Summary
Chapter 2 of Ganita Prakash (Grade 7) covers Arithmetic Expressions — teaching students how to read, write, compare, and evaluate mathematical phrases using the four operations, brackets, and the concept of terms.
This chapter begins by defining arithmetic expressions as mathematical phrases such as 13 + 2 or 12 × 5, each of which evaluates to a single value. Students learn to compare expressions using '=', '<', and '>' without always computing their full values, and discover how brackets and the notion of terms resolve ambiguity when an expression involves multiple operations. The chapter then builds three foundational properties — the commutative and associative properties of addition (terms can be swapped or regrouped without changing the sum) and the distributive property of multiplication over addition or subtraction — with worked examples and real-life situations. Students practise removing brackets, identifying how signs change when a bracket is preceded by a negative sign, and use these properties to evaluate or simplify expressions efficiently.
Key points & formulas
- 01An arithmetic expression is a mathematical phrase formed using numbers and operations (+, –, ×, ÷); its value is the number it evaluates to, written with '=' (e.g., 13 + 2 = 15).
- 02Expressions can be compared using '=', '<', or '>' based on their values; comparisons can often be made by reasoning rather than full computation (e.g., 1023 + 125 < 1022 + 128 because Joy gains 3 more than he starts with fewer).
- 03Brackets resolve ambiguity: evaluate the expression inside brackets first before applying outer operations (e.g., 30 + (5 × 4) = 50, not 140).
- 04Terms are the parts of an expression separated by a '+' sign after all subtractions are converted to additions of negative numbers (e.g., 83 – 14 has terms 83 and –14).
- 05The commutative property of addition: swapping the order of terms does not change the sum (Term 1 + Term 2 = Term 2 + Term 1), and this holds even when terms are negative numbers.
- 06The associative property of addition: grouping terms in any order gives the same sum, so in an expression with only additions the terms can be added in any order.
- 07To evaluate an expression without brackets, first evaluate each term (products/quotients within a term), then add all terms together.
- 08Removing brackets preceded by a negative sign changes the sign of every term inside the bracket: e.g., 200 – (40 + 3) = 200 – 40 – 3, and 500 – (250 – 100) = 500 – 250 + 100.
- 09Removing brackets NOT preceded by a negative sign leaves the signs of the terms inside unchanged: e.g., 28 + (35 – 10) = 28 + 35 – 10.
- 10The distributive property: a number multiplied by a bracketed sum or difference equals the sum or difference of the products — e.g., 2 × (43 + 24) = 2 × 43 + 2 × 24, and (4 + 3) × 5 = 4 × 5 + 3 × 5. This also works with subtraction: (14 – 6) × 10 = 14 × 10 – 6 × 10.
Frequently asked questions
01What is an arithmetic expression?
An arithmetic expression is a mathematical phrase formed from numbers and the operations addition, subtraction, multiplication, and division — for example, 13 + 2, 20 – 4, 12 × 5, or 18 ÷ 3. Every arithmetic expression has a value, which is the number it evaluates to; for example, the value of 13 + 2 is 15.
02What is a term in an arithmetic expression?
Terms are the parts of an expression separated by a '+' sign. Because subtracting a number is the same as adding its inverse (e.g., 83 – 14 = 83 + (–14)), all subtractions are first converted to additions before identifying terms. For example, the expression 2 – 10 + 4 × 6 has terms 2, –10, and 4 × 6. A product like 6 × 5 counts as a single term because it contains no '+' sign.
03Why do we use brackets in arithmetic expressions?
Brackets resolve ambiguity when an expression has multiple operations and the intended order is not clear. For example, 30 + 5 × 4 could be read as (30 + 5) × 4 = 140 or as 30 + (5 × 4) = 50. The bracket specifies which operation to perform first: the expression inside the bracket is always evaluated before any outside operation. In the same way that a comma in a sentence clarifies meaning, brackets clarify mathematical meaning.
04How do you evaluate an expression when there are no brackets?
First identify the terms by separating the expression at '+' signs (after converting all subtractions to additions of negative numbers). Then evaluate each term on its own — that means computing any products or quotients within a term. Finally, add all the evaluated terms together. For example, 30 + 5 × 4 has terms 30 and 5 × 4; evaluating the second term gives 20, so the result is 30 + 20 = 50.
05What is the commutative property of addition?
The commutative property of addition states that swapping the order of two terms does not change their sum: Term 1 + Term 2 = Term 2 + Term 1. This holds even when the terms involve negative numbers — for example, (–4) + 6 = 6 + (–4) = 2.
06What is the associative property of addition?
The associative property of addition states that grouping (bracketing) terms in any way does not change the sum. For three terms A, B, C: (A + B) + C = A + (B + C). More generally, terms of an expression can be added in any order and the sum remains the same. For example, (–7) + 10 + (–11) gives –8 regardless of which two terms are added first.
07What is the distributive property and how is it used in this chapter?
The distributive property states that the multiple of a sum (or difference) equals the sum (or difference) of the multiples: for example, 2 × (43 + 24) = 2 × 43 + 2 × 24, and (4 + 3) × 5 = 4 × 5 + 3 × 5. It also works with subtraction: (14 – 6) × 10 = 14 × 10 – 6 × 10. The chapter uses this property to multiply numbers efficiently — for instance, 97 × 25 = (100 – 3) × 25 = 100 × 25 – 3 × 25.
08What happens to the signs inside brackets when you remove them?
It depends on what precedes the bracket. If the bracket is preceded by a negative (minus) sign, every term inside changes its sign upon removal — for example, 200 – (40 + 3) = 200 – 40 – 3, and 500 – (250 – 100) = 500 – 250 + 100. If the bracket is NOT preceded by a negative sign (i.e., it is preceded by '+' or nothing), the signs of the terms inside do not change — for example, 28 + (35 – 10) = 28 + 35 – 10.
09How can you compare two expressions without fully evaluating them?
By reasoning about how the terms differ. For example, to compare 1023 + 125 and 1022 + 128: the first starts with 1 more, but the second adds 3 more, so the second is greater (1022 + 128 > 1023 + 125). Similarly, 113 – 25 = 112 – 24 because the first has 1 more to start with but also loses 1 more, leaving the same result. The chapter encourages this kind of reasoning instead of computing large numbers.
10Can different expressions have the same value?
Yes. The chapter gives the example of the number 12, which can be expressed as 10 + 2, 15 – 3, 3 × 4, or 24 ÷ 2 — four different expressions with the same value. More complex examples arise through the commutative, associative, and distributive properties, where rearranging or expanding/factoring expressions produces equivalent ones.
11How does the chapter use the distributive property for mental multiplication?
By rewriting a number close to a round number before multiplying. For example, 97 × 25 = (100 – 3) × 25 = 100 × 25 – 3 × 25; similarly, 63 × 18 = (53 + 10) × 18 = 53 × 18 + 10 × 18 = 954 + 180 = 1134. The chapter notes this method is especially useful when one number is close to a multiple of 10, 50, 100, etc.
12Is the NCERT Ganita Prakash Class 7 Chapter 2 PDF free to download? Do I need to sign up?
Yes — the PDF is completely free to read and download on cbseprepmaster.com. No account or sign-up is required.
More chapters in Ganita Prakash
This is the complete Ganita Prakash Chapter 2 as published by NCERT — every diagram, solved example, and exercise included, free. Browse all NCERT Class 7 textbooks.
Read offline with notes, solutions & mock tests
CBSE Prepmaster — free on iOS & Android