Answers Investigation 4

Answers|Investigation 4

Applications

1.+ = N

+ = N

N–=

2.–= N

–N=

N+ =

+ N=

3.N– =

N– =

+ = N

4.N + =

+N=

–= N

–N =

10.–

11.m =

12.Answers will vary: m = , n = ,
or any choices of m and n with m + n = ,
will solve the problem.

13.m =

14.×=

×=

÷=

15.÷=

÷=

×=

16.N=

17.N=

18.N=

19.N=

20.N= 7

21.N=

22.a.m =

b.m =

c.m =

23.

24.15

25.a.24 – – 1 – 1 = buns

b.64 servings, with of a bun left over
(which is of a serving)

26.

27.

28.hours (which is about 1 hour and
10 minutes) for one way and hours for
the round trip.

Answers|Investigation 4

Connections

29.a.N =

b.N =

c.The original expressions are not
equivalent. In part (a), you need to add
and before multiplying by N. In part
(b), you need to multiply by N before
adding .

30.

31.2

32.

33.3

34.

35.

36.

37.

38.

39. and 3. These are reciprocals.

40. and 4. These are reciprocals.

41. and 2. These are reciprocals.

42.+ is larger. There are many ways to
know this without computing. One way is
to reason that you can add 1 small thing
and 5 large things or 1 large thing and
5 small things. 5 large things will be larger
(assuming the large things are the same
size in both instances, and that the small
things are also). The two sums are and
, respectively.

Another way to tell that + is larger is to
note that . Thus,
+ = + + = + .
The two sums are and , respectively.

43.– is larger. There are many ways to
know this without computing. One way is
to observe that for a large difference, you
want the numbers to be far apart. Because
and , the first difference will
be greater than the second. The two
differences are and respectively.

Another way to tell that – is larger is to
note that and . Thus,
– – – . (Here you use the
fact that subtracting a larger number
from a given number results in a smaller
number.) The two differences are and
respectively.

44.N =

45.N = 1

46.In a simpler form this sentence is
+ m + n = 3. Using fact families to
rewrite it, you have m + n = . So
now you can choose any number for m
(less than if you are working with
positive numbers) and calculate n, since
n = – m. Possible solutions are m = 1
and n = , or m = and n = , or
m = and n = , and so forth.

Answers|Investigation 4

Extensions

47.0

48.0

49.1

50.1

51.Answers will vary. Identity means the
number that leaves the starting value
unchanged.

52.N = –

53.N = –

54.N = 2

55.N =

56.a.Yes; the additive inverse of a is –a.
The additive inverse is also called the
opposite of a number.

b.Nearly all numbers do, but 0 has no
multiplicative inverse. The multiplicative
inverse is also called the reciprocal of a
number.