Katerina, Tina, and Paul contributed $6, $10, and $4 respectively to buy a lottery ticket. They won $120,000, and agreed to split the winnings proportionally to their contributions. Calculating their shares as portions of the total $120,000 based on the original contribution ratios results in Katerina receiving $36,000, Tina receiving $60,000, and Paul receiving $24,000. Verifying that these shares add up to the total winnings confirms the correct application of proportional reasoning to split the prize.

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2. Katerina Tina and Paul each contributed the following amounts
to buy a Lottery Ticket:
Katerina $ 6
Tina $ 10
Paul $4
They agree to share any winnings in the same ratio as the
dollars 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 $4
Total 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 4
Katerina gets 6 parts = 6 x One Part = 6 x 6 000 = $ 36 000
Tina gets 10 parts = 10 x One Part = 10 x 6 000 = $ 60 000
Paul 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.
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6. The resulting Shares Ratio should simplify
to equal the Original Ratio value
36 000 : 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 : 4
Our sharing answer is definitely correct

7. Working Out Steps
Find 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 Answers
1. Check all the Shares Add Up to the original given Amount
- Do this by adding up all the share values to get a Total
2. 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 : 3
For the Ratio 2 : 3, the Total Parts are 2 + 3 = 5
Amount for One Part = Total Amount Shared
Total Parts
One Part = 40 / 5 = 8
The “2” in 2 : 3 is 2 Parts = 2 x One Part = 2 x 8 = 16
The “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 the
Ratio 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 = 7
Amount for One Part = Total Amount Shared
Total Parts
One Part = 21 / 7 = 3
Mel gets 4 Parts = 4 x One Part = 4 x 3 = 12 chocolates
Lana gets 3 Parts = 3 x One Part = 3 x 3 = 9 chocolates

11. Kyle puts in $ 4000 and Jason puts in $ 7000 to start an
Online Computer Games Store. They sell the business
two years later for $22 000. How much of the $22 000
should each person receive ?
For the Ratio 4000 : 7000, we first need to simplify to the
Ratio 4 : 7 by dividing by 1000. Total Parts are 4 + 7 = 11
One Part = Total Amount Shared = 22 000 / 11 = 2000
Total Parts
Kyle gets 4 Parts = 4 x One Part = 4 x 2000 = $8 000
Jason gets 7 Parts = 7 x One Part = 7 x 2000 = $14 000

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