GCSE Maths Practice: integers-and-directed-numbers

Question 10 of 10

This question tests how well you apply BIDMAS to operations involving two negatives and one positive.

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\( \begin{array}{l}\text{Which of the following is the correct value of }\\ -8 \times 5 + (-12)?\end{array} \)

Choose one option:

Predict the sign first, then perform each operation in BIDMAS order.

Reasoning with Negative Numbers and BIDMAS

At the Higher GCSE level, understanding how negative numbers interact within multi-step operations is essential. This question involves both multiplication and addition, each using negative values. By correctly applying BIDMAS—Brackets, Indices, Division and Multiplication, Addition and Subtraction—you can determine the result confidently and predict its sign before calculating.

Understanding the Process

Multiplication comes before addition in every case. If you reverse that order, your answer will be incorrect. Here, multiplying −8 by 5 gives a negative result because one number is negative and the other positive. Once that step is complete, the sum adds another negative value, which pushes the total further down the number line. The final value must therefore be negative.

Sign Logic Summary

  • Negative × Positive = Negative
  • Negative × Negative = Positive
  • Adding a Negative → moves left on the number line (decrease)

These sign rules never change, whether you are working with small integers or large algebraic expressions.

Worked Examples (Different from This Question)

  • Example 1: −7 × 4 + (−5) → multiplication first, then addition.
  • Example 2: −10 × 2 + (−8) → two negative steps combined.
  • Example 3: −6 × 3 + (−9) → similar structure, following BIDMAS.

Common Errors

  • Adding before multiplying, which breaks BIDMAS.
  • Assuming −8 × 5 = +40 by ignoring the sign rule.
  • Forgetting to apply brackets around negatives during addition, leading to dropped signs.

Predicting the Result Before Calculating

A strong mathematician can estimate the sign and magnitude of a result without full calculation. In this case, you can reason: multiplying −8 and 5 gives about −40, and adding another negative number decreases it further. Therefore, the answer must be slightly less than −40, confirming a negative outcome even before working it out.

Why BIDMAS Matters

Order of operations keeps mathematics consistent. If two people solved the same expression without a rule, they could get different answers. BIDMAS ensures multiplication or division are completed first, producing the same logical result every time. This concept becomes crucial in algebra, programming, and scientific formulae, where small order mistakes cause large numerical errors.

Real-World Applications

The same pattern occurs in finance (losses followed by extra costs), physics (forces acting in one direction), and data analysis (negative trends combining). Recognising how negatives accumulate prepares you for interpreting real-world information accurately.

FAQs

Q1: How can I quickly check if the result should be negative or positive?
A: Count how many negative factors you multiply—an odd number gives a negative, an even number gives a positive—and then note whether you are adding or subtracting a negative afterwards.

Q2: Why does adding a negative reduce the total?
A: Because adding a negative number is equivalent to subtracting its positive version.

Q3: What if I forget BIDMAS?

A: Use brackets to guide your order. For example, write (−8 × 5) + (−12) to remind yourself that multiplication comes first.

Study Tip

Before pressing any calculator keys, predict the sign of your final answer. This mental check trains your intuition and helps catch sign mistakes early. Consistent application of BIDMAS is one of the simplest yet most powerful habits in GCSE Maths problem-solving.