Which one of the following statements expresses a true proportion?
a) [tex]$3: 4=9: 12$[/tex]
b) [tex]$7: 9=8: 9$[/tex]
c) [tex]$2: 1=1: 2$[/tex]
d) [tex]$54: 9=6: 3$[/tex]
Answer (2)
Check if the ratios in each option are equivalent.
Option a) 4 3 = 12 9 is a true proportion because 12 9 simplifies to 4 3 .
Options b), c), and d) are not true proportions because their ratios are not equivalent.
The statement that expresses a true proportion is a) 3 : 4 = 9 : 12 , so the answer is a ) .
Explanation
Understanding the Problem We are given four statements, each expressing a proportion between two ratios. Our goal is to determine which statement expresses a true proportion. A proportion is true if the two ratios are equivalent.
Checking Each Option Let's examine each option: a) 3 : 4 = 9 : 12 can be written as 4 3 = 12 9 . Simplifying the right side, we get 12 9 = 4 3 . Thus, this is a true proportion. b) 7 : 9 = 8 : 9 can be written as 9 7 = 9 8 . Since the denominators are the same, we can compare the numerators. 7 = 8 , so this is not a true proportion. c) 2 : 1 = 1 : 2 can be written as 1 2 = 2 1 . This simplifies to 2 = 2 1 , which is false. Thus, this is not a true proportion. d) 54 : 9 = 6 : 3 can be written as 9 54 = 3 6 . Simplifying both sides, we get 6 = 2 , which is false. Thus, this is not a true proportion.
Conclusion Therefore, the only statement that expresses a true proportion is option a) 3 : 4 = 9 : 12 .
Examples
Proportions are used in everyday life, such as when scaling recipes. If a recipe calls for 2 cups of flour for 1 cake, you can use proportions to determine how much flour you need for 3 cakes. Setting up the proportion 1 cake 2 cups = 3 cakes x cups , you can solve for x to find that you need 6 cups of flour.
The statement that expresses a true proportion from the options given is a) 3 : 4 = 9 : 12 . In this case, the ratios are equivalent once simplified. Therefore, option a) is the correct choice.
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