Reciprocals

Discussion in 'Mathematics' started by CatherineSurtees, Nov 17, 2015.

1. CatherineSurteesNew commenter

With a top set year 8 class we have been looking at reciprocals of fractions and reciprocals of decimals.

I have had pupils ask what this is used for in real world or in any additional maths process'.

Can anybody give me examples of when and how reciprocals are used?

2. maths126New commenter

Reciprocals essential higher up the school when manipulating algebraic equations and expressions.
In real life, virtually every compound measurement involves reciprocals. For example, given speed = distance/time, how does one calculate the time a journey takes knowing speed and distance?

3. SkillsheetsOccasional commenter

The gradients of perpendicular lines are negative reciprocals of each other.

Also they are useful for explaining why dividing by 2 is equivalent to multiplying by a half.

Your student is wise to ask. It is one of those topics that gets taught in an isolated way with no apparent relevance.

You could also look at scale factors for enlarging shapes.

4. maths126New commenter

Another obvious everyday example - currency conversions when going abroad.
In fact, any conversion (except temperature!) between two different units.
Taking this further down the line in Science we get into Dimensional Analysis which is always fun!

The most explicit example I can think of is the period of something vs its frequency. So a frame rate of 30 FPS means the frame changes every 1/30th of a second. Very useful if you're doing video analysis.

6. ChallapalliChandraNew commenter

You can describe reciprocals of fractions/decimals this way:
How many halves (1/2's) are there in 1? 1/ 1/2 = 2
How many two thirds are there in one? 1/ 2/3 = 3/2 = one and a half.

A real world example: If each student can paint 0.5 (half or 1/2 or 50%) of the wall, how many students are required to completely paint the wall?

Continued fractions are one place where you need expertise with reciprocals of fractions. These appear in formulae for irrational numbers and also in fractal theory.

7. racroesusStar commenter

They are f-stops in photography.