Arithmetic Expressions Class 7 Notes

Arithmetic Expressions Class 7 Notes

Arithmetic Expressions Class 7 Notes

Important Terms and Their Meanings

1. Expression : An expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷) that represents a value. For example, (3 + 5) is an expression.

2. Terms in Expressions

1. Terms are parts of an expression separated by '+' or '-'
2. Example : In 12 + 7, the terms are 12 and 7.
3. expression 4 - 7
4. 4 + (-7)
5. The first term is (4).
6. The second term is (-7).

3. Operators : Operators are symbols that represent mathematical operations. The most common operators are :

1. Addition (+)
2. Subtraction (-)
3. Multiplication (×)
4. Division (÷)

4. Brackets : Brackets (parentheses) are used to group terms or expressions. They indicate that the operations within them should be performed first. For example, in the expression (2 × (3 + 5)), the addition inside the brackets is performed before the multiplication.

5. Evaluation : Evaluation is the process of calculating the value of an expression by substituting variables with numbers and performing the operations.

Main Components of Arithmetic Expressions

1. Structure : An arithmetic expression can be simple (like (5 + 3)) or complex (like (2 × (3 + 5) - 4)). The complexity often arises from the use of multiple terms and operations.

2. Order of Operations : This is crucial for evaluating expressions correctly. The standard order is :

1. Parentheses or Brackets
2. Multiplication and Division (from left to right)
3. Addition and Subtraction (from left to right)

This is often remembered by the acronym BODMAS (Brackets, Order, Division and Multiplication, Addition and Subtraction).

3. Properties of Operations :

1. Commutative Property : The order of addition or multiplication does not change the result. For example, (a + b = b + a) and (a × b = b × a).
2. Associative Property : The way in which numbers are grouped does not change the sum or product. For example, {{a + b) + c = a + (b + c)}.
3. Distributive Property : This property allows you to multiply a number by a sum or difference inside brackets. For example, a(b + c) = ab + ac.

Simple Expressions

1. Arithmetic expressions are mathematical phrases like 13 + 2, 20 - 4, 12 × 5, and 18 + 3.
2. Each expression evaluates to a value, e.g., 13 + 2=15.
3. The equality sign '=’ denotes the relationship between an expression and its value.
4. Real-world example : Calculating total expenses, like Mallika spending ₹ 25 daily for lunch over five days : 5 × 25.
5. Different expressions can yield the same value, e.g., 10 + 2, 15 - 3, 3 × 4, and 24 + 2 are all equal to 12.
6. This demonstrates the flexibility of arithmetic operations.

Comparing Expressions

1. Expressions can be compared using signs like '=’, '<' and '>'.
2. Example: 10 + 2 > 7 + 1 because 12 is greater than 8.
3. Real-world example : Comparing prices of products to find the best deal.