Understand that fraction is just another form of division.
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).
6 students share 3 tarts equally.
Is it 6/3 or 3/6?
What do you have? (Numerator)
What do you have to divide it by? (Denominator)
In the real world
Many laws of physics use fractions in their formula. For example: