MTH 085 – BASIC MATHEMATICS
CLASS 13: LECTURE NOTES – SECTION 1.5
1.5: DIVIDING WHOLE NUMBERS
Basic Terminology
____________________ is simply repeated subtraction.
For example, we can rewrite 12 – 3 – 3 – 3 – 3 = 0 : ___________ = _____.
We say 3 _______________ _______________ into 12, or 12 is _______________ by 3 since there is
nothing left over.
However, 13 – 3 – 3 – 3 – 3 = 1 : __________ =_________.
In this case 3 does not divide evenly into 13, or 13 is not divisible by 3. This time, there is a
_______________________ leftover.
Forms of division:
1. Standard division: _________________________________________________
2. Long division: _________________________________________________
3. Fractional division: _________________________________________________
Circular form of division:
Dividend ÷ divisor = quotient ⇔ ____________________________________________
Dividend ÷ divisor = quotient with remainder ⇔ ____________________________________________
For example,
12 ÷ 3 = 4 ⇔ 4 × 3 = 12
13 ÷ 3 = 4 r 1 ⇔ 4 × 3 + 1 = 13
MTH 085 – BASIC MATHEMATICS
CLASS 13: LECTURE NOTES – SECTION 1.5
Dividing by zero:
The divisor can never be zero!!!!!
For example,
3
0
0÷3=0
0
3
=0
BUT,
0
3
3 ÷ 0 = undefined
3
0
= 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
The remainder in division:
The remainder must be
1. __________________________________________________________________
2. __________________________________________________________________
3. ___________________________________________________________________
For example, consider 13 ÷ 3
3
13
3
13
3
13
Today’s Examples
1. Dividing by one-digit divisors (short division, no remainder)
2. Dividing by one-digit divisors (short division, with remainder)