Can someone please explain to me very elaborately ,in subtracting mixed fractions, how to solve the problem if the the first numerator is less than the next. For instance, numerators like 5 and 7 that can't be subtracted from each other. I'm having trouble understanding the borrowing process.

Question

amistre64 · Answer

realize that a number like:$$2\frac34=2+\frac34$$

amistre64 · Answer

if its borrwing you need, borrow 1

do you ahve an example we can work?

amistre64 · Answer

borrowing is just a way of rewriting a number into something equal but possibly simpler

  523  = 500 + 20 + 3
-416  = -400 -10 -  6


  523  = 500 + 20-10+10 + 3
-416  = -400 -10 -  6


  523  =  500 + 10 +13
-416  = -400 -10 -  6
-------------------
  107 =   100  +0   +7

amistre64 · Answer

we borrow a 'unit' measure to help out if need be.

since a fraction is less than 1,  the unit value to borrow is 1

$$~~~~2+\frac58\-1-\frac78$$

$$~~~~2-1+\frac88+\frac58\-1-\frac78$$

$$~~~~1+\frac{13}8\-1-\frac78\-------\
~~~~~0+\frac68
$$

anonymous · Answer

How about a question like...

anonymous · Answer

Understand that 9 is the same thing as 27/3, and that 7 is the same thing  as 21/3

anonymous · Answer

Okay thanks! I got it.

amistre64 · Answer

if you need to borrow, borrow 1 from the 9 and add it into the fraction

(9-1) + (3/3 + 1/3)

  8 + 4/3
-7  -2/3
---------
  1 +2/3