What I Have Learned About Grade 9 Fractions

What I Learned About Grade 9 Fractions

Number Lines

I learned that when locating a fraction in a number line, I have to look at the denominator first to know how many parts should be in between the whole numbers like 0 and 1. For Example:

$\frac{-2}{3}$ $\frac{2}{3}$

The first fraction has a negative sign. Negative numbers are normally located at the left side of zero which means I have to start from zero then move further left. While the second fraction is positive. which means I have to start on the right side of zero. The numerator tells us how many parts are chosen, while the denominator tells us the total number of equal parts into which 0 and 1 are divided.

|_____|_____|_____|_____|_____|_____|

-1 $\frac{-2}{3}$ $\frac{-1}{3}$ 0 $\frac{1}{3}$ $\frac{2}{3}$ 1

Notice that they both have the same distance from zero? When numbers have the same distance from 0, it creates zero pairs.

Comparing Fractions

I learned when comparing fractions, it’s way easier to compare them by finding their common denominator. If they are both positive fractions, the one that is far from zero is larger but if it’s closer to zero then it’s smaller. For example:

$\frac{6}{8}$ $\frac{4}{9}$

Since the denominator 8 and 9 don’t have anything in common, I’m going to multiply the numerator and denominator by 9 to get $\frac{54}{72}$ . Then I’m just doing the same process to the second fraction but I’m going to multiplying it by 8 so, I can get $\frac{32}{72}$ .

So, $\frac{54}{72}$ > $\frac{32}{72}$

The simplest way that I learned to compare fraction with a negative fraction is that a positive fraction is always greater than a negative fraction. $\frac{-3}{5}$ < $\frac{2}{5}$

If there are two negative fractions to compare like this:

$\frac{-1}{4}$ $\frac{-3}{4}$

I knew that -1/4 is greater than -3/4 because the closer you are to zero it’s larger but, if you are far from zero, then it’s smaller.

So, $\frac{-1}{4}$ > $\frac{-3}{4}$

Adding and Subtracting Fractions

I learned that when adding and subtracting fractions with different signs will be simpler if I’m going to find their LCM (least common multiple) first. For example:

$\frac{-2}{3}$ + $\frac{2}{4}$

The common denominator is 12 because 3 and 4 are equal to 12. Then multiply -2 by 4 is -8, and 2 multiplied by 3 is 6.

So, it’s now $\frac{-8}{12}$ + $\frac{6}{12}$ which equals to $\frac{-2}{12}$ . Lastly, I simplified this by dividing the numerator and denominator by 2 so the answer is $\frac{-1}{6}$

Another example for subtracting fractions:

$\frac{-1}{2}$ – $\frac{2}{7}$

$\frac{-7}{14}$ – $\frac{4}{14}$

$\frac{-11}{14}$

Multiplying and Dividing Fractions

Multiplying fractions are easy because all I have to do is multiply the numerators and denominators, and I can simplify the answer if possible. For example:

( $\frac{-6}{10}$ ) ( $\frac{-5}{8}$ )

$\frac{30}{80}$

$\frac{3}{8}$

The product turned into positive because if there are two signs that are the same, it turns positive, and if they’re both have different signs then it turns negative. Same thing in division, if there are even number of signs like 2 negatives then they turn into positive, if there are odd numbers of signs then it’s negative.

Dividing fractions got easier when I learned about reciprocal, which means switching the numerator and denominator and changing the operation from division to multiplication. For example:

$\frac{-5}{12}$ ÷ $\frac{-2}{3}$

$\frac{-5}{12}$ x $\frac{-3}{2}$

$\frac{15}{24}$

$\frac{5}{8}$

Aiessa Magi's Blog

What I Have Learned About Grade 9 Fractions

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