Remark
I'll do two from each group, leaving you with 1. I just leave the answer for the one I don't do or a hint it it is long. That's more than we are instructed to do (which is three parts per posted question).
One
Two ratios form a proportion because they both equal the same thing when you reduce them to the point where the ratios are prime to each other.
3/4 = 12/16
3/4 can't be reduced any further. When both 12 and 16 are divided by 4, the result is 3/4
Two
Formula
Sale Price/Original Price = 3/4
Solve
Sale Price / 64 = 3/4 Multiply both sides by 64
Sale Price = (3/4)*64
Sale Price = 48
Three
682 Trillion atoms of hydrogen.
Four
Formula
rotations / 40 seconds = rotations / second
Solve
2000 / 40 seconds = rotations / 1 second Just divide
50 rotations/1 second = rotations / second.
Five
Formula
Herd of cows / Total pounds of milk = 1 cow / pounds of milk
Given
Herd = 12
pounds total = 224998
Solve
12/224998 = 1 / x Cross multiply
12x = 224998
x = 18750 pounds of milk for 1 cow.
Six
0.5 m in 1 second.
Seven
Formula
Pages / hour = pages / minute
pages / hour = 4.5
1 hour = 60 minutes.
Solve
4.5 / 1 hour. But 1 hour = 60 min
4.5 pages / 60 min = 0.075 pages per minute.
Note this is not a true proportion. You just have to know how it is done.
Eight
This is also not a true proportion. The best way to do this is called unit analysis.
Each set of units on the right will cancel with a set of units on the left until all that you area left with is miles / hour. Then just multiply the numerator numbers together and denominator numbers together.
numerator: 18 * 1 * 3600 = 64800
denominator: 2 * 5280 * 1 = 10560
Now divide the numerator by the denominator.
answer: numerator/denominator = 64800/10560 = 6.14 miles per hour.
Nine
Note: there are 1760 yards in a mile.
1 gallon will take you 32000 yards or 18 miles. Do this the same way eight was done.