Use the cross product rule to determine which of the ratios is greater in each of the following cases:
1. 4:7 and 1:2 2. 3:5 and 7:10
3. 6:11 and 7:12
To compare ratios using the cross product rule, we will multiply the first term of the first ratio by the second term of the second ratio and compare it to the result of multiplying the second term of the first ratio by the first term of the second ratio.
1. For 4:7 and 1:2:
4 * 2 = 8
7 * 1 = 7
Since 8 is greater than 7, the ratio 4:7 is greater than 1:2.
2. For 3:5 and 7:10:
3 * 10 = 30
5 * 7 = 35
Since 30 is less than 35, the ratio 3:5 is less than 7:10.
3. For 6:11 and 7:12:
6 * 12 = 72
11 * 7 = 77
Since 72 is less than 77, the ratio 6:11 is less than 7:12.
Thanks for sharing your answer Bot GPT 3.5
You're welcome! If you have any more questions, feel free to ask.
Thanks again
You're welcome! I'm here to help, so if you have any more questions in the future, don't hesitate to ask. Have a great day!
You too have a great day!
Thank you! I appreciate the well-wishes. Have a fantastic day as well!
Is there any other way to solve this question? If so , please let me know
Yes, there is another way to solve these types of questions by finding the equivalent fractions for each ratio.
1. For 4:7 and 1:2:
To make the denominators equal, we can multiply the first ratio by 2/2 and the second ratio by 7/7:
4/7 * 2/2 = 8/14
1/2 * 7/7 = 7/14
Since 8/14 is greater than 7/14, the ratio 4:7 is greater than 1:2.
2. For 3:5 and 7:10:
To make the denominators equal, we can multiply the first ratio by 10/10 and the second ratio by 5/5:
3/5 * 10/10 = 30/50
7/10 * 5/5 = 35/50
Since 35/50 is greater than 30/50, the ratio 7:10 is greater than 3:5.
3. For 6:11 and 7:12:
To make the denominators equal, we can multiply the first ratio by 12/12 and the second ratio by 11/11:
6/11 * 12/12 = 72/132
7/12 * 11/11 = 77/132
Since 77/132 is greater than 72/132, the ratio 7:12 is greater than 6:11.
Using equivalent fractions allows you to compare ratios directly without involving cross products.