This apparently is not taught or emphasized in school, and I think that's really too bad, because it can be SUPER useful and helpful:
UNITS can be multiplied and divided, just like numbers.
This why you should always KEEP the units WITH the numbers when you're working through a problem. Doing that helps tremendously to keep you on the right path as you go through it. And when you finish, it helps you decide whether your answer is correct, because the answer needs to have the correct units as well as the correct digits.
#9 says . . . kg · (m/s) · (1/s) .
How do you multiply a number by a fraction ? You multiply the numerator of the fraction by the number. You do exactly the same with units. The first multiplication in #9 is:
kg · (m/s) = (kg·m/s)
How do you multiply two fractions ? You multiply their numerators, and write THAT product over the product of their denominators. You do exactly the same with units. The second multiplication in #9 is:
(kg·m/s) · (1/s) = (kg·m·1 / s·s) and that's (kg·m / s²)
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For #10, the first 2 multiplications give you
kg · s · (m/s) = (kg·m·s/s)
Now, before we go any farther ... What do you do with a fraction when the numerator and denominator both have the same factor in them ? You can 'simplify' the fraction ... divide the numerator and denominator both by the same factor, and 'cancel' it out of the fraction. You can do exactly the same with units.
Take that (kg·m·s/s) and cancel 's' out of the numerator and denominator. The simplified fraction is just kg·m .
NOW do the last multiplication in #10:
(kg·m) · (1/s²) = kg·m/s²
