There are two different properties of equality. They are the addition or subtraction property of equality and the multiplication or division property of equality. The addition or subtraction property of equality is to add or subtract the same element on both sides of the equal sign. The multiplication or division property of equality is to multiply or divide by the same element on both sides of the equal sign. One important reminder when using the multiplication or division property of equality is that you never divide by zero.
Although the addition or subtraction property of inequality is the same concept as the property of equality, the rule for multiplication or division property of inequality is different. The rule for this is that we can multiply or divide by a positive number on both sides…no problem, but if we multiply or divide by a negative number the inequality must be reversed. These rules are used for problem solving and are fairly easy to remember.
It feels like just yesterday when I was sitting in my 3rd grade classroom learning about inequalities. My teacher taught my class the “alligator trick.” The “alligator trick” is the idea that the alligator eats the larger number, but I have learned that the “alligator trick” is not a very good technique to teach to elementary students. This is because the idea that the alligator eats the larger number can become very confusing. An example of this is -5<-8 (-5 is less than -8) or -5>-8 (.5 is greater than -8). -5 is actually greater than -8 on a number line, but because most students look at the number before the sign it can get confusing. The picture below is also confusing because the 3 is written smaller than the 2 in size, but the 3 is actually greater than the 2 on a number line. Avoiding this trick is a good idea to avoid any confusion.