How many pounds? How many ounces? --part 1.

My new littlest, a boy, was born yesterday.  He weighed 7 lb., 12 oz.  If I let his birthweight be $w$, then

amath \qquad\qquad\qquad w = text(7  lb. + 12 \text( oz. endamath

Apposition is the writing of one thing beside another.  In my youngest son's birthweight, 7 lb. and 12 oz. are apposed, and this means they should be added.  Similarly, in a mixed fraction such as $7\frac34$, the 7 is apposed to the $\frac34$, and that, too, means that they should be added.  Notice that this well-established convention conflicts somewhat with the usual algebraic convention that when one thing is put beside another, they should be not added but multiplied, i.e.

$ \qquad\qquad\qquad 7\;a = 7 \times a. $

There is a formal rule for avoiding conflicts between these two different meanings of apposition: 

• Quantities with different units are to be added if they are separated by a comma and a space.
• A whole number and a fraction are to be added if the number comes before the fraction and there is no space between them.  
• Quantities are to be multiplied, as in algebra, if they are separated simply by a space.
  

Now that we have dealt with these conventions, let's write my youngest son's birthweight in a a variety of ways:

amath \qquad\qquad\qquad w = 7 \text( lb., 12 \text( oz. = 124 \text( oz. = 7 \frac{3}{4} \text( lb. endamath

The first of these keeps the numbers small, but uses two different units.  The second uses just one unit, at the price of a larger number.  The third also uses just one unit, at the price of employing a fraction.