GCSE Maths Practice: integers-and-directed-numbers
This task tests how confidently you can apply BIDMAS when negative numbers are involved.
Underline all negative signs and solve operations in order.
Understanding BIDMAS and Directed Numbers
In GCSE Mathematics, it is vital to follow the correct order of operations when simplifying expressions. The rule set known as BIDMAS (or sometimes BODMAS) stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction. This order guarantees that all students will reach the same result no matter how complex an expression becomes. Ignoring this structure is one of the most common causes of simple calculation mistakes in exams.
Another key topic that often appears together with BIDMAS is the idea of directed numbers. These are numbers that carry a direction—positive or negative. Positive numbers represent quantities moving upward, increasing, or forward. Negative numbers describe decreases, drops, or backward movements. The challenge arises when both appear in the same expression, especially when combined with brackets or multiple operations.
Sign Rules to Remember
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
- Negative × Positive = Negative
These sign rules form the foundation for algebraic manipulation and solving equations. Understanding them also helps when you start learning about expanding brackets and factorising quadratic expressions later in the GCSE course.
Worked Examples (Different from the Question)
- Example 1: (−4) + 3×2 → multiply first, then add.
- Example 2: 5 − (−6)×2 → multiply negatives first, then handle subtraction.
- Example 3: (−7)×(−3) + 2×(−5) → carry out each multiplication before addition.
Notice how each example follows the same rule pattern, regardless of the numbers used. The structure of the operation never changes: perform the multiplication or division before the addition or subtraction.
Common Mistakes
- Adding before multiplying, which changes the entire outcome.
- Forgetting that two negative numbers multiplied together give a positive result.
- Confusing subtraction with a negative sign; they are not always the same operation.
Real-Life Applications
Understanding directed numbers helps in interpreting real situations such as temperature changes, financial gains and losses, or elevation differences. For instance, a mountain climber descending 500 metres and then climbing 500 metres again ends up back at the same altitude. The maths behind that simple story follows the same logical rules as BIDMAS calculations with positive and negative values.
FAQ
Q1: What should I do first if I see both brackets and multiplication?
A: Always solve the operation inside the brackets first, following the BIDMAS order. Within the brackets, apply multiplication or division before addition or subtraction.
Q2: How can I double-check my signs?
A: Before starting, mark each number’s sign clearly and check the rule: same signs give positive, opposite signs give negative.
Q3: Does subtraction always mean the number is negative?
A: Not necessarily. Subtraction is an operation, while a negative sign changes direction. They coincide only sometimes.
Study Tip
When facing complex arithmetic expressions, highlight or underline negative signs before you begin. Then process the steps methodically following BIDMAS. This small habit helps prevent accidental sign errors and builds confidence for later topics such as algebraic fractions and simultaneous equations.
By mastering this skill, you strengthen not only your arithmetic accuracy but also your logical reasoning—an essential quality in higher-level mathematics and everyday problem solving.