Learning Objectives

Top

Identify and compare expressions without computation.
Create multiple expressions for a given value.
Understand and apply the commutative, associative, and distributive properties.
Evaluate expressions using terms and brackets.
Recognize the significance of order of operations in expressions.
Convert subtraction into addition using inverses.
Analyze and rewrite expressions to maintain equality.

Practice, Analyze & Improve 🚀

Dont just read—test your knowledge! Unlock the Student Workspace to take chapter tests and get instant performance insights.

Deep Analytics

Peer Comparison

Track Progress

Claim Free Account100% Free • No credit card required

Revision Notes & Summary

Top

Arithmetic Expressions Notes

Understanding Expressions

Expressions can be evaluated without computation by rewriting them using terms or removing brackets.
Example:
- For the expression 83 - 37 - 12:
  - Equal expressions include:
    - 84 - 38 - 12
    - 84 - (37 + 12)
    - 83 - 38 - 13
    - - 37 + 83 - 12

Properties of Addition

Commutative Property: The order of terms does not affect the sum.
- Example: Term 1 + Term 2 = Term 2 + Term 1
Associative Property: The grouping of terms does not affect the sum.
Distributive Property: Multiplying a number with an expression inside brackets is equal to multiplying the number with each term in the bracket.

Terms in Expressions

Terms are parts of an expression separated by a '+' sign.
- Example: In 12 + 7, the terms are 12 and 7.
Subtraction can be converted to addition of the inverse:
- Example: 83 - 14 = 83 + (-14)

Evaluating Expressions

When removing brackets preceded by a negative sign, the signs of the terms inside change.
- Example: 500 - (250 - 100) = 500 - 250 + 100

Examples of Expressions and Their Terms

Expression	Expression as the sum of its terms	Terms
13 - 2 + 6	13 + -2 + 6	13, -2, 6
5 + 6 X 3	5 + 6 x 3
4 + 15 - 9	+ +
23 - 2 X 4 + 16	+ +
28 + 19 - 8	+ +

Problem Solving with Expressions

Create different expressions using a set of numbers and operations to achieve specific values.
- Example: Using three 3's to create expressions like (3 + 3)/3 = 2.

Conclusion

Understanding the properties of addition and how to manipulate expressions is crucial for evaluating and comparing them effectively.

Do you belong in the Top 10%?

Our analytics show that most students struggle with specific concepts in Arithmetic expressions. Take a free diagnostic test to generate your personal Learning DNA profile.

Practice Test – MCQs, True/False

Top

No practice questions available for this chapter yet.

StudyTunnel

AI Learning Assistant

StudyTunnel Methodology

1

Master the Concepts

2

Conquer Boss Exams

3

The Redemption Arena

Arithmetic expressions