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Arithmetic Expressions – Class 7 Maths Chapter 2 Notes & NCERT PDF

Class 7MathematicsChapter 2NCERT book: Ganita Prakash - Mathematics Class 7

Notes and a simple summary of Chapter 2 of the NCERT Class 7 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 2: Arithmetic Expressions

Introduction

Mathematical phrases like 13 + 2, 20 – 4, 12 × 5 and 18 ÷ 3 are called arithmetic expressions. Every expression has a value — the number it evaluates to. This chapter teaches how to write expressions for real situations, compare them smartly, and evaluate complicated expressions without confusion using brackets and terms.

Key Ideas

2.1 Simple Expressions

  • Mallika spends ₹25 on lunch each school day. Her weekly (Monday–Friday) spending is 5 × 25.
  • Different expressions can have the same value: 10 + 2, 15 – 3, 3 × 4 and 24 ÷ 2 all equal 12.
  • We compare expressions by their values using =, < and >: 10 + 2 > 7 + 1.

    • Comparing without full calculation

  • Raja and Joy's marbles: 1023 + 125 vs 1022 + 128. Raja started with 1 more, but Joy got 3 more, so Joy has 2 more → 1023 + 125 < 1022 + 128.
  • 113 – 25 vs 112 – 24: Raja had 1 more but also lost 1 more → 113 – 25 = 112 – 24.

    • 2.2 Reading and Evaluating Complex Expressions

  • 30 + 5 × 4 — Purna added first and got 140; Mallesh multiplied first and got 50. Mallesh is right (30 marbles + 5 bags of 4).
  • Just as a comma changes the meaning of a sentence ("Shalini sat next to a friend with toys"), brackets fix the order in maths.
    • Brackets: evaluate the expression inside the brackets first.
  • Irfan buys biscuits (₹15) and toor dal (₹56) and pays ₹100. His change is 100 – (15 + 56) = ₹29, not 100 – 15 + 56 = 141 (absurd!).

    • Terms

    Terms are the parts of an expression separated by a '+' sign.
  • Subtracting a number is the same as adding its inverse: 83 – 14 = 83 + (–14), so the terms are 83 and –14.
  • 6 × 5 + 3 has terms 6 × 5 and 3; 2 – 10 + 4 × 6 has terms 2, –10 and 4 × 6.
  • To evaluate: first evaluate each term, then add the terms. 5 × (3 + 2) + 7 × 8 + 3 = 25 + 56 + 3 = 84.

    • Swapping and Grouping

  • Swapping two terms doesn't change the sum — the commutative property of addition. (Madhu's drone: 6 + (–4) = (–4) + 6 = 2 m.)
  • Grouping terms differently doesn't change the sum — the associative property of addition. (–7) + 10 + (–11) = –8 in any order.
  • So Manasa, who forgot to include 9055 in her long sum 11749, need not start again — she just adds 9055.
  • Everyday contrast: hat and shoes can be worn in any order, but socks must go before shoes!

    • Removing Brackets — I

  • 200 – (40 + 3) = 200 – 40 – 3 = 157.
  • 500 – (250 – 100) = 500 – 250 + 100 = 350.
    • When brackets preceded by a minus sign are removed, the sign of every term inside changes. When they are preceded by a plus sign, the signs stay the same: 28 + (35 – 10) = 28 + 35 – 10 = 53.

    Removing Brackets — II (Distributive property)

  • Lhamo and Norbu each order a cutlet (₹43) and a rasgulla (₹24): total = 2 × (43 + 24) = 2 × 43 + 2 × 24 = ₹134.
  • Republic Day parade: 4 rows of 5 scouts and 3 rows of 5 guides → 4 × 5 + 3 × 5 = (4 + 3) × 5 = 35.
    • The multiple of a sum (difference) is the same as the sum (difference) of the multiples.

    Tinker the Terms

  • Changing a term changes the value by the same amount: if 53 × 18 = 954, then 63 × 18 = 954 + 10 × 18 = 1134.
  • 97 × 25 = (100 – 3) × 25 = 2500 – 75 = 2425.

    • Worked Examples

  • Find 39 – 2 × 6 + 11 using terms. Terms: 39, –(2 × 6) = –12, 11. Sum: 39 – 12 + 11 = 38.
  • Ruby sat out and 33 students played "Fire in the mountain". When the teacher called '5', Ruby wrote 6 × 5 + 3 — six groups of 5 and 3 left out (value 33).
  • Four friends, four dosas at ₹23 each, plus ₹5 tip: 4 × 23 + 5 = 92 + 5 = ₹97.
  • Remove brackets: 14 – (12 – 10). Signs inside change: 14 – 12 + 10 = 12.
  • Kannan pays ₹432: 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1 = 432 (other ways are possible).
  • Melvin reads one two-page story every day except Tuesday and Saturday. In 8 weeks he reads (7 – 2) × 8 = 7 × 8 – 2 × 8 = 40 stories.

    • Figure it Out — hints

  • Before calculating, mark the terms of the expression.
  • For comparison questions, look at how the numbers differ instead of evaluating fully.
  • When removing a bracket, check the sign in front of it.
  • For puzzles like the snail (climbs 3 cm, slips 2 cm on a 10 cm post), track day by day — it reaches the top on the 8th day, because on the last day it doesn't slip.

    • Maths Words

  • Arithmetic expression (अंकगणितीय व्यंजक)
  • Value (मान)
  • Term (पद)
  • Brackets (कोष्ठक)
  • Inverse / Additive inverse (योज्य प्रतिलोम)
  • Sum (योग)
  • Difference (अंतर)
  • Product (गुणनफल)
  • Commutative property (क्रमविनिमेय गुण)
  • Associative property (साहचर्य गुण)
  • Distributive property (वितरण गुण)
  • Equality sign (बराबर का चिह्न)

    • Connections

  • The Token Model of integers from Grade 6 explains why swapping and grouping work even with negative numbers.
  • Puzzles like "Expression Engineer" (make 1–20 using four 4's) build flexible thinking.

    • Common Mistakes

  • Evaluating left to right blindly: 30 + 5 × 4 ≠ 140.
  • Forgetting to change signs when removing brackets after a minus: 500 – (250 – 100) ≠ 500 – 250 – 100.
  • Treating 6 × 5 as two terms — a product is one term.
  • Thinking 5 × 4 + 3 = 5 × (4 + 3). The first is 23, the second is 35.

    • Maths in Daily Life

    Bills, change from a shop, sharing costs among friends and calculating savings (like Binu's monthly budget) all need correctly written expressions with brackets.

    💡 Key Learning Points

    • ✓Write arithmetic expressions for real situations and find their values.
    • ✓Compare expressions by reasoning (e.g. 1023 + 125 < 1022 + 128) without full calculation.
    • ✓Identify terms (parts separated by '+') and evaluate each term before adding.
    • ✓Use brackets correctly, and change signs of terms when removing brackets preceded by a minus sign.
    • ✓Apply commutative, associative and distributive properties to simplify calculations.

    👨‍🏫 Teaching Tips

    • →Begin with the Shalini sentence (with and without a comma) to show why brackets matter.
    • →Act out Raja and Joy's marbles with real counters to compare expressions without calculating.
    • →Ask students to circle each term in an expression with a coloured pencil before evaluating.
    • →Use shopping role-play: students write the expression for change (100 – (15 + 56)) and test the wrong version.
    • →Show the parade picture (rows of scouts and guides) to make the distributive property visual.
    • →Run a 'Tinker the Terms' quick-fire game: change one number and predict the new value.
    • →Close with the 'Expression Engineer' challenge using four 4's to make 1 to 20.

    📋 Assessment Questions

    1. Can the student write an expression with brackets for Irfan's change and evaluate it correctly?
    2. Can the student list the terms of 23 – 2 × 4 + 16?
    3. Can the student remove brackets correctly in 14 – (–12 – 10)?
    4. Can the student use the distributive property to find 97 × 25 quickly?
    5. Can the student explain why 5 × 4 + 3 ≠ 5 × (4 + 3)?

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    All chapters in Ganita Prakash - Mathematics Class 7

    1. 1. Large Numbers Around Us
    2. 2. Arithmetic Expressions
    3. 3. A Peek Beyond the Point
    4. 4. Expressions Using Letter-Numbers
    5. 5. Parallel and Intersecting Lines
    6. 6. Number Play
    7. 7. A Tale of Three Intersecting Lines
    8. 8. Working with Fractions