We use greatest common factors all the time with fractions, and as fractions are used a lot in everyday life, this makes GCF very useful! By finding the GCF of the denominator and numerator, you can then successfully simplify a fraction or ratio. E.g. We can simplify by knowing that its HCF is . Then we divide both parts by the HCF to simplify.
It also works for ratios, where you can simplify each side using HCF to find out a ratio. This can be useful if you are using a ratio for a recipe or order as you can use one piece of information to find out the right ratio for any combination. So, to put this into a situation, say you know that for every 5 people at a party, you need 15 sandwiches. The HCF of these two numbers is 5, so for each person you need:
3 sandwiches. Now, if 16 people come to your party, you know you have to make sandwiches. A final example is with recipes. Math can be very helpful in this situation! Here is a recipe for 10 cupcakes along with the serving size ratios for each: 100g flour = 10 people:100g = 1:10 80g sugar = 10 people:80g = 1:8 50g butter = 10 people:50g = 1:5 2 eggs = 10 people:2 eggs = 1:0.2 eggs So, if we want to give cakes to all our friends, and need 25 cupcakes (what a popular mathematician!) then you can just multiply out this ratio. Flour = 1:10 = 25:250 80g sugar = 1:8 = 1:200 50g butter = 1:5 = 25:125 2 eggs = 1:0.2 eggs = 25:5
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