Psychguy98 said:
If 0.002 ? a ? 0.05 and 0.01 ? b ? 0.50, then what is the greatest possible value of (a/b)^2 ?
I'm not sure where to start. Do i need to find a numerical value between a and b and plug it into (a/b)^2 ?
I know I'm repeating myself, but toasters and lamps can be "plugged in;" a value may be SUBSTITUTED for a variable.
That said, you may want to consider what happens when one number is divided by another. How does the relative size of the dividend (number being divided) and the divisor (the number you're dividing by) affect the size of the quotient (the result of the division)?
In a/b, "a" is the dividend. "b" is the divisor. "a/b" is the quotient.
So, we can think about how the relative size of the numerator and the denominator affect the value of a fraction.
Suppose we consider the fraction 8/8. The numerator and the denominator in this case are the same size, and the value of the fraction is 1.
What happens to the value of the fraction if we keep the numerator the same, but make the denominator smaller? If, for example, we make the denominator 6, how does that affect the value of the fraction? 8/6 is 4/3, or 1 1/3. The value of the fraction is INCREASED.
What happens to the value of the fraction if we make the denominator smaller yet? What if we change the denominator to 4? Then the fraction is 8/4, or 2. And 2 > 1 1/3, so the value of the fraction has increased again.
What happens if we start with 8/8, and make the denominator LARGER? For example, what if we change the denominator to 12? Then the fraction would be 8/12, or 2/3, and 2/3 < 1.
If we make the denominator larger yet, say change from 12 to 16? Then the fraction would be 8/16, or 1/2. And 1/2 < 2/3 < 1. The value of the fraction has gotten smaller yet.
a/b = 1 if a = b.
a/b > 1 if a > b.
a/b < 1 if a < b.
So, if you want the greatest possible value of a/b, you want to use the largest possible value of a, and the smallest possible value of b.
You are given a set of permissible values for "a"...choose the largest of those.
You are given a set of permissible values for "b"....choose the smallest of those.
If you have the largest possible numerator paired with the smallest possible denominator, the result of the division a/b should have its largest value.
