Question

which ratios and percentage are equivalent ? sort the pairs of ratios and percentages below based on if they are equivalent (left) or not equivalent (right). equivalent not equivalent evidence 7 items 5/25 ; 20% 4/25 ; 8% 50/100 ; 5% 10/50 ; 10% 33/100 ; 33% 75/100 ; 75%

Explanation:

To determine if a ratio (fraction) and a percentage are equivalent, we convert the fraction to a percentage by multiplying it by 100.

Step 1: Analyze \( \frac{5}{25} \) and \( 20\% \)

• Convert \( \frac{5}{25} \) to a percentage: \( \frac{5}{25} \times 100 = 20\% \). So, \( \frac{5}{25} \) and \( 20\% \) are equivalent.

Step 2: Analyze \( \frac{4}{25} \) and \( 8\% \)

• Convert \( \frac{4}{25} \) to a percentage: \( \frac{4}{25} \times 100 = 16\%

eq 8\% \). So, \( \frac{4}{25} \) and \( 8\% \) are not equivalent.

Step 3: Analyze \( \frac{50}{100} \) and \( 5\% \)

• Convert \( \frac{50}{100} \) to a percentage: \( \frac{50}{100} \times 100 = 50\%

eq 5\% \). So, \( \frac{50}{100} \) and \( 5\% \) are not equivalent.

Step 4: Analyze \( \frac{10}{50} \) and \( 10\% \)

• Convert \( \frac{10}{50} \) to a percentage: \( \frac{10}{50} \times 100 = 20\%

eq 10\% \). So, \( \frac{10}{50} \) and \( 10\% \) are not equivalent.

Step 5: Analyze \( \frac{33}{100} \) and \( 33\% \)

• Convert \( \frac{33}{100} \) to a percentage: \( \frac{33}{100} \times 100 = 33\% \). So, \( \frac{33}{100} \) and \( 33\% \) are equivalent.

Step 6: Analyze \( \frac{75}{100} \) and \( 75\% \)

• Convert \( \frac{75}{100} \) to a percentage: \( \frac{75}{100} \times 100 = 75\% \). So, \( \frac{75}{100} \) and \( 75\% \) are equivalent.

Equivalent Pairs:

• \( \frac{5}{25} \); \( 20\% \)
• \( \frac{33}{100} \); \( 33\% \)
• \( \frac{75}{100} \); \( 75\% \)

Not Equivalent Pairs:

• \( \frac{4}{25} \); \( 8\% \)
• \( \frac{50}{100} \); \( 5\% \)
• \( \frac{10}{50} \); \( 10\% \)

Answer:

To determine if a ratio (fraction) and a percentage are equivalent, we convert the fraction to a percentage by multiplying it by 100.

Step 1: Analyze \( \frac{5}{25} \) and \( 20\% \)

• Convert \( \frac{5}{25} \) to a percentage: \( \frac{5}{25} \times 100 = 20\% \). So, \( \frac{5}{25} \) and \( 20\% \) are equivalent.

Step 2: Analyze \( \frac{4}{25} \) and \( 8\% \)

• Convert \( \frac{4}{25} \) to a percentage: \( \frac{4}{25} \times 100 = 16\%

eq 8\% \). So, \( \frac{4}{25} \) and \( 8\% \) are not equivalent.

Step 3: Analyze \( \frac{50}{100} \) and \( 5\% \)

• Convert \( \frac{50}{100} \) to a percentage: \( \frac{50}{100} \times 100 = 50\%

eq 5\% \). So, \( \frac{50}{100} \) and \( 5\% \) are not equivalent.

Step 4: Analyze \( \frac{10}{50} \) and \( 10\% \)

• Convert \( \frac{10}{50} \) to a percentage: \( \frac{10}{50} \times 100 = 20\%

eq 10\% \). So, \( \frac{10}{50} \) and \( 10\% \) are not equivalent.

Step 5: Analyze \( \frac{33}{100} \) and \( 33\% \)

• Convert \( \frac{33}{100} \) to a percentage: \( \frac{33}{100} \times 100 = 33\% \). So, \( \frac{33}{100} \) and \( 33\% \) are equivalent.

Step 6: Analyze \( \frac{75}{100} \) and \( 75\% \)

• Convert \( \frac{75}{100} \) to a percentage: \( \frac{75}{100} \times 100 = 75\% \). So, \( \frac{75}{100} \) and \( 75\% \) are equivalent.

Equivalent Pairs:

• \( \frac{5}{25} \); \( 20\% \)
• \( \frac{33}{100} \); \( 33\% \)
• \( \frac{75}{100} \); \( 75\% \)

Not Equivalent Pairs:

• \( \frac{4}{25} \); \( 8\% \)
• \( \frac{50}{100} \); \( 5\% \)
• \( \frac{10}{50} \); \( 10\% \)