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# Simplifying Fractions

### Simplifying Fractions

You can make fractions easier to read by simplifying them.

Pizza A was divided into four slices and two are left. What is this as a fraction?

Pizza B was divided into six slices and three are left. What is this as a fraction?

So there are a different number of slices left of each pizza

There are $\dfrac{2}{4}$ slices left of pizza A. There are $\dfrac{3}{6}$ slices left of pizza B.

There are a different number of slices but is this statement true or false?

*There is the same amount of pizza left in pizza A and in pizza B.*

In both cases, the remaining pizza takes up half a plate

So in fact, $\dfrac{2}{4}$ and $\dfrac{3}{6}$ stand for the same amount. **** We say they are **equivalent** to "one half" or $\dfrac{1}{2}$.

You can change for example $\dfrac{3}{6}$ into $\dfrac{1}{2}$ because they are equivalent. To do this, we need to __________ the fraction.

Simplifying fractions

When you simplify a fraction, you make it easier to read. For example, it is much easier to read $\dfrac{1}{2}$ than to read $\dfrac{46}{92}$.

True or false? *There is the same amount of cake left in both cake A and in cake B.*

What is the fraction of cake left on plate A?

The fraction of cake on plate B is $\dfrac{2}{6}$.

This shows that $\dfrac{3}{9}$ and $\dfrac{2}{6}$ are equivalent fractions, they are the same amount of cake.

True or false? *You can simplify* $\dfrac{3}{9}$ *and* $\dfrac{2}{6}$ *to* $\dfrac{1}{3}$.

Pizza A has four out of eight slices left or $\dfrac{4}{8}$. What is the simplified equivalent fraction for this?

Pizza B has four of six slices left or $\dfrac{4}{6}$. What is the simplified equivalent fraction to this?

Although both pizzas have four slices left there is more of pizza B left than pizza A.

This shows that $\dfrac{2}{3}$ and $\dfrac{1}{2}$ are not equivalent fractions.

Is it correct to simplify $\dfrac{4}{12}$ to $\dfrac{2}{6}$?

However!

If you simplify $\dfrac{4}{12}$ to $\dfrac{2}{6}$, you haven't simplified the fraction **fully** - it can be simplified further!

Which fraction is the simplest fraction that is equivalent to $\dfrac{4}{12}$ and $\dfrac{2}{6}$?

$\dfrac{1}{3}$ is *fully simplified* - it is as simplified as it can be

Fractions cannot contain decimals, so you **can't** change $\dfrac{1}{3}$into $\dfrac{0.5}{1.5}$, for example.

How simplifying fractions really works

How do you actually get from $\dfrac{3}{9}$ to $\dfrac{1}{3}$ when simplifying the fraction?

$\dfrac{12}{30}$ can be fully simplified to $\dfrac{2}{5}$. What number have you divided both the numerator and the denominator by?

When simplifying a fraction you must divide the numerator and the denominator by the same number.

$\dfrac{12\div 6}{30\div 6}=\dfrac{2}{5}$ you can see that the same number is used for both the numerator and the denominator.

You have fully simplified a fraction when there is no number that divides into both the numerator and denominator. Which fraction here is not fully simplified?

Which number can we use to simplify $\dfrac{4}{10}$?

We can divide the numerator and denominator in $\dfrac{4}{10}$ by $2$.

This gives $\dfrac{2}{5}$ which is fully simplified!

Fully simplify $\dfrac{24}{72}$

We can do this in one step or several steps.

First let's notice that both numbers here are even so we can divide them by $2$. What to we get when we do that $\dfrac{24\div 2}{72\div 2}=$?

Is $\dfrac{12}{36}$ fully simplified?

We can simplify further. What happens now $\dfrac{12\div 12}{36\div 12}=$?

We have simplified the fraction from $\dfrac{24}{72}$ to $\dfrac{1}{3}$.

This is now fully simplified!

Fully simplify $\dfrac{12}{15}$.

Fully simplify $\dfrac{48}{64}$.

Summary! Simplifying fractions makes them easier to read

The original fraction and the simplified fraction have to represent the **same amount**.

You have *fully* simplified a fraction when the numerator and denominator can't get any smaller

This means that there is no number that divides into both the numerator and denominator.

To fully simplify $\dfrac{30}{75}$: First $\dfrac{30\div 5}{75\div 5}=\dfrac{6}{15}$ and then $\dfrac{6\div 3}{15\div 3}=\dfrac{2}{5}$.

Or do it in one step $\dfrac{30\div 15}{75\div 15}=\dfrac{2}{5}$