Download CMP3_G6_LBR_ACE4

A C E
Answers |
Investigation 4
Applications
1.
2.
1
16
+
1
12
=N
2
3
×
5
7
=
10
21
1
12
+
1
16
=N
5
7
×
2
3
=
10
21
14.
N–
1
16
=
1
12
10
21
÷
5
7
=
2
3
N–
1
12
=
1
16
10
21
÷
2
3
=
5
7
4
5
=N
3
4
÷ 11 =
1
2
3
4
÷
1
2
= 11
×
1
1
2
=
3
4
1
2
=
3
4
5
4
–
5
4
–N=
4
5
4
5
4
5
=
5
4
+N=
5
4
N+
15.
1
2
1
3. N – 1 1 = 2 2
N–
1
13
3
2
2
3
1
1
13
=
2
1
2
×
16. N =
2
3
17. N =
2
15
1
13
+ 22 = N
18. N =
2
3
2
3
+ 11 =N
19. N =
3
5
2
3
13
=
1
3
4
3
+N=
1
3
1
3
–
1
3
–N=
4. N +
4
3
4
3
20. N = 7
21. N =
7.
17
20
8.
1
2
9.
1
8
5
8
b. m =
5
8
c. m =
5
8
4
3
23. 32 1
12
1
20
1
3
22. a. m =
=N
5. 1 5
6.
2
2
24. 15
25. a. 24 –
1
2
– 1 – 1 = 21 1 buns
2
b. 64 servings, with
(which is
26.
10. – 1
8
11. m =
of a bun left over
of a serving)
4
9
27. 18 2
6
10
3
12. Answers will vary: m =
3
10
,n=
3
10
28. 1
,
or any choices of m and n with m + n =
3
5
7
44
hours (which is about 1 hour and
10 minutes) for one way and 2
,
7
22
hours for
the round trip.
will solve the problem.
13. m =
1
2
1
6
6
10
Let’s Be Rational
1
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
Investigation 4
A C E
Answers |
Investigation 4
Connections
29. a. N =
6
7
b. N =
3
4
43.
equivalent. In part (a), you need to add
1
3
and
(b), you need to multiply
1
4
adding
30.
5
6
before multiplying by N. In part
1
3
1
8
is larger. There are many ways to
>
5
8
and
1
8
1
6
<
, the first difference will
be greater than the second. The two
by N before
differences are
.
17
24
11
24
and
1
2
note that
5
6
1
3
–
1
8
>
5
6
>
5
8
and
5
8
–
1
8
>
5
8
1
6
–
respectively.
5
6
–
>
1
8
Another way to tell that
31. 2
32.
–
know this without computing. One way is
to observe that for a large difference, you
want the numbers to be far apart. Because
c. The original expressions are not
1
4
5
6
1
6
1
8
is larger is to
. Thus,
. (Here you use the
fact that subtracting a larger number
from a given number results in a smaller
33. 3
34.
3
2
35.
4
3
36.
2
5
37.
4
5
38.
12
7
39.
1
3
and 3. These are reciprocals.
40.
1
4
and 4. These are reciprocals.
41.
1
2
and 2. These are reciprocals.
42.
1
8
number.) The two differences are
11
24
17
24
and
respectively.
44. N =
1
3
45. N = 1
46. In a simpler form this sentence is
1
13
24
+ m + n = 3. Using fact families to
rewrite it, you have m + n = 1 11 . So
+
5
6
24
now you can choose any number for m
(less than 1 11 if you are working with
24
positive numbers) and calculate n, since
is larger. There are many ways to
n = 1 11 – m. Possible solutions are m = 1
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 23 and
24
and n =
m=
15
24
11
24
, or m =
and n =
20
24
5
24
and n = 1
6
24
, or
, and so forth.
24
19
24
, respectively.
Another way to tell that
note that
5
6
+
1
8
=
1
6
>
1
8
1
+
4
6
The two sums are
Let’s Be Rational
+
5
6
is larger is to
. Thus,
 +
6
1
8
1
8
23
24
>
 +
1
+
4
6
8
and
19
24
1
8
=
1
6
+
5
8
.
, respectively.
2
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
Investigation 4
A C E
Answers |
Investigation 4
Extensions
47. 0
54. N = 2
48. 0
55. N =
49. 1
3
2
56. a. Yes; the additive inverse of a is –a.
The additive inverse is also called the
opposite of a number.
50. 1
51. Answers will vary. Identity means the
number that leaves the starting value
unchanged.
b. Nearly all numbers do, but 0 has no
multiplicative inverse. The multiplicative
inverse is also called the reciprocal of a
number.
52. N = – 1
2
53. N = – 2
3
Let’s Be Rational
3
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
Investigation 4