8 pounds and grown by---how much?

Our littlest, born Thursday morning, and weighing  7 pounds, 12 ounces then, but 7 pounds, 6 ounces at his checkup late Friday afternoon, was weighed at his second checkup today.

It is common for newborns to lose weight and only come up to birthweight between one and two weeks, apparently, but that has not been the time scale with our children.  Today, our littlest weighed in at 8 pounds even.  (No, again, I am not faking the figures.  I am starting to wonder whether those who measure him round to the nearest quarter pound, but I don't think they do.)

This provides an opportunity to look at subtraction of mixed units, otherwise known as compound subtraction.  It is reasonably obvious that my newborn has experience net growth of four ounces between his birth weighing and today's weighing.

One way to subtract is to do it term by term, so that

`\qquad\qquad\qquad (8" lb."  +  0" oz.")  -  (7"  lb."  +  12" oz."),`
`\qquad\qquad\qquad\qquad =  (8 - 7)" lb."  +  (0 - 12)" oz.,"`
`\qquad\qquad\qquad\qquad =  1" lb."  + \bar{12}" oz.,"`

where the overbar represents negation, as before.  This result is true, but not in standard form.  We rectify by a subtractive kinds of carrying, known as borrowing :

`\qquad\qquad\qquad 1" lb."  + \bar{12}" oz."  =  0" lb."  +  16" oz."  + \bar{12}" oz.,"`
`\qquad\qquad\qquad\qquad =  0" lb."  +  (16 - 12)" oz.,"`
`\qquad\qquad\qquad\qquad =  4" oz."`