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# Simplifying Ratios

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### Simplifying Ratios

1. 1. Image Source: http://www.createdby-diane.com
2. 2. Lets say we want to make some of our favourite Peanut Butter Cookies,which normally requires the ingredients shown on the previous slide.However, when we check in the fridge, we only have one egg, and not two.To make our cookies with only one egg, we will need to halve the recipeby dividing all of the ingredients by two.Eg. Use 1 egg, 1 packet of butter, 1/2 a cup of Peanut Butter, and so on.This way we keep the ratios, or proportions, of the ingredients the same,and so our cookies should still work out okay.Breaking down big ratios into smaller simplified ratiosis what we will be working on in this lesson.
3. 3. Simplifying Number Ratios is a lot like simplifying fractions.We need to find the biggest factor numberwhich goes into both parts of our Ratio.The biggest number which goes into a pairof number values is called:the "Greatest Common Factor" (GCF) orthe "Highest Common Factor" (HCF). GCF and HCF are the exact same thing.
4. 4. The steps we need to do to simplify a number ratio are:- Find the GCF or HCF for our two numbers.(Do this using Factor Trees for our two number values, or just work out the biggest number that goes into both).- Divide both our number values by the GCF or HCF value.(Dividing both values by the biggest number that goes into both of them will produce the smallest simplified ratio).- Write down the simplified answer ratio.
5. 5. Simplify the Ratio 6 : 15First find the GCF or HCF for our two numbers. 6 15 2 3 3 5 The biggest common factor is 3.Next we need to divide both 6 and 15 by the GCF of 3. (See next slide)
6. 6. Simplify the Ratio 6 : 15Divide both our number values by the GCF of 3. 6 : 15 3 3 2 : 5 The simplified Ratio Answer is 2 : 5
7. 7. Simplifying Ratios – Example 2 Simplify the Ratio 16 : 12 16 12 2 8 2 6 2 4 2 3 2 2 The biggest common factor is 2 x 2 = 4
8. 8. Simplifying Ratios – Example 2 Simplify the Ratio 16 : 12Divide both our number values by the GCF of 4. 16 : 12 4 4 4 : 3 The simplified Ratio Answer is 4 : 3
9. 9. Simplifying Ratios – Example 3 Simplify the Ratio 5 cm : 10 mmConvert both into the smaller sized mm unit. 5 cm : 10 mm x 10 50 mm : 10 mm 10 10 5 : 1The simplified Ratio Answer is 5 : 1
10. 10. The steps we need to do to Fractions are as follows:- Convert any Mixed Numbers into Improper Fractions.(Multiply the denominator by the whole number, then add on top numerator of the fraction part, and put it over denominator).- Multiply the Ratio by the Lowest Common Denominator.(If we have a Number on one side, and a Fraction on the other, then the “L.C.D.” will be the denominator of the fraction).- Work out the simplified answer ratio.
11. 11. Simplifying Ratios – Example 4 1 Simplify the Ratio 3 : 24Convert Mixed Number to Fraction and Simplify. 1 3 : 24 4 x 2 +1 9 3 : 4 x4 x4 L.C.D. 12 : 9 3 3 GCF 4 : 3
12. 12. We need to do an extra step at the start of these questions.This step involves getting both decimals into whole numbers.We do this by multiplying both decimals by either 10, 100,1000, etc depending on the number of decimal placedigits after the point.- If there is only one digit after the point, multiply by 10- If there are two numbers after the point, multiply by 100-If there are three numbers after the point, multiply by 1000(If there is a mixture of places, multiply by the highest number)
13. 13. Simplifying Ratios – Example 5 Simplify the Ratio 3.0 : 2.4Convert Decimals to Whole Numbers and Simplify. 3.0 : 2.4 1dp x10 1dp x10 30 : 24 6 6 GCF 5 : 6 The simplified Ratio Answer is 5 : 6
14. 14. Simplifying Ratios – Example 6 Simplify the Ratio 0.75 : 2.15Convert Decimals to Whole Numbers and Simplify. 0.75 : 2.15 2dp x100 2dp x100 75 : 215 5 5 GCF 15 : 43 The simplified Ratio Answer is 15 : 43
15. 15. Simplifying Ratios – Example 7 Simplify the Ratio 2.4 : 1.44Convert Decimals to Whole Numbers and Simplify. 2.4 : 1.44 x100 2dp x100 240 : 144 12 12 CF 1 20 : 12 4 4 CF 2 5 : 3