Division

Division is "the action of separating something into parts or the process of being separated."

— Oxford Languages & Dictionary

Quick Overview of Division:

There are five parts of division: the dividend, the division symbol, the divisor, the equal sign, and the quotient

Example problem/equation: $128 / 16 = 8$

Terminology:

• Dividend - the number that we need to divide into smaller parts. This number will always be on the far left-hand side (LHS) of the equation. In the problem above, the dividend is 128

• Divisor - the number that will determine how many parts we divide the dividend into. This number will always be closest to the dividend and on the left-hand side (LHS) of the equation. In the problem above, the divisor is 16

• Division symbol ( $/$or $÷$ ) - this is how you know what operation the problem is. If the symbols look like / or ÷ then it is a division problem. In the problem above, the symbol, /, is shown so it is a division problem

• Equal Sign - the symbol (=) in the middle of the equation. This symbol sets the left-hand side (LHS) EQUAL to the right-hand side (RHS)

• Quotient - the number that is the result of the dividend being divided by the divisor. This number will always be on the right-hand side (RHS) of the equation. In the problem above, the quotient is 8

Rules of Division:

• Rule one - you can NEVER divide a number by 0. For example, $6 / 0$is not a valid division equation. Try typing in $6 / 0$on any calculator, the answer should say "undefined"

• Rule two - any number divided by 1 will always be itself. For example, $10 / 1= 10$. That rule won't change no matter how big or small the numbers get, or how complex the problem gets either

• Rule three - divided by 10, 100, 1,000, etc is the same as taking away the number of zeros you're dividing by. For example, $1,000,000 / 1,000$, is the same as taking away three zeros from both 1,000,000 and 1,000. So the answer would be 1,000. That means dividing by 100 would be taking away two zeros from both sides as well

Application of Division:

• Normally, division is used in order to split people, objects, etc into smaller groups. For example, if you have 26 students and you want to split them into groups of 2, how many groups would you have? Well, the equation would be $26 / 2$which would equal 13 groups

• While division may seem like a concept you just use in math, division is used a lot in real life. If you're able to get a good foundation to learn division, you can become more successful at a lot of things.

• Most times, multiplication and division go hand-in-hand, so if you can understand one then you can most likely understand the other too!

Complex Division:

• Complex division can mean many different things! It can mean decimal or fractional division, division involving larger numbers, and/or word problems

• Luckily, the concept of division will never change even while doing complex problems. So, if you're able to get good fundamentals, you can do any division problem!

• Some example problems are:

  • $6.2 / 1.7$

  • $1/4 ÷ 2/3$

  • And many more you will see later on!

Links to resources, videos, and worksheets:

• The Story of Mathematics (Website)

• Math Is Fun (Website)

• Math Is Fun (Worksheets)

Division Tables up to 12!

Lesson Complete!