What I have Learned About Grade 9 Fractions

Grade 9 Fractions – By: Emily Rosh

October 11th, 2018.

In this post, I will be demonstrating how to:

  • Display Negavite fractions on a numberline
  • Compare Fractions
  • Add & Subract Negative Fractions
  • Multiply & Divide Negative Fractions

How to Display Negative Fractions on a Number line:

Let’s start off with the basics… To display negative fractions, you will need to always remember; negative numbers are to the left of zero & the farther to the left the smaller the number is. Positive numbers are to the right of zero & the farther to the right the bigger the number is. You should also have learned how to add, subtract, multiply, and divide integers before learning the following.

 \frac{-4}{6}

Step 1 (Denominators):

A simple way to find fractions on a number line is knowing what the denominator represents. The denominator corresponds to the number of steps between one whole number and the next (How many parts to “Divide” or “Break” the line into before the next whole number). Tip: A helpful way to keep track is to draw “Bubbles or Bumps” to count your denominator steps.

Eg.

Step 2 Finding the Numerator:

To find the numerator on a number line; Look at the fractions numerator and count the number of spaces/steps (starting at zero) in the direction either negative or positive depending on your fraction.

How to Compare Fractions:

Comparing fractions can be very easy, as it can be hard. When comparing you always want to be careful and pay attention to the negative numbers. To show which one is greater or lesser we use symbols like <, >, or =.

\frac{11}{4} \frac{-13}{3}

Step 1:

When working with fractions, you often encounter a Mixed Number Fraction or an Improper Fraction. For comparing fractions, you want to work with Improper fractions if possible, this is because you can clearly see the differences in size/amount.

Comparing fractions means looking at two fractions and figuring out which one is greater. To compare fractions, all you have to do is to make it so that they have the same denominator and then see which fraction has the greater numerator.

The first thing you want to you do is turn both fractions into Improper Fractions if they aren’t already. You do this by multiplying the whole numbers by the denominator, then add the numerator.

Eg.

Step 2:

From there, you are going to find the common denominator between both fractions. (You can simply multiply one by the other).

 

Step 3:

Once both fractions have a common denominator its will be clear which one has the greater or least fraction. Remember to watch out for any negative symbols as it can change the answer. Now at this stage you may use <, >, or =.

 

Adding and Subtracting Fractions:

Adding Example (Rules apply to both adding & subtracting):

2\frac{-3}{5}  +  \frac{6}{3}

Step 1:

When adding  fractions, you always want to start off with making both fractions Improper. You do this by multiplying the whole numbers by the denominator, then add the numerator.

Eg.

Step 2:

Now, you need to find the common denominator.  An easy way to do this is multiply them by each other.

Eg.

Step 3 Tug of War:

This is your final step. Now, you want to add (or subtract) the numerators (Keeping Demoninators the same). Tip: Let’s use a “Tug of War” scenario, and the numbers are “people”. The more people (total of numbers) who show up on either will win.

eg.



So, the answer for this example (adding) is: $latex \frac{-9}{15}.

Multiplying and Dividing Fractions:

Multipying:

\frac{-3}{4} x \frac{6}{12}

Step 1:

Multiplying fractions is very simple. To start, you will want to make sure both of your fractions are Improper Fractions if they are not already. You do this by multiplying the whole numbers by the denominator, then add the numerator.

Step 2:

Multiplying Fractions is very simple. You multiply the numerator by the numerator, and the denominator by the denominator.

Eg.

Step 3:

From there you may choose to simplify. You do this by dividing both the Numerator and denominator by the same divisible number.

Eg.

 

Dividing:

\frac{2}{9}  ÷ -1\frac{2}{3}

Step 1: To start, you will want to make sure both of your fractions are Improper Fractions if they are not already. You do this by multiplying the whole numbers by the denominator, then add the numerator.

Eg.

Step 2:

 

Now, you multiply by the reciprocal (This means to flip one fraction and multiply across). (Appling the multiplication skills from above)

Eg.

Step 4:

From there you may choose to simplify. You do this by dividing both the Numerator and denominator by the same divisible number.

Eg.

Criteria:

Explain and show how negative fractions are:

  • a) displayed on a number line
  • b) how you compare fractions
  • c) adding and subtracting fractions (where at least one is negative)
  • d) multiplication and division of fractions (where at least one is negative)
  • due:  Weds Oct 17th – tag:  fractions

*All images used were made from word and screenshots by Emily*

Leave a Reply