Fractions

Fractions

11-2-2020

Open Ended

We're going to do a mini-games to start today. I'll check your answers later.

Write down as many fractions as you can that are equal to 1. You have 2 minutes.

Fractions = to 1

Here are a few examples you could have typed. Notice the pattern:

2/2 , 3/3, 4/4, 5/5, 11/11, 15/15, 24/24, 117/117, 357/357

In order for a fraction to be equal to 1, it has to have the same numerator and denominator.

All the examples I provided have the same numerator and denominator, so they are all equal to 1. They are all cut into different amount of pieces, but since there numerator is equal to their denominator the value of all of my fractions are the same.

Ok, why is that important?

Knowing an infinite number of fractions = to 1 is important because this unit is all about changing fractions in order to get a common denominator.

Example 1:

5/6 + 11/12 =

These cannot be added unless the number on the bottom of both fractions is the same.

However, I know that I can get 5/6 to have a denominator of 12 by multiplying it by 2/2.

So 5/6 x 2/2 = 10/12.

The reason this works is because 2/2 is equal to 1. All I'm doing is multiplying 5/6 times 1. I didn't change the value of 5/6, only the name.

Example 1 cont...

5/6 + 11/12

Now that I've changed 5/6 by multiplying by 2/2 to get 10/12. All I have to do is add the fractions together.

10/12 + 11/12 = 21/12. (good answer)

1 9/12 One and nine twelths (better answer )

Example 2

2/3 + 1/4 =

Here, I need to find a common denominator for these fractions.

I know that both denominators are in the fact family of 12, so that is what I'm going to change them to.

2/3 can be multiplied by 4/4 to get me the denominator I want. And 1/4 can be multiplied by 3/3 to get the denominator I want.

2/3 x 4/4 = 8/12

1/4 x 3/3 = 3/12

In a nutshell

All we are doing every time is getting a common denominator for 2 fractions by multiplying by a version of 1. (2/2 or 3/3 or 4/4 or whatever we need to use to get the denominator we want.)