Question

use what you learned to solve these problems.
6 put these five numbers in order from least to greatest: |-3| 3/4 -2 1.25 50%
show your work.

solution
7 determine which comparisons are true. select all that apply.
a 7/20 is equivalent to 35%.
b 3.0 ≠ 300%
c 0.45 < 8/25
d 12% = 6/50
e 8% = 0.8
f |-5| > 2

8 tell whether 31/25 and 124% are equivalent. show your work.

Explanation:

Problem 6

Step1: Convert all numbers to decimals

• \(|-3| = 3\) (absolute value of -3 is 3)
• \(\frac{3}{4}=0.75\) (divide 3 by 4)
• \(-2\) remains as -2
• \(1.25\) remains as 1.25
• \(50\%=\frac{50}{100} = 0.5\) (convert percentage to decimal)

Step2: Order the decimal numbers from least to greatest

The numbers in decimal form are: -2, 0.5, 0.75, 1.25, 3

So the order from least to greatest is: \(-2, 50\%, \frac{3}{4}, 1.25, |-3|\)

• Option A: Convert \(\frac{7}{20}\) to percentage. \(\frac{7}{20}=7\div20 = 0.35\), and \(0.35\times100\% = 35\%\). So \(\frac{7}{20}\) is equivalent to \(35\%\). This is true.
• Option B: Convert \(300\%\) to decimal. \(300\%=\frac{300}{100}=3.0\). So \(3.0 = 300\%\), the statement \(3.0

eq300\%\) is false.

• Option C: Convert \(\frac{8}{25}\) to decimal. \(\frac{8}{25}=8\div25 = 0.32\). Now compare \(0.45\) and \(0.32\). Since \(0.45>0.32\), the statement \(0.45<\frac{8}{25}\) is false.
• Option D: Convert \(\frac{6}{50}\) to percentage. \(\frac{6}{50}=6\div50 = 0.12\), and \(0.12\times100\% = 12\%\). So \(12\%=\frac{6}{50}\). This is true.
• Option E: Convert \(8\%\) to decimal. \(8\%=\frac{8}{100}=0.08\). Since \(0.08

eq0.8\), the statement \(8\% = 0.8\) is false.

• Option F: Calculate \(|-5|\). \(|-5| = 5\). Now compare \(5\) and \(2\). Since \(5>2\), the statement \(|-5|>2\) is true.

Step1: Convert \(\frac{31}{25}\) to decimal

\(\frac{31}{25}=31\div25 = 1.24\)

Step2: Convert \(124\%\) to decimal

\(124\%=\frac{124}{100}=1.24\)

Since both \(\frac{31}{25}\) and \(124\%\) equal \(1.24\) in decimal form, they are equivalent.

Answer:

\(-2, 50\%, \frac{3}{4}, 1.25, |-3|\)

Problem 7