Master Chapter 2 Class 7 - Arithmetic Expressions (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
Start Learning NowWelcome to Chapter 2: Arithmetic Expressions, from your Class 7 Maths book, Ganita Prakash.
This chapter is all about the fundamental language of mathematics: how we write and understand "mathematical phrases" built with numbers and operations.
A simple phrase like 13 + 2 is an arithmetic expression. We know its value is 15. But what happens when expressions get more complicated, like 30 + 5 × 4?
If you just go from left to right, 30 + 5 is 35, and 35 × 4 is 140. But if you do the multiplication first, 5 × 4 is 20, and 30 + 20 is 50. Which one is correct? Without a clear set of rules, mathematics would be confusing, with different people getting different answers for the same problem.
This chapter provides the essential rules and tools that everyone agrees on, so that an expression can only be understood in one way.
We will learn the tools and rules for reading, writing, and evaluating complex expressions in a clear, step-by-step order.
Simple Expressions and Comparison
We'll start by looking at simple expressions and how to compare their values. We will also learn how to reason about expressions without calculating them, for example, determining if 1023 + 125 is greater or less than 1022 + 128 just by looking at the numbers involved.
The Role of Brackets
The most powerful tool for avoiding confusion is brackets. You will learn the first and most important rule: always evaluate the expression inside the brackets first. For example, in 100 - (15 + 56), we must first calculate 15 + 56 (which is 71) before we subtract it from 100.
Understanding Terms
This is the most important concept in the chapter. We will learn that expressions are made of terms, which are the parts separated by addition ('+') signs. You'll learn the key idea that subtraction is just adding the inverse (a negative number).
For example, in the expression 83 - 14, we can rewrite it as 83 + (-14). The terms are 83 and -14.
In the expression 30 + 5 × 4, the terms are 30 and (5 × 4).
The Order of Operations
By understanding terms, we get a clear rule:
First, evaluate each term (doing all multiplications and divisions).
Second, add the values of the terms together.
This is why 30 + 5 × 4 is correctly evaluated as 30 + 20 = 50.
Properties for Smart Calculation
Once we have the rules, we will learn properties that make calculations faster and easier:
Commutative and Associative Properties: These rules show us that we can swap (commute) or group (associate) terms and add them in any order we want.
Removing Brackets: You'll learn the rules for removing brackets, such as how 100 - (15 + 56) becomes 100 - 15 - 56.
Distributive Property: This is a key "shortcut" that shows how 2 × (43 + 24) is the same as (2 × 43) + (2 × 24).
This chapter is the foundation for all future mathematics, including algebra. At Teachoo, we break down every concept, from identifying terms to using the distributive property, with clear, step-by-step examples to ensure you master these rules.
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