Dividing a Whole in a Given Ratio

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Dividing a Whole in a Given Ratio DIVIDING A WHOLE IN A GIVEN RATIO (e.g., a🅱️c) THE CONCEPT: Distributing a Total Amount into Parts Dividing a whole amount in a given ratio means splitting it into different parts according to the proportional relationship defined by the ratio. REAL-LIFE EXAMPLE: Splitting a Prize Fund Three friends (Alice, Bob, Charlie) win a prize in a competition. They decide to split it in the ratio based on their contribution.WORKED EXAMPLE: Calculating Individual Shares Scenario: How much does each person get from the prize? STEP 1: Find the Total Number of Parts. Ratio is . Total Parts parts. STEP 2: Calculate the Value of One Part. Total Amount = $600. STEP 3: Calculate Each Person's Share.Alice's Share (3 parts) . Bob's Share (2 parts) . Charlie's Share (1 part) = . STEP 4: Verify the Total. Check: $300 + $200 + $100 = $600. (Correct!)FINAL ANSWER: Alice gets , Bob gets , and Charlie gets $100.ALTERNATIVE METHOD: Using FractionsEach share is a fraction of the total amount. Alice's share = (3/6) of $600= (1/2) * $600 = $300. Bob's share of . Charlie's share of . Same result!General Rule for Dividing a Whole When you need to divide a total amount (the "whole") into a ratio like 𝑎:𝑏:𝑐 : Add up the ratio numbers to find the total number of parts (𝒂+𝒃+𝒄). Divide the total amount by the total number of parts. This tells you the value of one single part. Multiply that value by each number in your ratio to get the final amounts. Let’s do some questions now