Integers | Year 7 Mathematics (Cambridge) PDF Download

Understanding Integers

Integers are whole numbers that can be positive or negative, including zero. They are used to represent quantities in real-world situations where direction or debt needs to be considered.

Examples

• Positive integers: 1, 2, 3
• Negative integers: -1, -2, -3
• Zero: 0

Real-World Examples

• Temperature: Positive integers for temperatures above zero, negative integers for temperatures below zero.
• Finance: Positive integers for money earned or gained, negative integers for debts or losses.

Operations with Integers

Addition and Subtraction

• Adding Integers: When adding integers with the same sign, add their absolute values and keep the sign.
  • Example: 3 + 5 = 8
  • Example: −3 + (−5) = −8
• Subtracting Integers: Subtracting integers is similar to adding but with different signs.
  • Example: 3 − 5 = −2
  • Example: −3 − (−5) = 2

Multiplication and Division

• Multiplying Integers: The product of two integers with the same sign is positive; with different signs, it's negative.
  • Example: 3 × 5 = 15
  • Example: −3 × (−5) = 15
  • Example: −3 × 5 = −15
• Dividing Integers: Division of integers can result in positive or negative quotients depending on the signs.
  • Example: 15 ÷ 3 = 5
  • Example: 15 ÷ (−3) = −5

Examples in Context

• Adding/Subtracting Finances: Adding income (+) and subtracting expenses (-).
• Multiplying/Dividing Temperatures: Multiplying temperature changes (e.g., −2 times −3 degrees).

Summary

Understanding integers is essential for dealing with both positive and negative numbers in various contexts, from temperature changes to financial transactions. Mastering operations with integers involves knowing how to add, subtract, multiply, and divide them effectively, reflecting real-world scenarios accurately.