Dedication:
For my friend.
I (Mathematicus, a.k.a. Mathematikos) love angle bisectors (and line bisectors), which I learned about in 6th grade. I also love fractions. I love especially changing a decimal into a fraction or percent, or vice versa.
But this blog post is not about anything but fractions. I like multiplying fractions, and dividing them especially. 😀 This is about subtracting fractions, though.
The subtraction of fractions (you’ll be learning that in 6th grade, I did) I describe below (please read it, even if you don’t quite get it).
Your subtraction problem is:
7 1/6 – 3 1/3 = 3 5/6
So, like, say Mom made seven pies, and an extra one-sixth of a pie (I don’t know why she did that). Then Minny smuggled three pies and one-third of another pie to to the dog (taking some of it for herself, of course, but if I told you that amount, it would make it more confusing). So, how much pie is left that Minny and the dog didn’t eat?
Right now your math problem is set up like this:
7 1/6
– 3 1/3
________
(difference, a.k.a. answer for a subtraction problem)
Well, you have to make the denominators the same. The denominator is the part of the fraction that tells you into how many pieces the thing was divided, not how many pieces there are. In one-sixth ‘sixth’ is the denominator. ‘one’ tells how many sixths. This part is considered the numerator.
You can’t subtract one-sixth from one-third without getting a negative number (just focus on the fractions right now, not the whole numbers).
You must find an equivalent fraction, which is a fraction that is equal to another fraction (a half is the equivalent fraction of two quarters, but a half is the reduced fraction).
Since you can’t make one-sixth into one-third without making the numerator of one-sixth into 0.5 (which you could do, although I don’t recommend it), you have to make the denominator of one-third into sixth. (You could change the denominator into twelfth, but it’s unnecessary in this problem to change both fractions.)
You must change the numerator of one-third as well, because one-sixth is half of one-third, and you want to have equivalent fractions. The numerator must be two, because the denominator sixth is half of third (the fraction you started out with).
Now your fraction reads two-sixth (2/6).
Now your math problem is set up like this:
7 1/6
– 3 2/6
________
(difference)
Congrats! You have officially set up your math problem (finally!).
Now, you can’t subtract 1/6 from 2/6 without getting a negative number (which is -1/6). However, we have a whole number (7, to be precise) just waiting for you! So do carrying. cross out the 7 and replace it with a 6. Now since 6/6 (six-sixths) equals a whole (another equivalent fraction), and you just took a whole away from 7, you must give the whole (6/6) to the 1/6. But since you have 1/6, you must add 1/6 to 6/6 (equaling 7/6, an improper fraction) before putting the fraction down.
As a note, your 7 1/6 number didn’t go away, you just carried, giving 1/6 a whole (6/6).
Now you math problem is set up like this:
6 7/6
– 3 2/6
_______
(difference)
Now you just have to subtract! Do the fractions first. Now that you aren’t going to get a negative number, just ignore the denominator and subtract the numerators (7 – 2 , which is elementary). Put your answer down, like this (including the denominator, which doesn’t change when you subtract (it does when you multiply, but let’s not get into that quite yet):
6 7/6
– 3 2/6
________
5/6
Isn’t this working out nicely?
So now, just subtract 6 from 3, and put your answer down like this:
6 7/6
– 3 2/6
_______
3 5/6
And your answer is 3 5/6 (three and five-sixth)!!!
Congrats!
You survived a crash course in the subtracting of fractions!
