Math 130 Ch 4.1

9b A 40-member club will elect a pair of co-presidents. How many possible outcomes are there?

780. Co-Presidents must be two different members of the club. So there are 40 choices for one of the co-presidents and 39 choices for the other co-president. But choosing, for example, Bob first and Barb second yields the same pair of co-presidents as choosing Barb first and Bob second. The reasoning thus far counts each pair of co-presidents twice, so there are in fact (40*39) /2 sets of co-presidents

6 Write a Multiplicative Comparison problem in which you describe one quantity as 3 times as much as another quantity but which cannot be solved by multiplying the numbers given in the problem.

Answers will vary. For example, Jill and Jacinto are comparing their baseball card collection. Jacinto has 78 baseball cards. Jacinto has 3 times as many cards as Jill. How many baseball cards does Jill have?

2 Write an Array word problem for 6 *8 =?. Explain clearly why the problem can be solved by multiplying 6 * 8 by using the definition of multiplication in this section.

Answers will vary. Possible answer: A Kindergarten classroom has 6 equal rows where 8 cubbies are in 1 row. How many cubbies are there? We can multiply 6 and 8 together because each row is one group of 8 cubbies, so there are 6 groups of 8 cubbies altogether

3 Write an Ordered Pair word problem for 6*8 = ?. Explain clearly why the problem can be solved by multiplying 6* 8 by using the definition of multiplication in this section.

Answers will vary. Possible answer: A couple that has just had a baby boy has 6 first names chosen out and 8 middle names. If they choose one first name and one middle name, how many different pairs are possible? We can multiply 6 and 8 because each first gives us the first element of an ordered pair (which can correspond to rows in an array) and each middle name gives us the second element (which can correspond to columns in an array.)

5a Write a Multiplicative Comparison word problem for 3*5=?.

Answers will vary. Possible answer: There are 5 ants in Griffin's ant farm. Tabisha's ant farm has 3 times as many ants as Griffin's. How many ants are in Tabisha's ant farm?

4 Write a Multiplicative Comparison word problem for 6*8 =?. Explain clearly why the problem can be solved by multiplying 6* 8 by using the definition of multiplication in this section.

Answers will vary. Possible answer: There are 8 cookies in a small box at the fair. The big box of cookies has 6 times as many cookies as the small box. How many cookies are in the big box? Using our interpretation of multiplication, the big box contains 6 equal groups of small boxes or 6 equal groups where there are 8 cookies in 1 group or 6 times 8 cookies in all`

1 c. Use this section's definition of multiplication to explain why each of the following problems can be solved by multiplying: Will is driving 65 miles per hour. If he continues driving at that speed, how far will he drive in 3 hours?

At the speed Will is driving, each hour is the same as 65 mi. Three hours would be seen as three equal groups where 65 mi. are "in" 1 group. By definition of multiplication, this is 3*65=195 mi.

7a Your laundry basket contains 4 plain socks: a red one, a blue one, a yellow one, and a green one. The basket also contains 4 striped socks: a red striped one, a blue striped one, a yellow striped one, and a green striped one. If you want to wear a plain sock on your left foot and a striped sock on your right foot, how many options do you have? (For example, a plain yellow sock on your left foot and a red striped sock on your right foot is one option.)

Each "pair" of socks can be represented by an Ordered Pair: (plain sock, striped sock). Using the Ordered Pair interpretation of multiplication, we multiply 4*4

1 b. Use this section's definition of multiplication to explain why each of the following problems can be solved by multiplying: There are 5280 feet in a mile. How long in feet is a 4-mile-long stretch of road

Each mile can be considered to be a group of 5,280 feet. Four miles is four equal groups with 5,280 mi. in 1 group. By definition of multiplication, this is 4*5,280=21,120 feet.

1 a. Use this section's definition of multiplication to explain why each of the following problems can be solved by multiplying: There are 3 feet in a yard. If a rug is 5 yards long, how long is it in feet?

Each yard of the rug's length can be considered to be a group of three feet. There are five yards, I.e., five equal groups where there are three feet in 1 group. By the definition of multiplication, this is 5*3= 15 feet

5b Draw a strip diagram for your problem in part (a) and explain how this section's definition of multiplication applies to solve the problem.

See Figure 4.1. Tabisha's ant farm can be seen as 3 equal groups, each of the same size as Griffin's ant farm of 5 ants. Therefore, according to the definition of multiplication, Tabisha has 3 times 5 ants in her ant farm

5c Reword your problem in part (a) so that it is about the same situation but you use the fraction 1 3 in the statement of the problem.

Tabisha's ant farm has 15 ants. Griffin's ant farm has 1/3 as many ants as Tabisha's. How many ants are in Griffin's ant farm?

9c Are the answers to (a) and (b) the same or dif-ferent? Explain why they are the same or why they are different.

The answe

7b Your laundry basket contains 4 plain socks: a red one, a blue one, a yellow one, and a green one. The basket also contains 4 striped socks: a red striped one, a blue striped one, a yellow striped one, and a green striped one. If you want to pick out a pair of socks consisting of one plain sock and one striped sock, and then wear that pair of socks how many options do you have? (For example, a red striped sock on your left foot and a plain yellow sock on your right foot is one option.)

There are at least two ways to view this question. View 1: The question is asking how many different pairs of socks can we make? This works the same as problem a. because it has the same Ordered Pair structure (plain sock, striped sock) View 2: The question is asking how many different pairs of socked feet can we make? In this view, the Ordered Pairs (plain sock, striped sock) and (striped sock, plain sock) are counted differently, so there are 16*2=32 possibilities

7c Your laundry basket contains 4 plain socks: a red one, a blue one, a yellow one, and a green one. The basket also contains 4 striped socks: a red striped one, a blue striped one, a yellow striped one, and a green striped one. If you reach into the laundry basket, pick out a sock, and put it on your left foot and then reach in again, pick out another sock, and put it on your right foot, how many different possible outcomes are there?

This works differently from the other two because we will not necessarily have one striped sock and on plain sock. Instead, there are 8 possibilities for the first sock and 7 for the second sock, so there are 56 possible pairs.

9a A 40-member club will elect a president and then elect a vice president. How many possible outcomes are there?

1560. We have 40 choices for president, leaving 39 choices for vice-presidents (or vice-versa) giving 40*39 was of filling the two offices.

8 John, Trey, and Miles want to know how many two-letter secret codes there are that don't have a repeated letter. For example, they want to count BA and AB, but they don't want to count doubles such as ZZ or XX. John says there are 26 + 25 because you don't want to use the same letter twice; that's why the second number is 25. Trey says he thinks it should be times, not plus: 26 # 25. Miles says the number is 26 # 26 - 26 because you need to take away the double letters. Discuss the boys' ideas. Which answers are correct, which are not, and why? Explain your answers clearly and thoroughly, drawing on this section's definition of multiplication.

Trey and Miles are correct because they both calculate 25*26 combinations. You have 26 choices for the first letter. Since you don't want a repeated letter, you have 25 choices for the second letter. Each of the 26 choices is a group. All the groups are of equal size. For each group, there are 25 second choices that correspond to 25 two-letter-codes got each group. So by the definition of multiplication, 26 equal groups with 25 in 1 group Is 26*25. Miles is also correct. Making ALL combinations and subtracting out the repeats gives the same results