In the first couple weeks of Grade 9 math, we have learned about how to place fractions and improper fractions on the number lines, using both negative integers and positive integers. To do so first, you have to find a common denominator and then make sure that the number line is split into sections of said number. To place a mixed number on the number line, you can either change it into an improper fraction, or keep it as it is, but not if the denominator is different than what the sections of the number line is divided into.
Comparing fractions is slightly easier, as you only need to find a common denominator, and the multiply accordingly to get the same denominator. However, what you do to the bottom, you must do to the top number, so you have to multiply it by the same number as you did with the bottom. The larger number is always the larger one, but if it is a negative number for both fractions, the number closest to 0 is the largest.
Adding and subtracting is quite the same deal. You have to find a common denominator, and whatever you multiplied by to find it, you have to repeat that to the top number. For multiplying, you can just do the question as it is, but you must remember to reduce the answer further if you can. Dividing isn’t quite the same deal. For dividing, you must change the question into a multiplication question, but instead you must invert the fraction to the right of the multiplication sign.
One thing I have learned is that if you have a positive number over a negative number in a fraction, you can move the negative sign to the top number. That makes it a lot easier, and a good saying is “to work smarter, not harder,”