Mathematics for Elementary Teachers with Activities (5th Edition)
Mathematics for Elementary Teachers with Activities (5th Edition)
5th Edition
ISBN: 9780134392790
Author: Beckmann, Sybilla
Publisher: PEARSON
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Chapter 2.4, Problem 20P

Suppose you start with a proper fraction and you add 1 to both the numerator and the denominator.

For example, if you started with 2 3 , then you’d get a new fraction 2 + 1 3 + 1 = 3 4 .

a. Give at least 5 examples of proper fractions A B . In each example, compare the sizes of A B and A + 1 B + 1 What do you notice? Make sure you are working with proper fractions (where the numerator is less than the denominator).

b. Frank says that if A B B is a proper fraction, then A + 1 B + 1 is always greater than A B because A + 1 B + 1 has more parts.

Regardless of whether Frank’s conclusion is correct, discuss whether Frank’s reasoning is valid. Did Frank give a convincing explanation that A + 1 B + 1 is greater than A B ? If not, what objections could you make to Frank’s reasoning?

c. Explain the phenomenon you discovered in part (a). Compare the sizes of A B and A + 1 B + 1 Explain why the fraction you say is larger really is larger.

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Chapter 2 Solutions

Mathematics for Elementary Teachers with Activities (5th Edition)

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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