use the problem from the previous page to help you understand how to compare and order rational numbers given in different forms. 1 label the points in picture it. how can a number line help you when comparing numbers given in different forms? 2 complete the model it table. are any numbers in the set of $\frac{1}{8}$, 1.8, and 18% equivalent? how can you tell from the table? 3 what could you do first to compare 0.3 and 25%? why? 4 how can writing numbers in equivalent forms help you to compare and order them? 5 reflect think about all the models and strategies you have discussed today. describe how one of them helped you better understand how to solve the try it problem.

Question

Accepted Answer

### Question 2 Solution: # Explanation: ## Step 1: Convert $\frac{1}{8}$ to decimal To convert a fraction to a decimal, divide the numerator by the denominator. So, $1\div8 = 0.125$. ## Step 2: Convert $18\%$ to decimal To convert a percentage to a decimal, divide by 100. So, $18\%\div100 = 0.18$. ## Step 3: Compare the decimals We have $\frac{1}{8}=0.125$, $1.8 = 1.8$, and $18\% = 0.18$. Since $0.125 eq1.8$, $0.125 eq0.18$, and $1.8 eq0.18$, none of the numbers are equivalent. We can tell from the table (by looking at their decimal forms) because equivalent numbers would have the same decimal value. # Answer: $\frac{1}{8}=0.125$, $1.8 = 1.8$, $18\% = 0.18$. None of the numbers are equivalent. We can tell from the table by comparing their decimal forms (equivalent numbers have the same decimal value). ### Question 3 Solution: # Explanation: ## Step 1: Choose a conversion method To compare $0.3$ (a decimal) and $25\%$ (a percentage), we can either convert $25\%$ to a decimal or $0.3$ to a percentage. Converting $25\%$ to a decimal is a common first step. ## Step 2: Convert $25\%$ to decimal To convert a percentage to a decimal, divide by 100. So, $25\%\div100 = 0.25$. ## Step 3: Explain the reason Converting $25\%$ to a decimal (or $0.3$ to a percentage) allows us to compare two numbers in the same form (both decimals or both percentages), making the comparison straightforward. For example, after converting $25\%$ to $0.25$, we can easily see that $0.3>0.25$ (so $0.3 > 25\%$). # Answer: You could first convert $25\%$ to a decimal (or $0.3$ to a percentage). Converting $25\%$ to a decimal (by dividing by 100, getting $0.25$) or $0.3$ to a percentage (by multiplying by 100, getting $30\%$) allows you to compare two numbers in the same form (both decimals or both percentages), which simplifies the comparison. For example, $25\% = 0.25$, and then we can compare $0.3$ and $0.25$ (or $30\%$ and $25\%$). ### Question 4 Solution: # Explanation: ## Step 1: Understand equivalent forms Writing numbers in equivalent forms (e.g., converting fractions to decimals, percentages to decimals, decimals to fractions, etc.) helps because: - It allows us to represent all numbers in the same format (e.g., all decimals, all fractions, or all percentages). - When numbers are in the same format, we can easily compare their values (e.g., comparing decimals by looking at place values, comparing fractions by finding a common denominator, etc.). - For ordering, we can line up the numbers (in the same form) and arrange them from least to greatest (or vice versa) based on their values. For example, to compare $\frac{1}{2}$, $0.6$, and $55\%$, we can convert them all to decimals: $\frac{1}{2}=0.5$, $55\% = 0.55$. Then we can order them as $0.5<0.55<0.6$ (so $\frac{1}{2}<55\%<0.6$). # Answer: Writing numbers in equivalent forms (e.g., converting to the same form like all decimals, all fractions, or all percentages) helps because it allows us to compare and order numbers easily by having them in a consistent format. For example, converting $\frac{1}{2}$, $0.6$, and $55\%$ to decimals ($0.5$, $0.6$, $0.55$) makes it simple to order them as $\frac{1}{2}<55\%<0.6$. ### Question 5 Solution: # Explanation: ## Step 1: Choose a model/strategy One of the models/strategies discussed is converting numbers to equivalent forms (e.g., fractions to decimals, percentages to decimals) or using a number line. Let's take converting numbers to equivalent forms as an example. ## Step 2: Explain how it helped When solving the "Try It" problem (presumably a problem about comparing/ordering rational numbers), converting numbers to a common form (like all decimals) helped me better understand how to solve it. For example, if the problem had numbers like $\frac{3}{4}$, $0.8$, and $70\%$, converting $\frac{3}{4}$ to $0.75$ and $70\%$ to $0.7$ allowed me to easily order them as $70\%<\frac{3}{4}<0.8$ (by comparing the decimals). This strategy made the comparison and ordering straightforward by having all numbers in the same format. # Answer: For example, converting numbers to equivalent forms (e.g., all decimals) helped me better understand how to solve the "Try It" problem. It allowed me to compare/order numbers easily by having them in a consistent format (e.g., comparing decimals directly). This strategy simplified the process of determining which numbers were greater or less than others.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 2 Solution:

Step 1: Convert \(\frac{1}{8}\) to decimal

Step 2: Convert \(18\%\) to decimal

Step 3: Compare the decimals

Step 1: Choose a conversion method

Step 2: Convert \(25\%\) to decimal

Step 3: Explain the reason

Step 1: Understand equivalent forms

Answer:

Question 3 Solution: