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What I have learned about grade 9 fractions

Fractions on number line- For this you take the denominator and count how many spaces between each whole number. And you take the numerator and count the amount of spaces from 0. You do the same thing for negative numbers, all the same rules apply you just count to left on the number line.

 

\frac{2}{1}

 

_____________________________________________________________*________________________

0                              1                                 2                            3

 

Comparing Fractions- The first thing you have to do is change the denominator and change them so they are the same. Next you have to do whatever you did to the bottom to the top so that means times the top by whatever  number you did on the bottom. (<>=) If you have a negative and a positive fraction you already know whats bigger as one is positive. If you are comparing two negative fractions the same rules apply as if you are comparing positive ones.

\frac{2}{4} \frac{1}{2}

\frac{2}{4}  < \frac{2}{4}

Adding/subtracting fractions- You have to find the smallest common denominator then multiply the top by whatever you did to the bottom. Once you do that add/subtract the top numbers together but leave the denominator. After that if you can reduce it than you do. When adding or subtracting with negative numbers you have to remember were it goes on the number line and I like to think about the tug a war way.  You still find a commun denominator. You follow all the same steps you just have to find out if the answer will be positive or negative for your final answer but all the steps are the same.

\frac{2}{4} + \frac{5}{8}

\frac{4}{8} + \frac{5}{8}

\frac{9}{8}

Subtracting:

\frac{-3}{8} – \frac{-11}{12}

\frac{-9}{24} – \frac{-22}{24}

\frac{-22}{24}

 

 

Multiplying/dividing fractions

To multiply just put it into its lowest terms or simplify after and then multiply both of the denominators and numerators. To do this with negatives you follow all the same steps but you use the sign rules witch are if you multiply/divide a -/+ it would equal negative, but -/- and +/+ will both equal positive.

\frac{4}{2} x \frac{1}{2}

4×1

_____

2×2

\frac{4}{4}

=1

And for dividing you pretty much do the same thing but you flip the last fraction and multiply it.

I learnt how to reduce numbers because i was never that sure. To reduce a fraction to lowest terms, divide the numerator and denominator by their greatest common factor. I also learnt how to understand a more visual way of learning math because iI have never really had a teacher teavh like that before.

\frac{14}{49} = \frac{2}{7}