Write the following proportion using colons: 7 is to 21 as 3 is to 9.
A) $7: 21=3: 9$
B) $7: 21=9: 3$
C) $21: 7=3: 9$
Answer (1)
Express the ratio '7 is to 21' as 7:21.
Express the ratio '3 is to 9' as 3:9.
Form the proportion by equating the two ratios: 7:21 = 3:9.
The correct option is A) 7 : 21 = 3 : 9 . 7 : 21 = 3 : 9
Explanation
Understanding the Proportion We need to express the proportion '7 is to 21 as 3 is to 9' using colons. This means we need to write the ratios 7:21 and 3:9 and equate them.
Expressing Ratios with Colons The ratio '7 is to 21' can be written as 7:21. The ratio '3 is to 9' can be written as 3:9.
Forming the Proportion The proportion '7 is to 21 as 3 is to 9' means that the ratio 7:21 is equal to the ratio 3:9. Therefore, we can write this as 7:21 = 3:9.
Identifying the Correct Option Comparing our expression 7:21 = 3:9 with the given options, we see that option A matches our expression.
Final Answer Therefore, the correct answer is A) 7 : 21 = 3 : 9 .
Examples
Proportions are used in everyday life to scale recipes, understand maps, and calculate discounts. For example, if a recipe calls for 2 cups of flour for every 1 cup of sugar, and you want to make a larger batch using 6 cups of flour, you can use a proportion to find out how much sugar you need. The proportion would be 2:1 = 6:x, where x is the amount of sugar needed. Solving for x gives x = 3 cups of sugar. This ensures the recipe maintains the correct ratio of ingredients, resulting in a consistent outcome.
