Choose the statement that correctly lists equivalent ratios.
A. [tex]$1: 6=20: 120=5: 30$[/tex]
B. [tex]$1: 6=4: 18=6: 36$[/tex]
C. [tex]$1: 8=20: 120=3: 24$[/tex]
D. [tex]$1: 8=3: 32=5: 48$[/tex]
Answer (2)
Check if the ratios in option A are equivalent: 6 1 = 120 20 = 30 5 , which simplifies to 6 1 = 6 1 = 6 1 .
Check if the ratios in option B are equivalent: 6 1 = 18 4 = 36 6 , which simplifies to 6 1 = 9 2 = 6 1 .
Check if the ratios in option C are equivalent: 8 1 = 120 20 = 24 3 , which simplifies to 8 1 = 6 1 = 8 1 .
Check if the ratios in option D are equivalent: 8 1 = 32 3 = 48 5 .
The statement that correctly lists equivalent ratios is A: 1 : 6 = 20 : 120 = 5 : 30 .
Explanation
Understanding the Problem We need to identify the statement where all ratios are equivalent. This means that when each ratio is expressed as a fraction and simplified, all fractions in the correct statement will be equal.
Checking Each Option Let's examine each option:
Option A: 1 : 6 = 20 : 120 = 5 : 30 . This can be written as 6 1 = 120 20 = 30 5 . Simplifying each fraction, we get 6 1 = 6 1 = 6 1 . All fractions are equal.
Option B: 1 : 6 = 4 : 18 = 6 : 36 . This can be written as 6 1 = 18 4 = 36 6 . Simplifying each fraction, we get 6 1 = 9 2 = 6 1 . Not all fractions are equal.
Option C: 1 : 8 = 20 : 120 = 3 : 24 . This can be written as 8 1 = 120 20 = 24 3 . Simplifying each fraction, we get 8 1 = 6 1 = 8 1 . Not all fractions are equal.
Option D: 1 : 8 = 3 : 32 = 5 : 48 . This can be written as 8 1 = 32 3 = 48 5 . These fractions are not equal.
Identifying the Correct Statement Since option A is the only statement where all the simplified fractions are equal, it is the correct answer.
Examples
Understanding equivalent ratios is crucial in various real-life scenarios. For instance, when scaling a recipe, you need to maintain the ratios of ingredients to ensure the dish tastes the same. If a recipe calls for 1 cup of flour and 2 cups of water, an equivalent ratio would be 2 cups of flour and 4 cups of water. Similarly, in map reading, the scale represents a ratio between the distance on the map and the actual distance on the ground. Maintaining equivalent ratios ensures accurate measurements and proportions in these practical applications.
The correct statement that lists equivalent ratios is option A: 1 : 6 = 20 : 120 = 5 : 30 . In this option, all ratios simplify to the same fraction, 6 1 . Options B, C, and D contain at least one ratio that does not equal the others when simplified.
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