Fractions - As Division (Intro)
Concepts
- Understand that fraction is just another form of division.
- Equivalent fractions.
- Mixed fractions
Introduction
Fractions is pretty easy to understand. You had one bone. Now there are two. Ouch! Jokes apart, think of fraction as just division. Usually, you divide a whole into pieces, and you get a “proper” fraction. Pizza’s are your go to tool here.
Fractions as division
You have a huge pizza. You have 10 eager children. How do we “divide” the pizza so that each one get’s the same amount.
- You cut the pizza into 10 pieces.
- You give each one 1 piece.
- So each one got 1/10.
- And that’s fractions for you. Specifically a “proper” fraction.
Fractions as division - intermediate
What if you had 5 small pizzas and you had to now divide it by 7 children? Still the same rules. Each one will get 5/7th of a pizza. That is:
- Cut each pizza into 7 pieces.
- Give 5 pieces to each child.
Fractions as division - advanced
What if you flipped it around - you have 7 pizzas and only 5 children to divide it by. Intuitively
- Each one gets a whole pizza.
- Of the two remaining pizzas, you split by 5 children.
- Each one gets 2/5 pizza.
- So total they get 1 and 2/5 pizza.
- This is called a mixed fraction because it “mixes” a whole number and a fraction.
- You can also say they get 7/5 pizza
- This looks odd, and is rightly called an “improper fraction”
- In an improper fraction the number on the top (the numerator) is greater than the number on the bottom (the denominator).
Misconceptions
- 6 students share 3 tarts equally.
- Is it 6/3 or 3/6?
- Think:
- What do you have? (Numerator)
- What do you have to divide it by? (Denominator)
- Answer:
- 3/6
In the real world
- Many laws of physics use fractions in their formula. For example:
- Density = Mass / Volume, a fraction.
- Dividing things equally, for example:
- 18kg of rice to 100 people