If the ratio of a to b is equal to the ratio of b to a, what can you say about the two numbers a and b? Are they the same or different? What are some some examples of this?
If b/a = a/b, then a^2 = b^2
a = +b or -b
In this case, the numbers are the same right?
I am going to work on some more examples of this.
Thanks.
Hi classmate. You took the words right out of my mouth!
No. That a = b is not the 0NLY answer. They can differ in sign. Read my previous post again
If the ratio of a to b is equal to the ratio of b to a, it implies that a divided by b is equal to b divided by a. In other words, a/b = b/a.
To determine what can be said about the numbers a and b, we can simplify this equation further by cross-multiplying: a * a = b * b.
From this equation, it becomes evident that the square of a is equal to the square of b. Taking the square root of both sides, we find that the magnitude of a is equal to the magnitude of b: |a| = |b|.
Based on this conclusion, we can say that the two numbers, a and b, have the same magnitude but may have opposite signs. This means that a and b can be either the same number or opposites of each other.
Here are some examples:
Example 1:
a = 3, b = 3
In this case, a and b are the same number, and the ratio of a to b (3/3) is equal to the ratio of b to a (3/3).
Example 2:
a = -4, b = 4
Here, a and b are opposites of each other, and again, the ratio of a to b (-4/4) is equal to the ratio of b to a (4/-4).
So, to summarize, the numbers a and b can be the same or opposites of each other when their ratios are equal.