Final answer:
The ratio 14:1 can be rewritten as both 140:10 and 70:5, since both reduce to 14:1 when simplified. These are the only two options provided that are equivalent to the original ratio.
Step-by-step explanation:
The ratio 14:1 can be written in different ways by multiplying or dividing both terms of the ratio by the same number. Looking at the options provided:
- a. 7:2 - This cannot be correct because if you multiply 7 by 2, you do not get 14.
- b. 28:2 - This is also incorrect because dividing 28 by 2 gives us 14, but dividing the second term, 2, by 2, we get 1, which is the original ratio 14:1.
- c. 140:10 - This is correct; if we divide 140 by 10, we get 14, and dividing 10 by 10, we get 1, maintaining the 14:1 ratio originally provided.
- d. 70:5 - This also represents the same ratio because if we divide 70 by 5, it reduces down to 14:1.
Only options c. 140:10 and d. 70:5 accurately represent the ratio 14:1. Therefore, the ratio can be written as both 140:10 and 70:5. To check if ratios are equivalent, you can simply reduce them to the simplest form and see if they match the original ratio.