# What I have learned about grade 9 fractions

A fraction is a way to show a portion of a number. It’s also another way of writing a decimal. A numerator is the number on top and denominator is the number on the bottom.

When displaying numbers on a number line always remember the left side of the zero is negative and the right side is positive. In the examples below I am locating -3/4 and 2  1/2

Step 1=  Give them a common denominator.

Step 2= Since their denominators are four, map out every four lines on the map.

Step 3= Note: for every star that represents a whole number, every line between the whole numbers would equal 1/4.

Step 4=  Now that you know where the fractions all are, place them where they belong.

When comparing fractions, you use the following symbols >, =, <. If the two fractions are equal, then you put the = sign. Whatever fraction is smaller you put the arrow pointing at it, so if the smaller number is on the right you would use this > sign. If one number is negative and one is positive, the negative will always be smaller because it is below 0, unlike a positive number which would always be above 0. A easy way to compare the fractions are to give them a common denominator. When comparing two positive numbers the bigger number is always bigger, but when it comes to comparing positive fractions the bigger number is smaller. If you look at a number line the negatives start at negative one and as you look to the left  the number goes up by one. The number on the number line that is further to the left is ALWAYS the smaller number.

Example of comparing fractions:

When adding fractions, first you find a common denominator. A good trick to find a common denominator is to just multiply the two denominators together. Then you add the numerators. If you are working with a positive and a negative number, a good method to use is tug of war. Tug of war is where you put all the positives on one side and all the negatives on another, then add all the positives up and all the negatives. Then you look for the difference between the two numbers and that’s your numerator. (Note; the denominator will be the one you found earlier).

Example of adding fractions:

Example of tug of war:

When subtracting fractions, first you will find a common denominator. Then you will subtract the numerators. Hint: If it is a number subtracted by a negative, you will change it to a number plus a positive. Think of those two negative signs beside each other as a broken positive that you must put back together.

Example of subtracting fractions:

Example of a number subtracted by a negative:

When multiplying fractions, you first make sure that any fractions that have a whole number are improper (an improper fraction is a fraction where the numerator is bigger than the denominator).  Then “you just do it”, this means you multiply the bottom numbers together and the top. Then if one of the fractions is negative and one is positive, then the answer will be negative. If both fractions are positive, or both fractions are negative, then the answer will be positive.

Example of multiplying fractions:

If one of those fractions is negative then the answer will be negative. If both those fractions were negative it will still be a positive answer.

When dividing fractions, you first make sure that any fraction with a whole number is changed to an improper fraction. Then you switch the division sign with a multiplication sign and then you flip the second fraction so that the numerator is now the denominator and the denominator is now the numerator. Then “Just do it”.

Example of dividing fractions:

If one of those fractions is negative then the answer will be negative. If both those fractions were negative it will still be a positive answer.