Calculate -7 mod 3

Step by step

The question

Question: work out −7 mod 3.

Mod 3 means: the remainder after dividing by 3.

It is always a whole number from 0 to 2.

1 Divide by 3

Divide −7 by 3.

For a negative number we go down to the multiple of 3 just below it: 3 × (−3) = −9.

Then up 2.

Careful!

A remainder is never negative.

We go down to the multiple just below, then count up.

2 On the clock

Think of a clock with 3 numbers, 0 to 2.

So −7 mod 3 = 2.

3 Check

Multiply back: 3 times (−3), plus 2, is −7.

And 2 is from 0 to 2.

Right!

Let's look back.

First: divide by 3.

Then: on the clock.

Last: check.