December 2021 – Makayla’s Blog

In this blog post I am going to focus on word problems- specifically a dilution question. Dilution meaning ” how many mL/L of water should be added to ___”. For these types of questions all you have to do is set the equation up properly and then solve. So the most important thing is to make sure you’re very careful when you’re reading the question.

Word problem: “How much bleach should be added to 50L of water to make the solution 8% bleach?”.

Step 1: The first thing we need to do is a let statement… this is so whoever is correcting your work will know what x is representing, because without a let statement you would more just have to guess. In this equation x is going to equal the amount of bleach added because everything else we already have numbers to insert into our equation but x is missing, it is what we are looking for.

Step 2: Now you need to set up your equation. So we know that 8/100 is what we are starting with. So that goes first. And that is equal to x/x+50 because x is our new amount of bleach, and our new amount of bleach+50 is our new concentration.

8/100=x/x+50

Step 3: Now we just cross multiply and solve for X.

8x+400 = 100x

400 = 92x

400/92 = 92x/92

x=4.3 L of bleach

Step 4: Always finish off with a sentence answer. ” 4.3L of bleach needs to be added to 50L of water to make 8% bleach solution. ”

And that is all. Make sure you always take your time and understand what the question is asking you.

This week we worked on adding/subtracting rational expressions. Just like adding or subtracting regular fractions, we need to have a common denominator meaning whatever we multiply the denominator by we need to multiply the numerator by, and then after that simplifying the equation and doing whatever factoring is needed.

Example:

Step 1: The first step is to make sure everything is factored. In this example everything was already factored so that step is done. Next state the restrictions. I find it much easier to do it at the start so I don’t forget when I have completed the question. The restrictions is anything that would make the denominator =0.

Step 2: Now we are going to look at the denominator and see what is missing from either side. I can see they both have a (d-2), so I don’t need to do anything with that. But the right side is missing a (d-4) as the left side is missing (d+1). So what I need to do is multiply either numerator with the missing denominator.

Step 3: Next, I FOIL the top, making sure I don’t make any mistakes as that would really mess up the rest of the question. I usually do this step twice to make sure everything was done correctly, as it’s very easy to make mistakes on.