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

8 months ago

Answered by Rudolfs, an IB Maths tutor with MyTutor

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


PremiumJosh R. GCSE Maths tutor, A Level Maths tutor, 13 plus  Maths tutor, ...
View profile
£24 /hr

Josh R.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

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. ”

PremiumChristopher S. A Level Maths tutor, GCSE Maths tutor, A Level Spanish...
View profile
£26 /hr

Christopher S.

Degree: Mathematics (Masters) - Bristol University

Subjects offered: Maths, Spanish+ 1 more

Further Mathematics

“ I am extremely passionate about mathematics and I love the Spanish language! ”

Sanveer R. IB Maths tutor, IB Economics tutor
View profile
£20 /hr

Sanveer R.

Degree: Management (Bachelors) - LSE University

Subjects offered: Maths, Economics


“Who Am I: My name is Sanveer, but you can call me Sunny. I have Indian origins, but I grew up in Switzerland, where I lived for 14 years before moving to the UK. My passions include basketball and music. I am a student studying Manage...”

About the author

Rudolfs T. IB Physics tutor, IB Maths tutor
View profile
£22 /hr

Rudolfs T.

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

Subjects offered: 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

What are the key elements to include in your Math assignment?

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

Solve the equation log(1-x) - log(x) = 1 where log() is the logarithmic function, base 10.

Differentiate y = e^(x^2 - 3x).

View IB Maths tutors


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