The expression gives the Q−P/2 difference between and a Q population half the size of For P. instance, if and this Q=150 P=100, difference equals 150−100/2=100. To see why the second of these is bigger, write (Q−P)/2=Q/2−P/2 In the expression we subtract Q−P/2, from But in (Q−P)/2, we P/2 Q. subtract the same value, from a P/2, smaller amount, Q/2. The expression is larger. Q+50t In both expressions, the same value, 50t, is added to the population. Since adding 50t to results in P<Q, P a smaller value than adding the same amount to Q. The expression 0.5 is larger. The total size of the two populations put together is so the expression P+Q, gives the fraction of this total PP+Q population belonging to Since P. there are fewer animals in population than this fraction is less than 12. P Q, For instance, if and P=100 Q=150, this fraction equals 100/(100+150)=0.4. and can be interpreted in two PQ QP different ways. can be interpreted as a unit rate, PQ namely, the number of animals in population for every 1 animal in P population Similarly, can be Q. QP interpreted as the number of animals in population for every 1 animal in Q population Since there are more P. animals in population the unit rate Q, will be greater than the unit rate QP PQ. For example, if and P=100 Q=150, then 100150=23, so there would be 23 of an animal in population for P every 1 animal in population while Q, 150100=32, so there would be 32 of an animal in population for every 1 Q
The expression Q−P/2 gives the difference between Q and a population half the size of P. For instance, if Q=150 and P=100, this difference equals 150−100/2=100. To see why the second of these is bigger, write (Q−P)/2=Q/2−P/2 In the expression Q−P/2, we subtract P/2 from Q. But in (Q−P)/2, we subtract the same value, P/2, from a smaller amount, Q/2. The expression Q+50t is larger. In both expressions, the same value, 50t, is added to the population. Since P<Q, adding 50t to P results in a smaller value than adding the same amount to Q. The expression 0.5 is larger. The total size of the two populations put together is P+Q, so the expression PP+Q gives the fraction of this total population belonging to P. Since there are fewer animals in population P than Q, this fraction is less than 12. For instance, if P=100 and Q=150, this fraction equals 100/(100+150)=0.4. PQ and QP can be interpreted in two different ways. PQ can be interpreted as a unit rate, namely, the number of animals in population P for every 1 animal in population Q. Similarly, QP can be interpreted as the number of animals in population Q for every 1 animal in population P. Since there are more animals in population Q, the unit rate QP will be greater than the unit rate PQ. For example, if P=100 and Q=150, then 100150=23, so there would be 23 of an animal in population P for every 1 animal in population Q, while 150100=32, so there would be 32 of an animal in population Q for every 1
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