Ratio & Proportion Ratio A ratio is very similar to a fraction in that it compares one thing to another In the shape on the right: How many total segments does it have? How many segments are shaded? As a fraction we could write this as As a ratio we can write it as We read this as 4 to 7 The Golden Ratio A ratio found in nature is called the golden ratio or 1:1.618 Fibonacci Sequence (0,1,1,2,3,5,8,.) Found in lots of different places Fact or FictionFact or Fiction Equivalent Ratio & Simplifying Ratio Just like when we compare things in fractions we always try and write a ratio in its lowest terms Try and stick to natural numbers. The ratio 36:12 could be re-written as We find the HCF of both numbers and divide them by it. In this case the HCF is 12 Direct Proportion When we have equivalent ratios we can call this a direct proportion Every time one part of a ratio changes the other part changes as well to keep the ratio equivalent For example; Baking Making cement Enlarging photographs We can also show this graphically Indirect or Inverse Proportion This is when a ratio is not fixed. If we increase one part the other part will decrease For example If Michael hires a taxi to the match it costs him 12 If his friend John goes with him then its 6 each If another friend Alex goes with them its 4 each Every time the amount of people increases the cost decreases Indirect or Inverse Proportion Question If it takes 12 builders four days to build a barn 1. How long would it take if four of the builders quit? 2. The customer said they wanted it done in 3 days? Strategy Find out how long it would take one person working on their own If 8 people are working divide your total by 8 Divide the total by 3 to find the amount of workers needed.