Which two ratios are equivalent?
(1)3/5 and 30/50
(2)5/8and 50/88
(3)6/11and66/110
(4)7/12and 49/80
3 / 5 = 3 / 5 ∙ 10 / 10 = 30 / 50 These two numbers are equal.
For the rest you use a calculator.
5 / 8 = 0.625 , 50 / 88 = 0.56818181 These two numbers are not equal.
6 / 11 = 0.545454545 , 66 / 110 = 0.6 These two numbers are not equal.
7 / 12 = 0.5833333 , 49 / 80 = 0.6125 These two numbers are not equal.
The equivalent ratios are:
(1) 3/5 and 30/50:
To check if they are equivalent, we need to simplify both ratios.
We can simplify 3/5 by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case.
So, 3/5 simplifies to 3/5.
Similarly, we can simplify 30/50 by dividing both the numerator and denominator by their greatest common divisor, which is 10 in this case.
So, 30/50 simplifies to 3/5.
Since both ratios simplify to 3/5, the first option (1) is correct.
(2) 5/8 and 50/88:
To check if they are equivalent, we need to simplify both ratios.
We can simplify 5/8 by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case.
So, 5/8 simplifies to 5/8.
We can simplify 50/88 by dividing both the numerator and denominator by their greatest common divisor, which is 2 in this case.
So, 50/88 simplifies to 25/44.
Since 5/8 and 25/44 are not equal, the second option (2) is not correct.
(3) 6/11 and 66/110:
To check if they are equivalent, we need to simplify both ratios.
We can simplify 6/11 by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case.
So, 6/11 simplifies to 6/11.
We can simplify 66/110 by dividing both the numerator and denominator by their greatest common divisor, which is 2 in this case.
So, 66/110 simplifies to 33/55.
Since 6/11 and 33/55 are not equal, the third option (3) is not correct.
(4) 7/12 and 49/80:
To check if they are equivalent, we need to simplify both ratios.
We can simplify 7/12 by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case.
So, 7/12 simplifies to 7/12.
We can simplify 49/80 by dividing both the numerator and denominator by their greatest common divisor, which is 1 in this case.
So, 49/80 simplifies to 49/80.
Since both ratios simplify to 7/12, the fourth option (4) is correct.
Therefore, the two ratios that are equivalent are:
Option (1): 3/5 and 30/50
Option (4): 7/12 and 49/80
To determine which two ratios are equivalent, we need to simplify each ratio to its simplest form and compare them.
Let's simplify each ratio:
(1) Ratio: 3/5 -> Simplifying numerator and denominator by dividing both by their greatest common divisor (GCD), which is 1 in this case.
(2) Ratio: 30/50 -> Simplifying numerator and denominator by dividing both by their GCD, which is 10 in this case.
The simplified ratio is 3/5, which is equivalent to the ratio in option (1).
(3) Ratio: 5/8 -> Simplifying numerator and denominator by dividing both by their GCD, which is 1 in this case.
Ratio: 50/88 -> Simplifying numerator and denominator by dividing both by their GCD, which is 2 in this case.
The simplified ratios are 5/8 and 25/44. These two ratios are not equivalent, so option (2) is not correct.
(4) Ratio: 6/11 -> Simplifying numerator and denominator by dividing both by their GCD, which is 1 in this case.
Ratio: 66/110 -> Simplifying numerator and denominator by dividing both by their GCD, which is 22 in this case.
The simplified ratios are 6/11 and 3/5. These two ratios are not equivalent, so option (3) is not correct.
(5) Ratio: 7/12 -> Simplifying numerator and denominator by dividing both by their GCD, which is 1 in this case.
Ratio: 49/80 -> Simplifying numerator and denominator by dividing both by their GCD, which is 1 in this case.
The simplified ratios are 7/12 and 49/80. These two ratios are not equivalent, so option (4) is not correct.
Hence, the two ratios that are equivalent are in option (1): 3/5 and 30/50.