3 — Keraki's Stall
Keraki prepares and supplies coconut–jaggery laddus. The price of a coconut is ₹35 and the price of 1 kg jaggery is ₹60. How much should she pay if she buys 10 coconuts and 5 kg jaggery?
\(10 \times 35 + 5 \times 60 = 350 + 300 = \)₹650.
How much for 8 coconuts and 9 kg jaggery? \(8 \times 35 + 9 \times 60 = 280 + 540 = \)₹820.
If \(c\) is the number of coconuts and \(j\) is the number of kilograms of jaggery, then the total amount paid (in ₹) is \(c \times 35 + j \times 60\). Short form: \(35c + 60j\).
| Quantity needed | Relationship | Expression |
|---|---|---|
| Cost of coconuts | Number of coconuts × 35 | 35c |
| Cost of jaggery | Number of kg × 60 | 60j |
| Total cost | Sum of above | 35c + 60j |
Using this expression for \(c=7, j=4\): \(35 \times 7 + 60 \times 4 = 245 + 240 = \)₹485.
Writing Convention
Instead of writing \(a \times 3\), mathematicians usually write \(3a\) (number first, letter after). Instead of \(c \times 35\) we write \(35c\). The multiplication sign is dropped when a letter-number is involved.Example 4 — Perimeter of a Square
The perimeter of a square is 4 times the length of one side. If one side is \(q\) units, the perimeter = \(4 \times q = 4q\) units.
Perimeter of square = 4q
What is the perimeter of a square with side-length 7 cm? Use the expression: \(4 \times 7 = 28\) cm.
Activity: Letters for My Age
L3 ApplyMaterials: Pencil and paper.
Predict: Can you write your father's age, your sister's age, and your uncle's age all in terms of your own age using letter-numbers?
- Let \(y\) be your age now.
- If your father is 27 years older than you, write the expression for his age.
- If your sister is 2 years younger than you, write the expression for her age.
- If your uncle is twice your father's age minus 10, write that expression.
Father: \(y+27\). Sister: \(y-2\). Uncle: \(2(y+27) - 10 = 2y + 44\).
Figure it Out
Q1. Write the expression for the perimeter of: (a) a triangle with all sides equal to \(s\) (b) a regular pentagon of side \(t\) (c) a regular hexagon of side \(h\).
(a) \(3s\) (b) \(5t\) (c) \(6h\).
Q2. Muniratha has a 20 m long pipe. She uses a length \(x\) m on one side, another piece of some length \(y\) m on the other side, and the remaining length is used for the garden. Give the expression for the length of the pipe going to the garden.
\(20 - x - y\) metres.
Q3. Krithika has 3 ₹100 notes, 5 ₹20 notes and 6 ₹5 notes. Total = 3×100 + 5×20 + 6×5 = 300+100+30 = ₹430. If she has 8 ₹100, 4 ₹20, and \(z\) ₹5, write the total.
Total = \(800 + 80 + 5z = 880 + 5z\).
Q4. Venkatalakshmi owns a flour mill. 15 seconds per kg of grain. 8 seconds to grind into powder. Machine is running, and \(y\) kg of grain was being milled when more was added. Complete grinding takes \(x\) kg. Which of the following describes the time taken? (a) \(10+8+y\) (b) \(10+8\)×\(y\) (c) \(10+8\)×\(y\) (d) \(10 \times 8 \times y\) (e) \(10 \times y + 8\).
The standard rule is "15 s per kg + 8 s setup". For \(y\) kg this is \(15y + 8\) (or equivalently an option that correctly isolates setup + per-kg time). Among the given options, (e) \(10y+8\) matches the form per-kg-time-times-kg + fixed-setup.
Competency-Based Questions
Scenario: A fruit vendor sells apples at ₹120/kg and oranges at ₹80/kg. A customer buys \(a\) kg of apples and \(o\) kg of oranges. A delivery charge of ₹30 is added for the order.
Q1. Write an expression for the total bill.
L3 ApplyTotal = \(120a + 80o + 30\) rupees.
Q2. For \(a=2, o=3\), find the bill. Analyse how the delivery charge changes the unit cost per kilogram.
L4 Analyse\(240 + 240 + 30 = ₹510\). Without delivery, ₹480 for 5 kg = ₹96/kg average. With delivery, ₹510/5 = ₹102/kg average. The ₹30 adds ₹6/kg when spread across 5 kg.
Q3. The vendor claims that the delivery charge becomes "negligible" for large orders. Evaluate this claim mathematically.
L5 EvaluateFor \(a+o\) = 10 kg, delivery adds ₹3/kg; for 100 kg, only ₹0.30/kg. As the order grows, the fixed ₹30 becomes a smaller fraction of the total. The claim is correct as an approximation for very large orders.
Q4. Design a combined expression for the vendor to compute the bill, including a 5% discount when total before delivery exceeds ₹500.
L6 CreateLet \(S = 120a + 80o\). Bill = \(S + 30\) if \(S \leq 500\); Bill = \(0.95S + 30\) if \(S > 500\).
Assertion–Reason Questions
A: The expression \(a+3\) gives Shabnam's age if \(a\) is Aftab's age.
R: Shabnam is 3 years older than Aftab, so Shabnam's age is obtained by adding 3 to Aftab's age.
R: Shabnam is 3 years older than Aftab, so Shabnam's age is obtained by adding 3 to Aftab's age.
(a)
A: In writing \(3 \times a\) as \(3a\), we are losing mathematical information.
R: The multiplication sign can always be dropped between a number and a letter-number without change in meaning.
R: The multiplication sign can always be dropped between a number and a letter-number without change in meaning.
(c) — A is false (no information is lost). R is true (convention).
Frequently Asked Questions
What are letter-numbers in Class 7 Maths?
Letter-numbers are letters such as x, y, n that stand for any number. They let us write general rules instead of specific calculations. NCERT Class 7 Ganita Prakash Chapter 4 introduces letter-numbers as the gateway from arithmetic to algebra.
Why do we use letters instead of numbers?
Letters express patterns and rules that work for every value. For example, 'the sum of any number and 0 is itself' becomes x + 0 = x. This general truth cannot be captured with specific numbers alone. NCERT Class 7 Chapter 4 motivates letters this way.
What is an algebraic expression?
An algebraic expression combines letter-numbers, numbers, and operations (+, -, x, /) without an equals sign. Examples: 2x + 3, 5y - 7, a + b. NCERT Class 7 Ganita Prakash Chapter 4 builds expressions step by step.
What is the difference between a variable and a constant?
A variable (letter-number) can take different values; a constant is a fixed number. In 3x + 5, x is the variable and 3, 5 are constants. NCERT Class 7 Ganita Prakash Chapter 4 defines this clearly.
Can letter-numbers represent zero or negative values?
Yes. A letter-number stands for any number, including 0 and negatives, unless the problem restricts it. NCERT Class 7 Ganita Prakash Chapter 4 reminds students of this generality when evaluating expressions.
How is '2x' different from '2 + x'?
2x means 2 multiplied by x. For x = 3, 2x = 6. 2 + x means 2 added to x. For x = 3, 2 + x = 5. These are very different expressions. NCERT Class 7 Ganita Prakash Chapter 4 stresses this distinction.
Frequently Asked Questions — Expressions Using Letter-Numbers
What is Notion of Letter-Numbers in NCERT Class 7 Mathematics?
Notion of Letter-Numbers is a key concept covered in NCERT Class 7 Mathematics, Chapter 4: Expressions Using Letter-Numbers. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Notion of Letter-Numbers step by step?
To solve problems on Notion of Letter-Numbers, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 4: Expressions Using Letter-Numbers?
The essential formulas of Chapter 4 (Expressions Using Letter-Numbers) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Notion of Letter-Numbers important for the Class 7 board exam?
Notion of Letter-Numbers is part of the NCERT Class 7 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Notion of Letter-Numbers?
Common mistakes in Notion of Letter-Numbers include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Notion of Letter-Numbers?
End-of-chapter NCERT exercises for Notion of Letter-Numbers cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 4, and solve at least one previous-year board paper to consolidate your understanding.
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