Final answer:
a. False; b. True; c. False; d. True
Step-by-step explanation:
For statement a, the ratio 3/8 to 4/9 does not have a unit rate of 1/6. To find the unit rate, we need to simplify the ratio. Simplifying 3/8, we get 3/8 = 9/24. Simplifying 4/9, we get 4/9 = 8/18. Dividing 9/24 by 8/18, we get 9/24 ÷ 8/18 = 9/24 × 18/8 = 3/4. Therefore, the unit rate for the ratio 3/8 to 4/9 is 3/4, not 1/6. So, statement a is false.
For statement b, the ratio 5/12:25/18 does have a unit rate of 3/10. To find the unit rate, we need to simplify the given ratio. Simplifying 5/12, we get 5/12. Simplifying 25/18, we get 25/18 = 50/36 = 25/18 = 5/3. So, the simplified ratio is 5/12:5/3. Dividing 5/12 by 5/3, we get (5/12) ÷ (5/3) = 5/12 × 3/5 = 15/60 = 1/4. Therefore, the unit rate for the ratio 5/12:25/18 is 1/4 = 3/12 = 3/10. So, statement b is true.
For statement c, the ratio 6/11 to 1/6 does not have a unit rate of 1 1/11. To find the unit rate, we need to simplify the ratio. Simplifying 6/11, we get 6/11. Simplifying 1/6, we get 1/6 = 11/66. Dividing 6/11 by 11/66, we get (6/11) ÷ (11/66) = 6/11 × 66/11 = 6/1 = 6. Therefore, the unit rate for the ratio 6/11 to 1/6 is 6, not 1 1/11. So, statement c is false.
For statement d, the ratio 4/7:8/21 does not have a unit rate of 3/2. To find the unit rate, we need to simplify the ratio. Simplifying 4/7, we get 4/7. Simplifying 8/21, we get 8/21 = 24/63 = 8/21. So, the simplified ratio is 4/7:8/21. Dividing 4/7 by 8/21, we get (4/7) ÷ (8/21) = 4/7 × 21/8 = 3/2. Therefore, the unit rate for the ratio 4/7:8/21 is 3/2. So, statement d is true.