BODMAS & Negative Numbers

What happened in the Laufenberg Bridge problem?

Germany and Switzerland built a bridge using different mean sea levels and misapplied plus/minus when correcting for 27 cm difference, resulting in a 54 cm error at the meeting point.

What does the bridge error demonstrate?

The importance of correct sign use (+/–) in calculations.

What Greek letter is α?

Alpha.

What Greek letter is µ?

Mu.

What Greek letter is ρ?

Rho.

What Greek letter is Δ?

Delta.

What Greek letter is π?

Pi.

What Greek letter is θ?

Theta.

What Greek letter is λ?

Lambda.

What Greek letters are Σ and σ?

Sigma (uppercase and lowercase).

What does BODMAS stand for?

B – Brackets
O – Operations (sin, cos, log, ln, e^x)
D – Division
M – Multiplication
A – Addition
S – Subtraction

Alternative names for BODMAS?

BOMDAS, BIRDMAS.

Why is BODMAS important?

It determines the correct order in which mathematical operations must be performed.

Example task given: Evaluate 3−2×5.

Multiply first: 2 × 5 = 10, so 3 - 10 = -7.

Example: 5 + 16 ÷ 2.

Division first → 16÷2=8, so result = 13.

Example: 31−2÷16.

Division first → 2÷16=0.1252, so result = 30.875.

How does addition work on the number line?

Moves the value to the right.

How does subtraction work on the number line?

Moves the value to the left.

Example: 0−3.

-3.

Example: 4-3.

1.

Example: 3+3.

6

Example: 3-6.

-3

Example: 3-8.

-5.

What does the expression “3−4−?=10” refer to?

Exercises in manipulating positive and negative signs.

What skill do these exercises test?

Rearranging and simplifying nested plus/minus expressions.

Rule for multiplying/dividing numbers with the same sign?

Result is positive.

Rule for multiplying/dividing numbers with different signs?

Result is negative.

What is “a double negative”?

Two negative signs next to each other act like multiplication:
Example: (−)(−)=+.

Example: -3x-1=?

+3

Example: -3×1=?

-3

Example: -3÷3=?

-1

Example: -3÷-3=?

+1

Example: -2x-5

+10

Example: 4×1

-4

Example: -8÷8

-1

Example: 4÷-4

-1

Example: -(3-6)=?

First inside brackets: –3 → outside negative makes +3.

Example: -(2-6)

Inside: –4 → outside negative = +4.

Why do scientists use Greek letters?

They are standard symbols for physical quantities in science and engineering.

What lesson does the Laufenberg Bridge story teach?

Small sign mistakes can cause large real-world errors.

Why is BODMAS essential?

Prevents incorrect results when expressions contain multiple operations.

Why must sign rules be mastered?

Misinterpreting sign interactions leads to repeated algebra and arithmetic mistakes.