1.1.4 Remainder

Let’s suppose we want to divide a number by a number which is NOT one of its divisors. From what we saw before, the result of such division is guaranteed NOT to be an integer.

For example, let’s say we want to divide 20 by 8 (8 is not a divisor). In those cases, we can express the division in the following three ways:

1. As a fraction (20/8)*
2. As a decimal (2.5)
3. As a quotient and remainder (2R4)

Convention: (/) represent a fraction (1/5 or “one fifth”), whilst (%) represents a division (1%5 or “one divided by five”).

We will look at 1. and 2. closer in the following lesson. Let’s now focus on 3.

There are only 3 steps to find the quotient and remainder of a division. We will see them through the following example.

Example: Find the quotient and remainder of 22 % 5**

Convention: In a fraction and a division, the number above the division/fraction line is called numerator and the number below that line is called the denominator.

① Find the Quotient: Try to “reach” the numerator using multiples of the denominator.

Multiples of 5: 5 (5 x 1), 10 (5 x 2), 15 (5 x 3), 20 (5 x 4), 25 (5 x 5)…

20 is the closest number to our numerator that does not exceed it. 4 (the number by which we multiply 5 to obtain 20) is our quotient.

② Find the Remainder: Figure out the difference between 20 and the numerator (the difference should always be positive).

That difference is 22 – 20 = 2. This is our remainder.

③ Express the division as quotient and remainder in the form [Insert Quotient] R [Insert Remainder].

Answer: 4 R 2.

Note: This method has the advantage that we can express the result of a division only with integers (2 and 4 in this case) and without the need of decimals or fractions.