Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Textbook Question
Chapter 2.4, Problem 16P
Minju says that fractions that use bigger numbers are greater than fractions that use smaller numbers. Make up two problems for Minju to help her reconsider her ideas. For each problem, explain how to solve it, and explain why you chose that problem for Minju.
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1. The regular representation of a finite group G is a pair (Vreg, Dreg). Vreg is a vector space
and Dreg is a homomorphism.
(a) What is the dimension of Vreg?
(b) Describe a basis for Vreg and give a formula for Dreg. Hence explain why the homo-
morphism property is satisfied by Dreg.
(c) Prove that the character ✗reg (g) defined by tr Dreg (g) is zero if g is not the identity
element of the group.
(d) A finite group of order 60 has five irreducible representations R1, R2, R3, R4, R5. R₁
is the trivial representation. R2, R3, R4 have dimensions (3,3,4) respectively. What is the
dimension of R5? Explain how your solution is related to the decomposition of the regular
representation as a direct sum of irreducible representations (You can assume without proof
the properties of this decomposition which have been explained in class and in the lecture
notes).
(e) A
group element
has characters in the irreducible representations R2, R3, R4 given
as
R3
R2 (g)
= -1
X³ (g) = −1 ; XR4 (g) = 0…
it's not algebra 4th grade
Not use ai please
Chapter 2 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Ch. 2.2 - Michael says that the dark marbles in Figure 2.25...Ch. 2.2 - When Jean was asked to say what the 3 in the...Ch. 2.2 - This rectangle of x’s is 45 of another (original)...Ch. 2.2 - This rectangle of x’s is 65 of another (original)...Ch. 2.2 - Kaitlyn gave 12 of her candy bar to Arianna....Ch. 2.2 - You were supposed to use 23 of a cup of coca to...Ch. 2.2 - Susan was supposed to use 54 of a cup of butter in...Ch. 2.2 - If 34 of a cup of a snack food gives you your...Ch. 2.2 - Make up a word problem or situation where one...Ch. 2.2 - Cake problem: Figure 2.26 represents two cakes of...
Ch. 2.2 - Harry wants to make 34 of a recipe of a potion....Ch. 2.2 - Figure 2.27 shows a picture of three pies. Draw a...Ch. 2.2 - Discuss why it can be confusing to show an...Ch. 2.2 - Draw a number line like the one in Figure 2.28 and...Ch. 2.2 - Draw a number line like the one in Figure 2.28 and...Ch. 2.2 - Draw a number line like the one in Figure 2.29....Ch. 2.2 - Give two different fractions that you can...Ch. 2.2 - Marquez says that the shaded region in Figure 2.31...Ch. 2.2 - NanHe made a design that used hexagons, rhombuses,...Ch. 2.2 - A county has two elementary schools, both of which...Ch. 2.3 - Use a math drawing to explain in your own words...Ch. 2.3 - Explain in two different ways why 23=2434Ch. 2.3 - Using the fractions 23 and 34 , describe how to...Ch. 2.3 - Using a math drawing, explain why dividing both...Ch. 2.3 - Using a math drawing with the exmaple 69 Describe...Ch. 2.3 - Draw a number line like the one in Figure 2.49....Ch. 2.3 - Draw a number line like the one in Figure 2.49....Ch. 2.3 - Draw a number line like the one in Figure 2.49....Ch. 2.3 - Draw a number line like the one in Figure 2.49....Ch. 2.3 - Draw a number line like the one in Figure 2.50....Ch. 2.3 - Draw a numebr line like the one in Figure 2.51....Ch. 2.3 - Draw a number line like the one in Figure 2.52....Ch. 2.3 - Draw a number line like the one in Figure 2.53....Ch. 2.3 - Erin says the tick mark indicated in Figure 2.54...Ch. 2.3 - First you poured 34 of a cup of water into an...Ch. 2.3 - First you poured 34 of a cup of water into an...Ch. 2.3 - You want to make a recipe that calls for 23 of a...Ch. 2.3 - Ken got 23 of a ton of gravel even though he...Ch. 2.3 - One serving of SnackOs is 23 of a cup. Jane wants...Ch. 2.3 - So far, Benny has run 12 of a mile, but that is...Ch. 2.3 - So far, Mahelia has run 32 miles, but that is only...Ch. 2.3 - See Figure 2.57. How many of Strip A does it take...Ch. 2.3 - The strips in Figure 2.60 show the relative...Ch. 2.3 - Draw a strip diagram like the one in Figure 2.60...Ch. 2.3 - Becky moves into an apartment with two friends on...Ch. 2.4 - Julie says that the drawing in Figure 2.65 shows...Ch. 2.4 - In your own words, explain in detail why we can...Ch. 2.4 - In your own words, explain in detail why we can...Ch. 2.4 - In your own words, explain in detail why it is the...Ch. 2.4 - Which fraction is greater, 35109or36104? To...Ch. 2.4 - Which fraction is greater, 1531or2347? To explain...Ch. 2.4 - Which fraction is greater, 35109or36104? To...Ch. 2.4 - Without using a calculator, order the following...Ch. 2.4 - Find a number between 2384 and 2998 and plot all...Ch. 2.4 - Find a number between 78134 and 124213 and plot...Ch. 2.4 - Find two different fractions between 25 and 35...Ch. 2.4 - Give two different methods for solving the...Ch. 2.4 - Give two different methods for solving the...Ch. 2.4 - A student says that 15 is halfway between 14 and...Ch. 2.4 - Sam has a method for comparing fractions: He just...Ch. 2.4 - Minju says that fractions that use bigger numbers...Ch. 2.4 - Malcolm says that 811710 because 87 and 1110...Ch. 2.4 - You may combine your answers to all three parts of...Ch. 2.4 - Consider the following list of fractions:...Ch. 2.4 - Suppose you start with a proper fraction and you...Ch. 2.5 - If your daily value of carbohydrates is 300 grams,...Ch. 2.5 - A road crew ordered 52 tons of gravel, but they...Ch. 2.5 - If your daily value of dietary fiber is 25 grams...Ch. 2.5 - If 36,000 people make up 15% of a population, then...Ch. 2.5 - If 180 milligrams of potassium constitute 5% of...Ch. 2.5 - In Happy Valley, the average rainfall in July is 5...Ch. 2.5 - If a 34 -cup serving of cereal provides your full...Ch. 2.5 - Mentally determine what percent 225 is of 250. Use...Ch. 2.5 - Show how to use a percent table and either “going...Ch. 2.5 - If a 23 cupserving of cereal provides your full...Ch. 2.5 - The Biggo Corporation hopes that 95% of its 4600...Ch. 2.5 - A company has bought 3.4 acres of land out of the...Ch. 2.5 - The mayor says that $3.6 million has been spent...Ch. 2.5 - Sixty percent of a city’s population of 84,000...Ch. 2.5 - Frank ran 80% as far as Denise. How far did Denise...Ch. 2.5 - GrandMart sells 115% as much soda as BigMart. How...Ch. 2.5 - Connie and Benton paid for identical plane...Ch. 2.5 - At a newsstand, 75% of the items sold are...Ch. 2.5 - A company produces two types of handbags and sells...Ch. 2.5 - A county has two elementary schools, school A and...Ch. 2.5 - Brand A soup is 20% solids and 80% water. Use this...Ch. 2.5 - At a store, there is a display of 300 cans of...Ch. 2.5 - Suppose that 200 pounds of freshly picked...
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