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Units and Parts

Labelling the before-ratio in units and the after-ratio in parts, then solving them together when everything changes.

⏱ 5 min · 🎯 4 things to master

The hardest ratio questions at the end of a PSLE paper have a nasty feature: both quantities change, and by different amounts. Nothing stays the same — no constant total, no constant difference, no unchanged quantity. For these you use units and parts: label the before-ratio in units and the after-ratio in parts, then write down how each person links the two. It is a gentle, primary-friendly version of algebra with two letters.

Parents: this is an advanced technique — let your child work through each link before revealing. The "Method tip" boxes name the move a marker rewards.

By the end you'll be able to set up a units-and-parts problem and combine the two statements to find one unit. Let's set it up.

When nothing stays the same

First, check that this really is an "everything changes" problem: a before-ratio and an after-ratio, where both quantities go up or down by different amounts. If so, the single-invariant tricks will not work, and units-and-parts is your tool.

🤔 Predict first: Ali to Billy is 2 : 1. Then Ali saves $60 MORE and Billy SPENDS $150, giving 4 : 1. Does any single quantity stay the same?

Label units, then parts

Write the before amounts in and the after amounts in . For our problem:

  • Ali: 2 units, and after saving $60 more he has 4 parts → 2u + 60 = 4p.
  • Billy: 1 unit, and after spending $150 he has 1 part → 1u − 150 = 1p.

Two clean statements, each linking the before and the after for one person.

🤔 Predict first: Billy was 1 unit and after spending $150 he is 1 part. Which statement is correct?

Combine the two

Now use one statement inside the other. From Billy, 1p = 1u − 150, so 4p = 4u − 600. Put that into Ali: 2u + 60 = 4u − 600. Tidy up: 660 = 2u, so 1 unit = 330. Ali had 2 units = $660 at first.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

  1. When should you reach for the units-and-parts method?

  2. A person was 3 units and after receiving $40 is 2 parts. Which statement is right?

  3. If 1p = 1u − 150, what is 4p equal to?

  4. Solving 2u + 60 = 4u − 600 gives 2u = 660. What is one unit?

  5. Why are units and parts written with different letters?

  6. How many linking statements do you write for a two-person units-and-parts problem?