номер 77
Analyzing a ratio sequence
So, for the numbers 10, 7, 49, and 70, I noticed that 10:7 could equal 70:49, though the last two seem reversed. It might also work to see 10:70 as 7:49, keeping the order and equality intact, since 10/70 = 7/49 = 1/7. This type of problem feels like a classic textbook exercise on ratios, where you arrange four numbers to show equal ratios. Both scenarios could be valid, but I'll highlight one specific arrangement.Explaining equal ratios
I’m breaking down how to find equal ratios. For instance, 12 can be expressed as 6 times 2, and 8 as 4 times 2. Similarly, 15 equals 3 times 5, while 25 is 5 times 5. For another example, 70 is 10 times 7, and 49 is 7 times 7, making the ratio of 10 to 7 equivalent to 70 to 49. Cross products can confirm this. I need to be meticulous with my wording and calculations, possibly using LaTeX formatting.
Краткий ответ:
- \(6:12=4:8\);
- \(3:5=15:25\);
- \(10:7=70:49\).
Как составить пропорцию: нужно подобрать два отношения с одинаковым значением.
- \(6:12=\frac12\), \(4:8=\frac12\).
- \(3:5=\frac35\), \(15:25=\frac35\).
- \(10:7=\frac{10}{7}\), \(70:49=\frac{10}{7}\).
Проверка по основному свойству пропорции — произведения крайних и средних членов равны:
- \(6\cdot8=12\cdot4=48\);
- \(3\cdot25=5\cdot15=75\);
- \(10\cdot49=7\cdot70=490\).
