MYTUTOR SUBJECT ANSWERS

354 views

Why is (-1)*(-1)=1?

Even though this question seems trivial to most people with some mathematical expertise, it actually cuts quite deep into an intuitive understanding of what multiplication truly is. When one writes an expression like "5*2=10" what they really mean is that if I take two piles of 5 apples (or 5 piles of 2 apples) I get a total of 10 apples, but sadly this intuitive approach doesn't really generalize well to negative numbers. What does it mean to take (-1) of some object? To intuitively understand what multiplication is a different approach is required. Imagine I take a meter-stick with length 5 and scale it by a factor of 2. I clearly get a new meter-stick that has a length of 10. I could also scale it by something like a factor of pi and get another meter-stick with some length, so clearly this approach doesn't rely on the fact that the number is an intiger. In this case multiplication by a negative number would simply reverse the direction of the meter stick. If it was initially pointing to the right (the positive number direction), after multiplying it by -1 it would simply point in the opposite direction. Multiplying by -2 would just be a combination of two operations: first of all we would scale the meter stick by a factor of 2 and follow the scaling by an inversion. So, clearly, if we start with the number -1, which is simply a meter-stick of length one in the negative direction, and multiply it by -1, we invert it and get a meter-stick in the positive direction, which also has length 1. Hence (-1)*(-1)=1

Rudolfs T. IB Physics tutor, IB Maths tutor

1 year ago

Answered by Rudolfs, an IB Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

33 SUBJECT SPECIALISTS

£26 /hr

Josh R.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I study Maths at Warwick, I hope to be able to teach your child to love Maths and how to achieve top exam grades. ”

£20 /hr

Carlota O.

Degree: Computer Science (Bachelors) - University College London University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Computing
Business Studies

“About meI am a Computer Science student at University College London. I have a passion for math and sciences and I look forward to help out with any of these areas.In high school, I completed the International Baccalaureate programm...”

£20 /hr

Martin S.

Degree: Economics (Bachelors) - Bristol University

Subjects offered: Maths, Economics+ 1 more

Maths
Economics
Accounting

“I am a second year economics undergraduate with an interest in maths. I believe that economics is a fascinating subject that is invaluable for personal development even if you aren’t going to pursue it in further education. The fact t...”

MyTutor guarantee

About the author

Rudolfs T.

Currently unavailable: for regular students

Degree: Physics with Theoretical Physics (Masters) - Manchester University

Subjects offered: Maths, Physics

Maths
Physics

“I am a theoretical physics student at the University of Manchester. Even though I'm only in my first year I've had a lot of interaction with science already. I have participated and obtained medals in the International Physics Olympia...”

You may also like...

Other IB Maths questions

How do you calculate the probability P(X < x) for a normally distributed random variable X?

The quadratic equation 2x^2-8x+1 = 0 has roots a and b. Find the value of a + b and ab

In a lottery, 6 numbered balls are drawn from a pool of 59. Calculate the probability of scoring a jackpot. There used to be 49 balls in the pool. Calculate by how much the addition of 10 balls has decreased the probability of scoring a jackpot

Solve the equation (2 cos x) = (sin 2 x) , for 0 ≤ x ≤ 3π .

View IB Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok