The “Get a Hint” posting for this exercise was closed to new questions, so I thought I would ask this here. I’m terrible at math, and am having a lot of trouble understanding how remainders work and why exactly they are used in code. Can someone please explain this to me?
5 % 2 = 1 because
Math.floor(5 / 2) = 2 (Quotient)
2 * 2 = 4
5 - 4 = 1 (Remainder)
Well, let’s forget the theory and have a look at a few examples
10 % 3 = 1
Why?
School maths:
10 / 3 = 3.3333333
Comp maths:
10 / 3 = 3
Okay, so 3 * 3 = 9, right? Now we take the original number which was 10 - 9, what’s the result? It’s 1 which is our reminder. In other words 10 % 3 = 1 ( give me the remainer of 10 % 3 )
7 % 2 = 1
School maths:
7 / 2 = 3.5
Comp maths:
7 / 2 = 3
3 * 2 is 6. But our original number was 7. So, we take our original number - what we have got, which is 6. Thus, 7 - 6 = 1 and that’s our remainder.
ps: for haters, I know that you’ll get different results based on the programming language you’re using, specifically, whether you’re working with ints/floats (doubles)
One possible use of the modulo, or remainder, operation is to “wrap around” to the beginning of an array when you reach its end. Consider this code:
const arr = [1, 2, 3]
const arrLength = arr.length
for (let i = 0; i < 6; i++) {
const remainder = i % arrLength
console.log(`i = ${i}, remainder = ${remainder}`)
console.log(`arr[remainder] = ${arr[remainder]}`)
}
This prints:
i = 0, remainder = 0
arr[remainder] = 1
i = 1, remainder = 1
arr[remainder] = 2
i = 2, remainder = 2
arr[remainder] = 3
i = 3, remainder = 0
arr[remainder] = 1
i = 4, remainder = 1
arr[remainder] = 2
i = 5, remainder = 2
arr[remainder] = 3
You can see that, even though i continues to increase, the remainder resets itself after reaching a multiple of the array’s length. In that way, you can continue to wrap around the array without worrying about resetting or decrementing i.
This is a good refresher for basic division and multiplication
Briefly the remainder is what’s left after division - it’s a little complicated in javascript because numbers in javascript are real numbers - so 7 is actually 7.0 - 7 is the whole or integer part and 0.0 is the fractional part
Math.floor returns the integer part of positive numbers - Math.floor(7) is 7 and Math.floor(7.3) is 7 and Math.floor(7.9) is 7
So 7 / 2 is 3.5 - so 7 goes into 2 three times evenly - we say 3 is the quotient of 7 / 2 - we can get the quotient by applying Math.floor(7/2)
What about the remainder - is it 0.5? It is - but we are often interested in the integer remainder - one way to get the integer remainder is to remove the whole multiple of 2 from 7 - what’s left is a whole number too - so it’s 7 - 2*3 which is 1
This operation of subtracting the whole multiple of the divisor from the dividend is called modulo or remainder and has the % operator in javascript
So 7 % 2 is 1 and 6 % 2 is 0