Final answer:
The pairs of ratios that form a proportion are those which are equivalent when simplified. From the options given, only the ratios 4/10 and 10/25 form a proportion, as they both simplify to 2/5.
Step-by-step explanation:
To determine which ratios form a proportion, we need to compare them by either cross-multiplying or simplifying to see if they are equivalent. A proportion is created when two ratios are found to be equivalent or equal.
- a) 4/10 and 10/25: Simplify both fractions. 4/10 simplifies to 2/5, and 10/25 simplifies to 2/5. Thus, 4/10 and 10/25 form a proportion.
- b) 3/5 and 9/25: Cross multiply to check for equality. 3 * 25 is 75, and 5 * 9 is 45. Since 75 does not equal 45, they do not form a proportion.
- c) 4/9 and 9/4: When you cross multiply here, you get 36 in both cases (4 * 9 and 9 * 4), suggesting they may be inverses rather than a proportion. A proportion would require multiplying each side by the same factor, not inverting.
- d) 4/11 and 6/13: Cross multiply to check for equality. 4 * 13 is 52, and 11 * 6 is 66. Since 52 does not equal 66, they do not form a proportion.
So, the ratios that form a proportion from the options provided are 4/10 and 10/25.