13. Chapter Revision Checklist

Before moving to the next chapter, make sure you can do each of the following without referring back to the notes:

• Reduce any ratio (including one with fractions or decimals) to its simplest whole-number form.
• Compare two or more ratios using cross-multiplication, without converting to decimals.
• Combine two separate ratios (a:b and b:c) into a single continued ratio a:b:c using the LCM-bridging method.
• Divide a given sum into 2, 3, or 4 parts according to a given ratio, including cases with an extra “difference” condition.
• State the difference between compound, duplicate, sub-duplicate, and triplicate ratios, and compute each correctly.
• Compute the mean proportional, third proportional, and fourth proportional between/to given numbers without hesitation.
• Distinguish direct proportion from inverse proportion in a word problem within the first reading.
• Apply componendo-dividendo both forward (deriving a ratio value) and in reverse (deriving a:b from a componendo-dividendo value).
• Solve simple partnership (same duration) and compound partnership (different durations, including mid-year capital changes) problems using the investment×time method.
• Set up and solve any ratio-based age problem using the ax, bx multiplier method.
• Convert fluently between “x% more/less than” language and ratio form, in both directions.
• Recall all 10+ formulas from the Quick Reference Formula Sheet (Section 7A) from memory.

If any box above feels shaky, revisit that section’s worked examples once more and re-attempt the corresponding practice questions from Sets A and B before proceeding — a solid grip on Ratio and Proportion will make the upcoming chapters on Average, Partnership, Ages, and Mixture and Alligation noticeably faster to learn.

End of Chapter 6: Ratio and Proportion.