Another fraction question

[KBKMNN]

Ok, I think my brains must be leaking out on my pillow at night because I learn something, leave it for awhile and then forget it. :doh :doh

Anyway, I am doing a review in math with my son and we are working on fractions again. I know the basics of adding/subtracting fractions with unlike denominators a/b - c/d = (a x d) - (c x b)
b x d
In other words, multiply the denominators to get the common denominator, then cross multiply and then subtract and simplify.
I am doing mixed numbers and was wondering how do you know (if it's not right away obvious) to borrow from the whole number. For example here's a problem (and I already have the answer) 12 2/7 - 11 5/9 = 46/63
Ok, now to dummy me, it's not obvious that I need to borrow from the 12 and make it 1 7/7 plus adding the 2 to make it 11 9/11, then you can do the problem.
Is there an easy way to figure out 'when' to borrow?

[KBKMNN]

ok, sorry I cannot get the stupid problem to come out in my post correctly.

[Love4Jesus]

This is how I will do it. Old style.

12 2/7- 11 5/9= 46/63

12x7+2= 86/7 11x9+5=104/9



Common Denominator: For both numbers the best is 63 ( Do you know how to do get it? )
(86x9) - (104x7)
------------------ =
63
=774-728/63


=46/63

[Love4Jesus]

Well, I love math. So I looked for what you were trying to do. This is what I found.
12 2/7-11 5/9=46/63
11 (1+2/7) -11 5/9= 46/63
11 (7/7+2/7) - 11 5/9 =46/63
11 9/7 - 11 5/9 =46/63
9/7-5/9=46/63 (This step the 11's are gone 11-11=0)
81/63-35/63=46/63

Well, there you have the long old way and the short way.

[JPE]

I am doing mixed numbers and was wondering how do you know (if it's not right away obvious) to borrow from the whole number. For example here's a problem (and I already have the answer) 12 2/7 - 11 5/9 = 46/63

Ok, now to dummy me, it's not obvious that I need to borrow from the 12 and make it 1 7/7 plus adding the 2 to make it 11 9/11, then you can do the problem.
Is there an easy way to figure out 'when' to borrow?

You will need to "borrow" from the whole number when the fraction that is being "taken away" is bigger than the fraction that you're "taking from."

For instance:

5 3/4 - 4 1/4 = 1 2/4

(which can be reduced to 1 1/2) is an easy problem that doesn't require any borrowing because 3/4 is a bigger fraction than 1/4 so can be subtracted without any borrowing.

Now try 5 1/4 - 4 3/4. That's not as easy because 1/4 is smaller than 3/4, so you'll need to borrow from the whole number and rewrite 5 1/4 as a "improper fraction" in order to work it out.

Like this:

(Remember that 5 1/4 is the same as 4 5/4 if you borrow from the whole number to make an improper fraction)

5 1/4 - 4 3/4 = 4 5/4 - 4 3/4

= 2/4

= 1/2

If you think about it, whenever you are subtracting any numbers, whether they have fractions or not, you must always borrow from the number that's sitting in the next higher decimal place (to the left) if the number on top is too small to subtract from.

For instance: 525-475=

this will require borrowing from the 5 that is in the hundreds place and rewriting it as a 4 (I made it bold since there's more than one 5 in my dumb example) and rewriting the 2 as a 12 so that you have a number big enough that you can subtract a 7 from it. Do you follow?

Fractions are the very same way--if you need to borrow from the next higher decimal place to make the subtraction possible, you do it by subtracting 1 from the whole number and adding "1/1" (or 2/2 or 3/3 or whatever form you choose) to the fraction, to turn it into a compound fraction.

I hope that helps!

An afterthought: If you are having trouble understanding the whole "borrowing from the number in the next larger decimal place" routine, think about money for a minute:

If you have 5 one dollar bills and 3 quarters ($5.75) and need to give someone $4.25, you wouldn't need to get any change, would you? Of course not, you'd give them 4 one dollar bills and 1 quarter and you'd be left with 1 dollar and 2 quarters ($1.50).

But what if you have 5 one dollar bills and 1 quarter, and you need to give someone $4.75? You'd have to go to a cash register and ask for change for a dollar because you don't have enough quarters. So you'd get change for one of your dollars and you would then have 4 one dollar bills and 5 quarters (which is still the $5.25 you started out with, it's just in a different form) and you could easily give them their $4.75 and you would be left with 2 quarters remaining, fifty cents!

Now...if you look back up at the first examples at the top of this post, I just rewrote them as decimals instead of fractions so we could visualize them as coins. If you understood the coin illustration at the bottom then the same problems, written in fraction form, should make sense too.

5 3/4 - 4 1/4 = 1 2/4

5 1/4 - 4 3/4 =1/2__________________

[KBKMNN]

Thanks. I think it's one of those things where I just needed to sit back and pay attention to the actual fractions. Math just overwhelms me and I get too worked up about it. :doh :hehee

[Love4Jesus]

Hopefully I did not write too much. It's kind of confusing. Just remember if you take away from the whole number you have to change in fraction.
For example:
12 3/4
11 (1+3/4)
11 (4/4+3/4)
11 7/4