This MCQ module is based on: Simple Expressions and Terms
TOPIC 4 OF 31
Simple Expressions and Terms
🎓 Class 7
Mathematics
CBSE
Theory
Ch 2 — Arithmetic Expressions
⏱ ~30 min
🌐 Language: [gtranslate]
🧠 AI-Powered MCQ Assessment
▲
📐 Maths Assessment
▲
This mathematics assessment will be based on: Simple Expressions and Terms
Targeting Class 7 level in Algebra, with Basic difficulty.
Upload images, PDFs, or Word documents to include their content in assessment generation.
2.1 Simple Expressions
You have seen mathematical phrases like 13 + 2, 20 – 4, 12 × 5, and 18 ÷ 3. Such phrases are called arithmetic expressions?.
Every arithmetic expression has a value? — the number it evaluates to. For example, the value of 13 + 2 is 15. We use the equality sign = to link an expression with its value:
13 + 2 = 15
📖 Arithmetic Expression
An arithmetic expression is a mathematical phrase that combines numbers using one or more operations (+, –, ×, ÷). It always has a single value when evaluated.
The expression can be read in words: 13 + 2 → "13 plus 2" or "the sum of 13 and 2".
Addition Expression
13 + 2 = 15
"the sum of 13 and 2"
Value: 15
"the sum of 13 and 2"
Value: 15
Multiplication Expression
5 × 25 = 125
"5 times 25" or "product of 5 and 25"
Value: 125
"5 times 25" or "product of 5 and 25"
Value: 125
Division Expression
18 ÷ 3 = 6
"18 divided by 3"
Value: 6
"18 divided by 3"
Value: 6
Subtraction Expression
20 – 4 = 16
"20 minus 4"
Value: 16
"20 minus 4"
Value: 16
📝 Example 1 — Writing an Expression from a Situation
Mallika spends ₹25 every day for lunch at school from Monday to Friday. Write an expression for the total she spends in a week.
Number of days: 5 (Monday to Friday)
Daily cost: ₹25
Expression: 5 × 25
Read as: "5 times 25" or "the product of 5 and 25"
Value: 5 × 25 = ₹125
Note: Different expressions can have the same value. E.g. 5 × 25 = 125 and 100 + 25 = 125 both equal 125.
Comparing Expressions with <, >, =
Just as we compare numbers, we can compare arithmetic expressions by comparing their values. We use the symbols < (less than), > (greater than), and = (equal to).
📝 Example 2 — Comparing Without Calculating
Which is greater: 1023 + 125 or 1022 + 128?
Joy starts with 1 less than Raja (1022 vs 1023), but gets 3 more (128 vs 125). Net gain for Joy over Raja: 3 − 1 = +2 more marbles.
So 1022 + 128 > 1023 + 125. ✔ Joy has more. (Verify: 1022 + 128 = 1150; 1023 + 125 = 1148. Indeed 1150 > 1148.)
💡 Reasoning Tip — Compare Without Calculating
When comparing a + b vs c + d, look at what changes:
- If the first number goes down by 1 (1023→1022) but the second goes up by 3 (125→128), the total goes up by 2.
- General: (c+d) – (a+b) = (c–a) + (d–b). If this is positive, c+d > a+b.
Arranging Expressions in Ascending Order
Consider these expressions:
(a) 67 – 19 (b) 67 – 20 (c) 35 + 25 (d) 5 × 11 (e) 120 ÷ 3
📝 Figure it Out — Section 2.1
Q1. Fill in the blanks to make the expressions equal on both sides of the = sign:
(a) 13 + 4 = __ + 6 (b) 22 + __ = 6 × 5 (c) 8 × __ = 64 ÷ 2 (d) 34 – __ = 25
(a) 13 + 4 = __ + 6 (b) 22 + __ = 6 × 5 (c) 8 × __ = 64 ÷ 2 (d) 34 – __ = 25
(a) LHS = 17. So 17 = __ + 6 → __ = 11
(b) RHS = 30. So 22 + __ = 30 → __ = 8
(c) RHS = 32. So 8 × __ = 32 → __ = 4
(d) 34 – __ = 25 → __ = 9
Q2. Arrange in ascending (increasing) order of value:
(a) 67 – 19 (b) 67 – 20 (c) 35 + 25 (d) 5 × 11 (e) 120 ÷ 3
(a) 67 – 19 (b) 67 – 20 (c) 35 + 25 (d) 5 × 11 (e) 120 ÷ 3
Values: (a) 48 (b) 47 (c) 60 (d) 55 (e) 40
Ascending order: (e) < (b) < (a) < (d) < (c)
i.e. 40 < 47 < 48 < 55 < 60
Compare using <, >, or = (without complicated calculation):
(a) 245 + 289 __ 246 + 285 (b) 273 – 145 __ 272 – 144 (c) 364 + 587 __ 363 + 589
(d) 124 + 245 __ 129 + 245 (e) 213 – 77 __ 214 – 76
(a) 245 + 289 __ 246 + 285 (b) 273 – 145 __ 272 – 144 (c) 364 + 587 __ 363 + 589
(d) 124 + 245 __ 129 + 245 (e) 213 – 77 __ 214 – 76
(a) 246+285: first goes up 1, second goes down 4 → net change = +1−4 = −3 → LHS > RHS >
(b) 272−144: first goes down 1, second goes down 1 → difference same → =
(c) 363+589: first goes down 1, second goes up 2 → net +1 → RHS > LHS → <
(d) Second term 245 same in both; first: 124 < 129 → <
(e) 214−76: first goes up 1, second goes up 1 → difference same → =
2.2 Reading and Evaluating Complex Expressions
Sometimes an expression can be read in more than one way — just like an ambiguous sentence in language. We need rules to resolve this ambiguity.
Mallesh is correct. In mathematics, we use two tools to eliminate ambiguity: (1) Brackets and (2) the concept of Terms.
Brackets in Expressions
Brackets ()? clarify which operation to perform first. The expression inside brackets is always evaluated first.
⚠️ The Bracket Rule
Always evaluate the expression inside brackets first, before applying any operations outside the brackets.
(30 + 5) × 4 = 35 × 4 = 140 ≠ 30 + (5 × 4) = 50
2.3 Terms in Expressions
What if an expression has no brackets? We use the concept of terms? to determine the order of operations.
📖 What Are Terms?
Terms are the parts of an expression separated by a '+' sign.
In the expression 12 + 7, the terms are 12 and 7.
A subtraction is rewritten as addition of a negative: 83 – 14 = 83 + (–14), giving terms 83 and –14.
Identifying Terms — Examples
Each multiplication/division group within an expression is a single term:
| Expression | As Sum of Terms | Terms |
|---|---|---|
| 13 – 2 + 6 | 13 + (–2) + 6 | 13, –2, 6 |
| 5 + 6 × 3 | 5 + (6 × 3) | 5, 6×3 |
| 4 + 15 – 9 | 4 + 15 + (–9) | 4, 15, –9 |
| 23 – 2 × 4 + 16 | 23 + (–2×4) + 16 | 23, –2×4, 16 |
| 4 + 100 ÷ 2 | 4 + (100÷2) | 4, 100÷2 |
| 28 + 19 – 8 | 28 + 19 + (–8) | 28, 19, –8 |
💡 The Term Rule (Order of Operations)
Within each term, multiplication and division are performed before the terms are combined by addition or subtraction.
23 – 2 × 4 + 16 = 23 + (–8) + 16 = 31
The term (–2×4) = –8 is evaluated first; then 23, –8, and 16 are added.
Swapping and Grouping Terms
A key question: does the order of adding terms affect the value? The answer is No!
✅ Key Property — Swapping and Grouping
In expressions having only addition (of terms), the order does NOT matter:
Term₁ + Term₂ = Term₂ + Term₁
This works because adding terms in any order gives the same value (Commutative and Associative properties of addition).
⚠️ Caution: This applies to terms, not to subtraction blindly. Rearranging requires converting subtractions to addition of negatives first.
🧮 Expression Evaluator with Term Breakdown
Type a simple arithmetic expression (using +, –, ×, ÷, and brackets) to see its value and a step-by-step breakdown.
Worked Examples — Expressions and Their Terms
📝 Example 7 — Hotel Bill with Tip
Four friends ordered 4 dosas (₹23 each) and tipped ₹5. Write an expression for the total and identify its terms.
Expression: 4 × 23 + 5
Terms: 4×23 and 5 (2 terms)
Evaluate: 4×23 = 92; then 92 + 5 = ₹97
If 7 friends: 7 × 23 + 5 = 161 + 5 = ₹166
📝 Example 9 — Rice Packets
Raghu had 4 packets of 2 kg rice. He bought 100 kg more and repacked it into 2 kg packets. Write an expression for the total packets he now has.
New packets from 100 kg: 100 ÷ 2
Expression: 4 + 100 ÷ 2
Terms: 4 and 100÷2
Value: 4 + 50 = 54 packets
📝 Figure it Out — Expressions and Terms
Q1. Find the values of the following expressions by writing the terms:
(a) 28 – 7 + 8 (b) 39 – 2 × 6 + 11 (c) 40 – 10 + 10 + 10 (d) 48 – 10 × 2 + 16 ÷ 2 (e) 6 + 4 ÷ 2
(a) 28 – 7 + 8 (b) 39 – 2 × 6 + 11 (c) 40 – 10 + 10 + 10 (d) 48 – 10 × 2 + 16 ÷ 2 (e) 6 + 4 ÷ 2
(a) 28 – 7 + 8: Terms = 28, –7, 8. Value = 28 – 7 + 8 = 29
(b) 39 – 2 × 6 + 11: Terms = 39, –(2×6), 11 = 39, –12, 11. Value = 39 – 12 + 11 = 38
(c) 40 – 10 + 10 + 10: Terms = 40, –10, 10, 10. Value = 40 – 10 + 10 + 10 = 50
(d) 48 – 10 × 2 + 16 ÷ 2: Terms = 48, –(10×2), (16÷2) = 48, –20, 8. Value = 48 – 20 + 8 = 36
(e) 6 + 4 ÷ 2: Terms = 6, (4÷2) = 6, 2. Value = 6 + 2 = 8
Q2. Write a story/situation for each expression and find its value:
(a) 89 + 21 – 10 (b) 5 × 12 – 6 (c) 4 × 9 + 2 × 6
(a) 89 + 21 – 10 (b) 5 × 12 – 6 (c) 4 × 9 + 2 × 6
(a) 89 + 21 – 10 = 100: Story — A library had 89 books. 21 new books arrived. Then 10 were borrowed. Books remaining = 89 + 21 – 10 = 100 books.
(b) 5 × 12 – 6 = 54: Story — 5 packets of 12 pencils each. 6 pencils used. Remaining = 60 – 6 = 54 pencils.
(c) 4 × 9 + 2 × 6 = 48: Story — 4 rows of 9 blue tiles and 2 rows of 6 red tiles. Total tiles = 36 + 12 = 48 tiles.
Q3. Three worked scenarios — write the expression, identify the terms, and find the value:
(a) A treasure of 100 gold coins shared: 2 equal groups + 100/2 extra
(b) Metro ticket: ₹40 adult, ₹20 child — find cost for (i) 4 adults + 3 children; (ii) two groups of 3 adults
(c) Find total window height from: top panel 40 cm, frame 5 cm, middle glass 60 cm, frame 5 cm, bottom panel 40 cm
(a) A treasure of 100 gold coins shared: 2 equal groups + 100/2 extra
(b) Metro ticket: ₹40 adult, ₹20 child — find cost for (i) 4 adults + 3 children; (ii) two groups of 3 adults
(c) Find total window height from: top panel 40 cm, frame 5 cm, middle glass 60 cm, frame 5 cm, bottom panel 40 cm
(a) Expression: 2 × 100 + 100/2. Terms: 2×100 and 100/2. Value = 200 + 50 = 250 gold coins.
(b)(i) Expression: 4 × 40 + 3 × 20. Terms: 4×40 and 3×20. Value = 160 + 60 = ₹220.
(b)(ii) Expression: 2 × (3 × 40). Value = 2 × 120 = ₹240.
(c) Total height = 40 + 5 + 60 + 5 + 40 = 150 cm. Expression: 2 × 40 + 2 × 5 + 60 = 80 + 10 + 60 = 150 cm.
🎲 Activity — Expression Builder Challenge
L6 Create
Choose any number and write as many different arithmetic expressions as you can that have that value.
- Pick a target number (e.g. 24).
- Write at least 6 different expressions using different operations: e.g. 12 + 12, 4 × 6, 48 ÷ 2, 34 – 10, 5 × 5 – 1, 3 × (2 + 6).
- For each expression, identify the terms.
- Challenge: use all four operations in one expression that still equals your target.
Sample expressions for 24:
- 12 + 12 — Terms: 12, 12
- 4 × 6 — Terms: 4×6
- 48 ÷ 2 — Terms: 48÷2
- 34 – 10 — Terms: 34, –10
- 3 × 8 — Terms: 3×8
- 5 × 4 + 4 — Terms: 5×4, 4
- 100 – 4 × 19 — Terms: 100, –(4×19) → 100 – 76 = 24 ✔
🏆
Competency-Based Questions — Arithmetic Expressions & Terms
Context: Understanding arithmetic expressions helps us communicate mathematical situations precisely. From calculating costs in a market to planning travel budgets, expressions model real life. Being able to identify terms, compare expressions without fully calculating them, and understand how brackets change meaning are essential skills for higher mathematics.
Q1. What is the value of the expression 48 – 3 × 5 + 8 ÷ 2?
L3 Apply
Answer: (A) 37
Terms: 48, –(3×5), (8÷2) = 48, –15, 4.
Value = 48 – 15 + 4 = 37.
Terms: 48, –(3×5), (8÷2) = 48, –15, 4.
Value = 48 – 15 + 4 = 37.
Q2. Priya has 67 beads. She gives away 19. Her friend Rina also has some beads and gives away 20, ending up with the same number as Priya. How many beads did Rina start with? Write expressions for both and compare.
L4 Analyse
Priya's final count: 67 – 19 = 48
Rina's expression: (Rina's start) – 20 = 48 → Rina started with 68 beads
Comparison: 67 – 19 = 68 – 20 = 48 ✔
Observation: Rina started with 1 more and gave away 1 more — the difference is preserved.
Rina's expression: (Rina's start) – 20 = 48 → Rina started with 68 beads
Comparison: 67 – 19 = 68 – 20 = 48 ✔
Observation: Rina started with 1 more and gave away 1 more — the difference is preserved.
Q3. Fill in the blanks:
(i) The expression 5 × 12 + 3 × 4 has ___ terms. The terms are ___.
(ii) 83 – 2 × 4 + 16 ÷ 2 = ___
(iii) The expression 30 + 5 × 4 has value ___, not 140.
L2 Understand
(i) The expression 5 × 12 + 3 × 4 has ___ terms. The terms are ___.
(ii) 83 – 2 × 4 + 16 ÷ 2 = ___
(iii) The expression 30 + 5 × 4 has value ___, not 140.
(i) 2 terms. Terms are: 5×12 and 3×4.
(ii) Terms: 83, –(2×4), (16÷2) = 83, –8, 8. Value = 83 – 8 + 8 = 83
(iii) Value = 30 + (5×4) = 30 + 20 = 50 (multiplication done first within its term).
(ii) Terms: 83, –(2×4), (16÷2) = 83, –8, 8. Value = 83 – 8 + 8 = 83
(iii) Value = 30 + (5×4) = 30 + 20 = 50 (multiplication done first within its term).
Q4. State True or False with reasoning:
(i) 245 + 289 > 246 + 285 (ii) 273 – 145 = 272 – 144 (iii) Adding terms in any order changes the value.
L5 Evaluate
(i) 245 + 289 > 246 + 285 (ii) 273 – 145 = 272 – 144 (iii) Adding terms in any order changes the value.
(i) True. 245+289=534; 246+285=531. 534 > 531. Reasoning: LHS first goes up 1, second goes down 4 → net −3 on RHS.
(ii) True. 273−145=128; 272−144=128. When both minuend and subtrahend decrease by 1, the difference stays the same.
(iii) False. Adding terms in any order gives the same value. This is the Commutative and Associative property of addition.
(ii) True. 273−145=128; 272−144=128. When both minuend and subtrahend decrease by 1, the difference stays the same.
(iii) False. Adding terms in any order gives the same value. This is the Commutative and Associative property of addition.
Q5. (HOT) Ananya says: "I can place brackets in 13 + 4 × 5 in two ways and get two different values." Raj says: "I can place brackets in 12 × 3 + 4 × 2 in three meaningful ways." Who is right? List all bracketings and their values.
L6 Create
Ananya (13 + 4 × 5):
• Default (no bracket): 13 + (4×5) = 13 + 20 = 33
• (13 + 4) × 5 = 17 × 5 = 85
Two different values ✔ — Ananya is correct.
Raj (12 × 3 + 4 × 2):
• Default: (12×3) + (4×2) = 36 + 8 = 44
• 12 × (3 + 4) × 2 = 12 × 7 × 2 = 168
• 12 × (3 + 4 × 2) = 12 × 11 = 132
• (12 × 3 + 4) × 2 = 40 × 2 = 80
At least 3 meaningful different values ✔ — Raj is also correct!
• Default (no bracket): 13 + (4×5) = 13 + 20 = 33
• (13 + 4) × 5 = 17 × 5 = 85
Two different values ✔ — Ananya is correct.
Raj (12 × 3 + 4 × 2):
• Default: (12×3) + (4×2) = 36 + 8 = 44
• 12 × (3 + 4) × 2 = 12 × 7 × 2 = 168
• 12 × (3 + 4 × 2) = 12 × 11 = 132
• (12 × 3 + 4) × 2 = 40 × 2 = 80
At least 3 meaningful different values ✔ — Raj is also correct!
🔬 Assertion–Reason Questions
(A) Both true; Reason is correct explanation (B) Both true; Reason is NOT the correct explanation (C) Assertion true; Reason false (D) Assertion false; Reason true
Assertion (A): The value of 30 + 5 × 4 is 50, not 140.
Reason (R): In an expression without brackets, multiplication is performed within its term before the terms are combined by addition.
Reason (R): In an expression without brackets, multiplication is performed within its term before the terms are combined by addition.
Answer: (A)
Both are correct. The Reason correctly explains the Assertion: "5 × 4" forms a single term (= 20), and 30 + 20 = 50. The erroneous value 140 comes from incorrectly treating (30+5) as a group first.
Assertion (A): The expressions –7 + 10 + (–11) and 10 + (–7) + (–11) have the same value.
Reason (R): In an expression with only additive terms, the order of adding the terms does not change the total value.
Reason (R): In an expression with only additive terms, the order of adding the terms does not change the total value.
Answer: (A)
Both true. Both expressions equal –8 (= –7+10–11). The Reason (commutativity of addition, including of negative terms) correctly explains why the value is unchanged.
Assertion (A): 23 – 2 × 4 + 16 has 2 terms.
Reason (R): Terms are the parts separated by '+' signs; 2 × 4 is a product within one term.
Reason (R): Terms are the parts separated by '+' signs; 2 × 4 is a product within one term.
Answer: (D)
The Assertion is false — 23 – 2×4 + 16 = 23 + (–2×4) + 16 has 3 terms: 23, –(2×4), and 16.The Reason is true — (–2×4) is indeed a single term (a product/term), but there are still 3 total terms in this expression.
Frequently Asked Questions
What is an algebraic expression?
An algebraic expression is a mathematical phrase combining variables, constants and operations like addition, subtraction, multiplication and division. For example, 2x plus 3y minus 5 is an algebraic expression with three terms. Variables represent unknown values. NCERT Class 7 Ganita Prakash Chapter 2 introduces this concept.
What is the difference between a variable and a constant?
A variable is a letter like x, y or n that represents an unknown or changing value. A constant is a fixed number like 5, minus 3 or 7. In the expression 4x plus 7, 4x contains the variable x while 7 is a constant. NCERT Class 7 Maths Chapter 2 explains this distinction clearly.
What is a coefficient in an algebraic expression?
A coefficient is the numerical factor multiplied by a variable in a term. In the term 5x, the coefficient is 5. In minus 3y, the coefficient is minus 3. If a variable appears without a number, the coefficient is 1 (as in x which means 1x). NCERT Class 7 Chapter 2 covers coefficients.
How do you identify terms in an expression?
Terms in an algebraic expression are the parts separated by plus or minus signs. In 3x plus 2y minus 5, the three terms are 3x, 2y and minus 5. Each term can be a variable term or a constant term. NCERT Class 7 Ganita Prakash Chapter 2 teaches term identification.
How do you form an expression from a word problem?
To form an expression, assign a variable to the unknown quantity and translate the verbal statement into mathematical operations. If a number is 5 more than twice x, the expression is 2x plus 5. NCERT Class 7 Maths Chapter 2 provides many such translation exercises.
Frequently Asked Questions — Arithmetic Expressions
What is Simple Expressions and Terms in NCERT Class 7 Mathematics?
Simple Expressions and Terms is a key concept covered in NCERT Class 7 Mathematics, Chapter 2: Arithmetic Expressions. 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 Simple Expressions and Terms step by step?
To solve problems on Simple Expressions and Terms, 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 2: Arithmetic Expressions?
The essential formulas of Chapter 2 (Arithmetic Expressions) 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 Simple Expressions and Terms important for the Class 7 board exam?
Simple Expressions and Terms 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 Simple Expressions and Terms?
Common mistakes in Simple Expressions and Terms 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 Simple Expressions and Terms?
End-of-chapter NCERT exercises for Simple Expressions and Terms 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 2, and solve at least one previous-year board paper to consolidate your understanding.
AI Tutor
Mathematics Class 7 — Ganita Prakash
Ready