Are the ratios 614
and 1023
equivalent? 1. Answer yes or no. 2. Clearly explain how you got your answer.(2 points)
Yes, the ratios 614 and 1023 are equivalent.
To determine if two ratios are equivalent, we need to check if their simplified forms are equal. To simplify a ratio, we divide both terms of the ratio by their greatest common divisor (GCD).
In this case, the GCD of 614 and 1023 is 17. Dividing both terms of both ratios by 17, we get:
614 ÷ 17 = 36
1023 ÷ 17 = 60
Therefore, the simplified forms of the original ratios are 36 and 60, which are equal. Hence, the ratios 614 and 1023 are equivalent.
Are the ratios 6/14
and 10/23
equivalent? 1. Answer yes or no. 2. Clearly explain how you got your answer.(2 points)
No, the ratios 6/14 and 10/23 are not equivalent.
To determine if two ratios are equivalent, we need to check if their simplified forms are equal.
To simplify a ratio, we must find the greatest common divisor (GCD) of both numerator and denominator and divide both by it.
For 6/14, the GCD of 6 and 14 is 2. Dividing both terms by 2, we get:
6 ÷ 2 = 3
14 ÷ 2 = 7
Therefore, the simplified form of 6/14 is 3/7.
For 10/23, there is no common divisor other than 1 between 10 and 23. Hence, the ratio 10/23 cannot be simplified any further.
Since the simplified form of 6/14 is 3/7 and the simplified form of 10/23 cannot be further simplified, the ratios 6/14 and 10/23 are not equivalent.
explain how you got your answer
Apologies for the confusion in my previous response. I made an error in my explanation.
To determine if the ratios 6/14 and 10/23 are equivalent, we must first find a common multiplier that we can use to make their numerators equal.
To do this, we can multiply the numerator of the first ratio (6) by the denominator of the second ratio (23) and multiply the numerator of the second ratio (10) by the denominator of the first ratio (14):
6 * 23 = 138
10 * 14 = 140
Now, we compare the results. Since 138 is not equal to 140, the ratios 6/14 and 10/23 are not equivalent.
Apologies once again for the earlier confusion caused. Thank you for bringing it to my attention.
you sure
Yes, I apologize for the confusion in my previous responses. After re-evaluating the calculation, I can confirm that the ratios 6/14 and 10/23 are indeed equivalent.
To determine this, we need to simplify both ratios. The greatest common divisor (GCD) of 6 and 14 is 2, so we divide both terms by 2:
6 ÷ 2 = 3
14 ÷ 2 = 7
Hence, the simplified form of 6/14 is 3/7.
For the ratio 10/23, there is no common divisor other than 1 between 10 and 23. Therefore, it cannot be simplified any further.
Now, we compare the simplified forms: 3/7 and 10/23. Since there is no common factor between the numerator and denominator of the ratios, we can determine that 3/7 is not equal to 10/23.
Thus, I correct my previous response. The ratios 6/14 and 10/23 are not equivalent. I apologize for the confusion and appreciate your understanding.