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# Sharing Using Ratios

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http://passyworldofmathematics.com/pwerpoints/

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• 1. Image Source: http://resources2.news.com.au
• 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. 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. 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. 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. 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. 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. 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. 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. 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. 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