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Integers, Rational Numbers and Real Numbers

Chapter 2 Study Notes

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Section 5 of 8
Contents▾
Why Negative Numbers Matter2.1Negative Numbers and Ordering2.2Addition and Subtraction of Integers2.3Multiplication and Division of Integers2.4Combined Operations (BODMAS)2.5Operations on Fractions and Decimals with Negatives2.6Rational and Irrational NumbersChapter Summary

2.4Combined Operations (BODMAS)

  1. Brackets
  2. Orders: powers and roots
  3. Division and Multiplication, left to right
  4. Addition and Subtraction, left to right

When negatives are present, the most common error is ignoring BODMAS and calculating left to right. Always apply BODMAS first, then handle the signs.

BODMAS with negatives

Evaluate (−3)2−4×(−5)+[8−(49+1)](-3)^2 - 4 \times (-5) + [8 - (\sqrt{49} + 1)].

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B and O: brackets and orders first. (−3)2=9(-3)^2 = 9 and 49=7\sqrt{49} = 7.
=9−4×(−5)+[8−(7+1)]= 9 - 4 \times (-5) + [8 - (7 + 1)]
Finish inside the square brackets: 7+1=87 + 1 = 8, then 8−8=08 - 8 = 0.
=9−4×(−5)+0= 9 - 4 \times (-5) + 0
D and M next: 4×(−5)=−204 \times (-5) = -20.
=9−(−20)+0= 9 - (-20) + 0
A and S last: subtracting −20-20 adds 2020.
=9+20+0=29= 9 + 20 + 0 = 29

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