Directed Numbers

Directed numbers are numbers with a sign (+ or -) that indicate their direction or position relative to zero. These numbers are used in real-world contexts like temperature, money (debt/savings), elevation (above/below sea level), and time zones.

The following diagram gives the rules for the addition, subtraction, multiplication and division of directed numbers. Scroll down the page for more examples and solutions on the operations for directed numbers.

 

How to add directed numbers?
Rule 1: If the signs are the same then add the numbers and keep the common sign.
Rule 2: If the signs are different then subtract: Big number minus small number. Keep the sign of the big number.

How to subtract directed numbers?
Subtraction of directed numbers can be changed to adding the opposite.
a − b = a + (−b)

How to multiply and divide directed numbers?
Rule 1: The answer is positive when all the numbers are positive or when there is an even number of negative signs in the problem.
Rule 2: The answer is negative when there is an odd number of negative signs in the problem.

Directed Numbers Worksheets
Practice your skills using the following worksheets:

• Directed Decimals Worksheets

  Positive, Negative Decimals: +, -
  Positive, Negative Decimals: x, ÷
  Positive, Negative Decimals: Mixed Op

Printable & Online Order of Operations Worksheets
Printable & Online Integer Worksheets

Directed Numbers Adding and Subtracting

Directed Numbers Multiplying and Dividing

• Show Video Lesson

Rules for adding, subtracting, multiplying and dividing positive and negative numbers

• Show Video Lesson

GCSE Maths - Negative Numbers (Adding, Subtracting,Multiplying, Dividing)

• Show Video Lesson

Real-life Applications of Directed Numbers:

• Temperature: Temperatures above zero are positive (e.g., +25°C), while temperatures below zero are negative (e.g., -5°C).
• Money: Having money is represented by a positive number (e.g., +$100), while owing money or being in debt is represented by a negative number (e.g., -$50).
• Elevation: Heights above sea level are positive (e.g., +150m), and depths below sea level are negative (e.g., -30m).
• Direction/Distance: Moving in one direction can be positive (e.g., +5 km east), while moving in the opposite direction is negative (e.g., -3 km west).
• Financial Transactions: Credits to an account can be positive, and debits can be negative.

How to Avoid Mistakes:
Memorize the sign rules for addition, subtraction, multiplication, and division.
Always follow the order of operations (PEMDAS/BODMAS).
Read word problems carefully and think about the context.
Be extra careful when working with negative numbers.
Double-check your work.
Practice regularly. The more you work with directed numbers, the more comfortable you’ll become.

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