Today Aiden and I continued working with isolating inequalities. We saw decimals and fractions in the inequalities and Aiden had to recall how to use inverse operations to solve. The only “trick” is to remember that when we multiply or divide by a negative number we must flip the inequality symbol. We practiced few problems with and without negatives. One problem required us to multiple by -3.4. Aiden forgot to flip the inequality sign, but realize he made an error somewhere when he checked his solution. Aiden said, “I understand we’re supposed to flip it, but I don’t understand why.” I explained to him that working with equations (equal signs), the equation will remain a true statement as long as “what you do to one side you do to the other”. However, when working with inequalities, this is not necessarily the case. For example if we start with 2<5 which is a true statement and we multiply both sides by -1 then according to equation rules -2<-5 should be a true statement. But we know it’s false, -2 is not less than -5. So to make it true, we have to manually switch the sign. I explained to Aiden that this is based off the premise that large negative numbers are actually smaller. Aiden put his hands on his head and said “Ah ha! It’s all coming back to me now!” With practice, flipping the sign will become more natural.