Today we discussed how to add and subtract fractions without common denominators. One way, the way most of us use first, is to find a common denominator and add or subtract the numbers like normal. This can be confusing though, even to us, so it may not be the best way to teach children.
Take the following for example:
7 1/3-4 3/4
My first thought when seeing this problem was to change both fractions to a denominator of 12, resulting in 7 4/12 and 4 9/12. This can get confusing though since 4 is less than 9, so you then have to subtract 5/12 from a whole, which is where most people make mistakes.
A more simple way, that is also more visually understandable, would be to use a number line.
We then moved on to multiplication and division of fractions. When discussing division of fractions, for example 4/6 divided by 3/4. You would write it as 3/4 of 4/6, and as most of us from elementary school can remember of=multiply.
We did a couple of example problems, and on Thursday we had a more in depth lesson on the division of fractions.
Thursday April 11th
As said above today we went more into division of fractions. The rule we've all been taught is to invert (flip) the second fraction (the dividend) and multiply it by the first number (the divisor). But none of us really know why we do this.
There are different ways of dividing fractions that actually allow us to conceptually understand what we're doing.
Partitioning: take the dividend and split into groups.
Repeated Subtraction: How many of the divisor go into the dividend.
For instance:
3 divided by 1/2...most people will answer this question with 1.5 (myself included)
The correct answer is actually 6. Because the problem isn't telling you to divide 6 in half, it's asking how many 1/2 groups are in 6.
We then went on to discuss an easier way to divide fractions, if the two fractions have common denominators (or you convert them so they do) you can just focus on the top numbers (the numerators) and divide those.
Take for example:
12/25 divided by 4/25
Since the denominators are both 25 you can just focus on the numerators and do 12 divided by 4, which equals three, which is your answer! Talk about easy.
Some people were confused by this. Why can you just ignore the bottom number?
Well if you don't ignore the bottom number you can see you end up with the same solution....
12/25 divided by 4/25 you would end up with 12÷4 over 25÷25...well 12÷4=3 and 25÷25=1 so you would end up with 3/1 which equals three. So knowing that the denominators equate to one, you can simply skip this step and just work with the top numbers.
We ended this class with some discussion of converting fractions to decimals and percents.
Hope this was helpful!
You did a really nice job of explaining how we were taught to find the common denominator. I had a hard time NOT using that method because it has been drilled into my head for so long! I really hate doing fractions but the way we talked about dividing the fractions really helped me. You did a really good job of explaining the step by step approach to finding the common denominators in dividing fractions and then just dividing straight across with the numerators. Christina always gives me an a-ha moment when she explains the new ways of doing these simple things we learned as kids! Great job on your post, it was a good refresher on the concepts we covered in class and made a lot of sense.
ReplyDeleteYour blog post was really good at having all the information needed to understand this topic. I had an issue with multiplying and dividing fractions with different denominators but this helped me understand it a lot better. One of your images is with black text so it was kind of hard to read it with the dark background. Maybe have it be in white font next time? Otherwise your visuals were very good and helpful as well. I really liked your number line image.
ReplyDeleteYour blog was great!
ReplyDeleteIt was full of information that we learned in class that was broken down quite nicely! I really liked the illustration that you had that went along with the number line. I liked how you did not include the old way of multiplying to find common denominator when we are adding and subtracting fractions. This is the way most of us learned and I am find out that it is not helpful or time efficient!
Great job on your blog!
ReplyDeleteI really liked how you included that handy picture of how to subtract fractions a different way, rather than using the "find the common denominator" way. It is definitely a bit confusing at first, subtracting in ways that you never have, at least for me. So that number line picture was very helpful!
You have one of the best put together blogs in the whole class every week! I like that you chose the specific example of 3 divided by 1/2 and how most people would end up with 1.5, but that would have been a multiplication problem. You did a good job of defining partitioning and using repeated subtraction, which was great because I often time mix up which method is which. Once again, really good blog!
ReplyDelete- Sam Gaume
your blog was explained very well! I really like the images you put in for examples so that we could visually see how to solve the problems. The way you solved the subtraction problem really made it easier for me.
ReplyDeleteYour blog does a very good job explaining everything covered in class, the methods are easy to understand and follow. The definitions of partitioning and repeated subtraction are short and straight to the point making them easy to comprehend. The pictures and examples you used are very helpful as well, but the division picture was hard to see with your background, other than that this is the best blog I've seen yet.
ReplyDelete