Which one of the following statements expresses a true proportion?
A) [tex]$7: 9=8: 9$[/tex]
B) [tex]$54: 9=6: 3$[/tex]
C) [tex]$2: 1=1: 2$[/tex]
D) [tex]$3: 4=9: 12$[/tex]
Answer (2)
A proportion states that two ratios are equal.
Check each option to see if the ratios are equal when expressed as fractions.
Option D, 3 : 4 = 9 : 12 , simplifies to 4 3 = 4 3 , which is a true proportion.
Therefore, the answer is D .
Explanation
Understanding Proportions A proportion is a statement that two ratios are equal. We need to determine which of the given options represents a true proportion. A ratio a : b can be written as a fraction b a .
Checking Each Option Let's examine each option to see if the ratios are equal.
Analyzing Option A Option A: 7 : 9 = 8 : 9 can be written as 9 7 = 9 8 . This is false because 7 is not equal to 8.
Analyzing Option B Option B: 54 : 9 = 6 : 3 can be written as 9 54 = 3 6 . We can simplify both fractions. 9 54 = 6 and 3 6 = 2 . Since 6 = 2 , this is false.
Analyzing Option C Option C: 2 : 1 = 1 : 2 can be written as 1 2 = 2 1 . This is false because 2 is not equal to 2 1 .
Analyzing Option D Option D: 3 : 4 = 9 : 12 can be written as 4 3 = 12 9 . We can simplify the fraction 12 9 by dividing both the numerator and the denominator by 3, which gives us 12 ÷ 3 9 ÷ 3 = 4 3 . Since 4 3 = 4 3 , this is true.
Conclusion Therefore, the true proportion is 3 : 4 = 9 : 12 .
Examples
Proportions are used in everyday life to scale recipes, convert measurements, and calculate discounts. For example, if a recipe calls for 2 cups of flour for 1 cake, a proportion can be used to determine how much flour is needed for 3 cakes. Similarly, proportions are used in maps to relate distances on the map to actual distances on the ground. Understanding proportions helps in making accurate estimations and decisions in various practical situations.
The true proportion among the options given is D) 3:4 = 9:12, as both ratios simplify to 4 3 .
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