Answer:
Step-by-step explanation:
First, you need to understand how to solve the problems, then you can do it yourself.
If you can multiply or divide both numbers of a ratio by the same number to get the other ratio, then the ratios are equivalent.
Example 1:
Question:
Are the ratios 2:3 and 8:12 equivalent?
Answer:
2 * 4 = 8
3 * 4 = 12
Both numbers of the first ratio 2:3 were multiplied by the same number, 4, to get the new ratio 8:12, so the ratios are equivalent.
Example 2:
Question:
Are the ratios 5:7 and 25:49 equivalent?
Answer:
5 * 5 = 25
7 * 7 = 35
The numbers of the first ratio 5:7 were multiplied by two different numbers, 5 and 7, to get the second ratio, 25:49, so the ratios are not equivalent.
9a. 7/12 = 14/24 (both numbers multiplied by 2) True
9b. 9 to 20 and 27:40. 9 * 3 = 27, but 20 * 3 = 60, not 40. False
9c. 8/11 and 16/22. Multiply both 8 and 11 by 2. True
9d. 40:8 and 20:2.Start with the second ratio. 20 * 2 = 40. 2 * 2 = 4, not 8. False
9e. 4 to 7; 8 to 14; 20 to 35. 4 * 2 = 8; 7 * 2 = 14; 4 to 7 and 8 to 14 are equivalent. 4 * 5 = 20; 7 * 5 = 35; 4 to 7 is equivalent to 20 to 35. True
9f. 50/75; 10/15; 5/7. Start with 5/7. Multiply 5 and 7 by 2. You get 10/14. False
For problem 10, multiply both number in the ratio by the same number. Choose any number you want, but use that same number in each ratio to multiply by twice. Here are my solutions showing the numbers I chose. You can choose any numbers you want to divide or multiply by.
10a. 8/13 = 16/26 (I multiplied both numbers by 2.)
10b. 28 to 49 = 4 to 7 (I divided both numbers by 7.)
10c. 2:3 = 20:30 (I multiplied both numbers by 10.)
10d. 7/9 = 35/45 (I multiplied both numbers by 5.)
10e. 80/20 = 8/2 (I divided both numbers by 10.)
10f. 45 to 35 = 9 to 7 (I divided both numbers by 5.)
