6.6 IN-DEPTH PATH simplifying algebraic fractions
Theory
As you can simplify fractions with only numbers, you can also simplify fractions with letters. Important to remember is that you always have to divide the numerator and the denominator by the same number and or/letter. If you can't divide the numerator and the denominator by the same letter and/or number, then you can't simplify the fraction any further.
If you need to add or subtract fractions, the denominators must be the same.
With multiplication the denominators do not have to be the same.
Test yourself exercise
You are going to learn how to simplify fractions with imaginary numbers. You are only able to understand this theory if you understand simplifying fractions with letters. To test yourself you can do this exercise.
Simplify
Algebraic fractions as applications in physics
Extra learning objectives
At the end of this paragraph you are able to...
...explain where the lens formula is used for.
...rewrite the lens formula.
The lens formula
The lens formula is a formula used in physics and looks like this:
f = focal length
b = object distance
v = image distance
But, where is this formula used for?
The formula is used to calculate the distances of lenses. In order to calculate the distances of the lenses, you need to know what the object distance, image distance and the focal length is.
The object distance(b) and the image distance(v) could be explained best by looking at the picture underneath.
The object distance (b) is the distance from the lens to the object where the light is been displayed. In this case the object is the screen.
The image distance (v) is the distance from the light source to the lens. In this case the lamp with the dia (= slide) is the image.
The focal length (f) could be best explained by looking at the picture underneath.
If you hold a magnifying glass in the sun and you point it on a piece of paper or on dry leaves. You would get a fire. This is the beams of light comes together to one point called the focal length (= brandpunt)
Rewrite the lens formula
The lens formula is given as a fraction with letters. However, you might want to know what b is or v or f and not what 1 divided by b is.
In this case it is easy if you can rewrite formulas. With rewriting formulas we mean that you can write the formulas in the form of b =... or f = ... or v = ...
Example of rewriting the lens formula to the form of b = ...
So, to rewrite formulas you need to think about the arithmetic rules: You may only add or subtract fractions if they have the same denominator. If you divide something in a formula, you need to divide EVERYTHING by the same number/letter. And most important, see the rewriting as little puzzles.
Exercises
Exercise 1:
Simplify
a)
b)
c)
Exercise 2:
Rewrite the lens formula to...
a) v = ...
b) f = ...
