Knowledge Organiser: Sharing in a Ratio
Key Terms
- Ratio: A comparison of two or more quantities using the : notation
- Parts: The individual shares that a ratio is divided into
- Total parts: The sum of all the numbers in the ratio
- One part: The total amount divided by the total number of parts
- Unequal sharing: Dividing a quantity so each person gets a different amount based on the ratio
Must-Know Facts
- Add the ratio numbers together to find the total number of parts
- Divide the total amount by the total parts to find the value of 1 part
- Multiply 1 part by each ratio number to find each share
- Always check: your shares must add back up to the original total
- If given the difference between two shares, find how many parts the difference represents
- Ratios can have 2, 3 or more parts (e.g. 2:3:5)
- The ratio 2:3 is the same as 4:6 but NOT the same as 2:5
Key Methods
- 3-step method: add parts → find 1 part → multiply each
- Difference method: if told A gets £x more than B, find the difference in parts, then 1 part = £x ÷ difference
- Working backwards: if one share is given, divide by its ratio number to find 1 part, then multiply total parts
- Check: shares must sum to the original amount
Common Mistakes
- Using total parts as the divisor: For ratio 3:5, divide by 8 (total parts), not by 5, add all parts of the ratio first
- Not checking shares sum to the total: Always verify your three (or two) shares add back to the original amount
- Difference method errors: If B gets £40 more than A in ratio 3:5, the difference is 5 − 3 = 2 parts = £40, so 1 part = £20, not 1 part = £40
- Wrong number of parts for three-way ratios: For a:b:c, total parts = a + b + c, students often forget to include all three