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# Sharing Using Ratios

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### Sharing Using Ratios

1. 1. Image Source: http://resources2.news.com.au
2. 2. Katerina Tina and Paul each contributed the following amountsto buy a Lottery Ticket: Katerina \$ 6 Tina \$ 10 Paul \$4They agree to share any winnings in the same ratio as thedollars which each person contributed.These friends get lucky and their ticket wins \$ 120 000 !
3. 3. Here is how we use ratios to share up the winnings. The original Contribution Ratio was as follows: Katerina : Tina : Paul 6 : 10 : 4 Total Parts = 6 + 10 + 4 = 20 \$6 \$10 \$4Total Amount of \$120 000 is to be shared in 20 Total Parts ( Continued on Next Slide )
4. 4. Total Amount of \$120 000 is being shared in 20 Total Parts Amount for One Part = 120 000 20 Amount for One Part = 6 000 6 10 4Katerina gets 6 parts = 6 x One Part = 6 x 6 000 = \$ 36 000Tina gets 10 parts = 10 x One Part = 10 x 6 000 = \$ 60 000Paul gets 4 parts = 4 x One Part = 4 x 6 000 = \$ 24 000
5. 5. The total of all of the shares must equal the original total amount.\$36 000 + \$60 000 + \$24 000 = \$120 000 ? \$120 000 = \$120 000 Our answer appears to be correct. Money Image Source: http://wallsdl.com
6. 6. The resulting Shares Ratio should simplify to equal the Original Ratio value36 000 : 60 000 : 24 000 = 6 : 10 : 4(Divide by common factor of 1000)36 : 60 : 24(Divide by common factor of 6) \$6 \$10 \$4 6 : 10 : 4Our sharing answer is definitely correct
7. 7. Working Out StepsFind the Total Number of Parts in the Ratio(Do this by adding up the number values in the Ratio to get a Total)Amount for One Part = Total Amount being Shared Total Number of Parts in Ratio (This tells us what one part is worth)Each Share = its Ratio Number x Amount for One Part (Calculate the share amount for each number value that is in the original given ratio by multiplying it by the “One Part” amount)
8. 8. Checking Sharing Amount Answers1. Check all the Shares Add Up to the original given Amount - Do this by adding up all the share values to get a Total2. Check the Ratio of the Shares simplifies to equal the original given ratio - Take the share amounts and write them as a Ratio - Simplify this Ratio by dividing by common factors - Check this simplified ratio (written in the correct order) matches the original sharing ratio that was given in the question.
9. 9. Divide 40 in the Ratio 2 : 3For the Ratio 2 : 3, the Total Parts are 2 + 3 = 5Amount for One Part = Total Amount Shared Total Parts One Part = 40 / 5 = 8The “2” in 2 : 3 is 2 Parts = 2 x One Part = 2 x 8 = 16The “3” in 2 : 3 is 3 Parts = 3 x One Part = 3 x 8 = 24 Addition Check for Answers = 40
10. 10. Mel shares 21 chocolates with her sister Lana in theRatio of 4 chocolates to Mel for every 3 to Lana.How many chocolates does each girl receive ?For the Ratio 4 : 3, the Total Parts are 4 + 3 = 7Amount for One Part = Total Amount Shared Total Parts One Part = 21 / 7 = 3Mel gets 4 Parts = 4 x One Part = 4 x 3 = 12 chocolatesLana gets 3 Parts = 3 x One Part = 3 x 3 = 9 chocolates
11. 11. Kyle puts in \$ 4000 and Jason puts in \$ 7000 to start anOnline Computer Games Store. They sell the businesstwo years later for \$22 000. How much of the \$22 000should each person receive ?For the Ratio 4000 : 7000, we first need to simplify to theRatio 4 : 7 by dividing by 1000. Total Parts are 4 + 7 = 11One Part = Total Amount Shared = 22 000 / 11 = 2000 Total PartsKyle gets 4 Parts = 4 x One Part = 4 x 2000 = \$8 000Jason gets 7 Parts = 7 x One Part = 7 x 2000 = \$14 000