Integers

Summary and Exam Tips for Integers

Integers is a subtopic of Number, which falls under the subject Mathematics in the Edexcel Lower Secondary curriculum. Integers are whole numbers that include positive numbers, negative numbers, and zero. They do not include fractions or decimals. A key property of integers is that the sum of any integer and its opposite is zero, such as $9 + (-9) = 0$.

Integers can be represented on both horizontal and vertical number lines, where positive integers are to the right or above zero, and negative integers are to the left or below zero. When comparing integers, think of positive numbers as balloons that lift up and negative numbers as weights that pull down.

Adding a positive number is straightforward addition, while subtracting a positive number is simple subtraction. Adding a negative number is akin to subtracting a positive number, and subtracting a negative number is the same as adding a positive number. For multiplication and division, the rules are: multiplying or dividing two positive integers results in a positive integer, while multiplying or dividing two negative integers results in a positive integer. However, multiplying or dividing a positive integer with a negative integer results in a negative integer.

Exam Tips

• Understand Integer Properties: Remember that the sum of an integer and its opposite is always zero. This is crucial for solving problems involving integer operations.

• Use Number Lines: Practice plotting integers on number lines to visualize addition and subtraction, especially when dealing with negative numbers.

• Sign Rules: Keep in mind that two like signs (e.g., $+$ and $+$, or $-$ and $-$) result in a positive sign, while two unlike signs (e.g., $+$ and $-$) result in a negative sign.

• Practice Operations: Regularly practice adding, subtracting, multiplying, and dividing integers to become comfortable with the rules and operations.

• Real-World Applications: Relate integers to real-world scenarios, such as temperatures or financial transactions, to better understand their practical applications.