# How do you simplify the fraction \frac{18}{24} ?

How do you simplify the fraction $$\displaystyle{\frac{{{18}}}{{{24}}}}$$ ?

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turtletalk75
Explanation:
When simplifying a fraction you always would like to find a common number that goes into both the denominator and numerator, so both values can be simplified by that common number. This number has to be the highest value that can fit into both numbers.
As 18 is the lowest number, that common number must be $$\displaystyle\le{18}$$. By trial and improvement, we can conclude that 6 is the highest common multiple that can fit into both numbers. Therefore we divide both 18 and 24 by 6 to simplify the fraction.
$$\displaystyle{\frac{{{18}}}{{{24}}}}\to{\frac{{34}}{}}$$
As..
$$\displaystyle{\frac{{{18}}}{{{6}}}}={3}$$
$$\displaystyle{\frac{{{24}}}{{{6}}}}={4}$$
$$\displaystyle{\frac{{{18}}}{{{24}}}}\to{\frac{{{3}}}{{{4}}}}$$
###### Not exactly what you’re looking for?
Medicim6
Explanation:
I will show two methods:
Method 1:
We can rewrite 18 as $$\displaystyle{2}\cdot{3}\cdot{3}$$ and 24 as $$\displaystyle{2}\cdot{3}\cdot{4}$$. This may seem strange, but it will prove to be very useful. Our new fraction is:
$$\displaystyle{\frac{{{2}\cdot{3}\cdot{3}}}{{{2}\cdot{3}\cdot{4}}}}$$
$$\displaystyle{\frac{{{2}\cdot{3}\cdot{3}}}{{{2}\cdot{3}\cdot{4}}}}$$
Here, the 2s and 3s on the top and bottom will cancel, and we're just left with $$\displaystyle{\frac{{34}}{}}$$
Method 2:
Alternatively, this is the more traditional method. We need to divide the numerator and denominator by a common factor. We can divide by 6 to get:
$$\displaystyle{\frac{{34}}{}}$$
nick1337

Explanation:
The first thing to recognize is that $$18=2\cdot9=2\cdot3\cdot3$$ and
$$24=2\cdot12=2\cdot2\cdot6=2\cdot2\cdot2\cdot3$$
So, $$\frac{18}{24}=\frac{2\cdot3\cdot3}{2\cdot2\cdot2\cdot3}$$
From here, you can cancel terms appearing in both the numerator and denominator:
$$\frac{2\cdot3\cdot3}{2\cdot2\cdot2\cdot3}=\frac{3}{2\cdot2}=\frac34$$