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Units and Parts | The PSLE Mathematics Method for Ratios, Fractions and Equal Units

Units and Parts is a Primary Mathematics method for problems where quantities are related by equal abstract parts but the value of one part is not known at first. Ratios, fractions and multiplicative comparisons often become easier when the student temporarily stops thinking in dollars, marbles or pupils and thinks in units.

Students searching for units and parts method, unitary method PSLE, ratio units, fraction units or Primary 5/6 problem sums often know how to divide once the units are written. The hard part is deciding what one unit represents and ensuring units from different states are genuinely comparable.

This page is the canonical Units and Parts owner under the PSLE Mathematics Heuristics hub.

Quick answer: what is a unit?

A unit is one equal part in a mathematical relationship. In a ratio 3:5, the quantities are represented as 3 equal units and 5 equal units. The units are not actual values until the problem gives enough information to convert them.

Structure first, value second.

The four-step unit method

  1. Write the unit relationship.
  2. Count the relevant units.
  3. Match those units to a known actual value.
  4. Find one unit, then scale to the required quantity.

Example 1: total known

Problem: The ratio of boys to girls is 3:5. There are 64 pupils altogether. How many girls are there?

Total units: 3 + 5 = 8 units.
1 unit: 64 ÷ 8 = 8 pupils.
Girls: 5 × 8 = 40 pupils.

Example 2: one quantity known

Problem: The ratio of apples to oranges is 4:7. There are 28 apples. How many oranges are there?

4 units: 28.
1 unit: 28 ÷ 4 = 7.
7 units: 49 oranges.

Example 3: difference known

Problem: The ratio of Aisha’s savings to Ben’s savings is 7:4. Aisha has $45 more than Ben. How much does Ben have?

Difference in units: 7 − 4 = 3 units.
3 units: $45.
1 unit: $15.
Ben: 4 × $15 = $60.

This is a critical pattern: when the actual difference is known, match it to the difference in units, not the total units.

Example 4: fraction as units

Problem: 5/8 of a tank contains 35 litres. What is the full capacity?

5 parts: 35 L.
1 part: 7 L.
8 parts: 56 L.

Example 5: remaining fraction

Problem: 3/7 of a sum was spent. $80 remained. What was the original sum?

If 3/7 was spent, 4/7 remained.
4 units: $80.
1 unit: $20.
7 units: $140.

The challenge is identifying which fraction the known value belongs to.

Units are labels, not numbers

Writing “3 units = 45” is safe. Writing “3 = 45” is not. The word unit protects the student from treating the ratio number itself as the actual quantity.

Units also need identity. “1 unit of Aisha’s ratio” and “1 unit after the change” are not automatically the same. Before-and-after ratio problems require an invariant to connect states.

When units can be compared directly

  • same ratio state
  • same whole split into equal parts
  • same unit size explicitly preserved
  • quantities scaled from one common actual value

When units cannot be compared directly

  • ratio changes after transfer
  • whole changes between fractions
  • one side gains while another loses and the unit size changes
  • different diagrams use independently defined units

This is where constants become essential. Use Constant Total, Constant Difference and Constant Part.

The unit bridge

A unit bridge connects an abstract relationship to an actual value.

Example: ratio 5:8, difference = 21.
Difference = 3 units = 21.
Therefore 1 unit = 7.

Always state the bridge explicitly during learning. It reduces accidental division by the wrong number of units.

Common unit-method errors

  • Adds ratio units when difference is known.
  • Subtracts ratio units when total is known.
  • Uses spent fraction instead of remaining fraction.
  • Assumes unit size remains unchanged across a changed ratio.
  • Finds one unit correctly but scales to the wrong side.
  • Forgets the units represent equal parts, not actual counts.

A mixed decision table

  • Total known: add units.
  • Difference known: subtract units.
  • One side known: match that side’s units.
  • Fraction known: match numerator parts to actual value.
  • Remainder known: identify remaining fraction first.
  • Before/after ratio: identify constant before equating unit values.

Transfer drill

Take one ratio 3:5 and create four different problems: total known, difference known, smaller quantity known, larger quantity known. The ratio is identical but the unit bridge changes. This teaches structure instead of a fixed operation.

Frequently asked questions

What is the difference between units and actual values?

Units describe proportional structure. Actual values are found only after the problem gives a bridge between units and real quantities.

When do I add ratio numbers?

When the total of both quantities is known.

When do I subtract ratio numbers?

When the difference between the quantities is known.

Can one unit change size?

Yes across different ratio states. Do not equate units across before/after situations unless a constant justifies the connection.

Is this the same as the Model Method?

Units and Parts often uses bar models, but the core reasoning is the equal-unit relationship.

Where does this sit in Atlas?

This is the canonical Units and Parts owner under PSLE Mathematics Heuristics.

The final Units rule

Ask what the known number represents in units. Total? Difference? One side? Remaining fraction? Once the unit bridge is correct, the arithmetic is usually straightforward.

Explore the connected learning guides

Choose the question that brought you here. Open one useful guide, try a small task, and stop when you have what you need.

Take one question further

The same learning habit can travel across subjects, while each subject keeps its own methods. These routes help you notice a difficulty, understand one part of it, and return to something you can do.

A word is familiar, but using it is difficult.

Move from recognising a word to retrieving it in a new context. Understand vocabulary plateaus.

Try it without the guide: Choose one word you already know. Close the guide and use it in a new sentence. Explain why it fits; try another context tomorrow.

A piece of writing has ideas, but the reader loses the thread.

Make the order of events and the links between sentences clear. Explore composition writing.

Try it without the guide: Choose one short paragraph. Read the relevant explanation, close it, and revise the paragraph. Ask someone to tell you what happened and why.

The Mathematics seems familiar, but marks still disappear.

Find the first point where the working stops being reliable. Find Secondary 4 A-Math mark leakage.

Try it without the guide: For a Secondary 4 A-Math question you have attempted, locate the first uncertain line. Repair that step, then try a comparable question without the worked answer.

A Science fact is remembered, but the explanation is incomplete.

Connect the evidence to a scientific idea and the resulting change. Follow the Primary Science learning route.

Try it without the guide: Choose a familiar Primary Science example. Explain the evidence, the idea and the result without notes. Then change one condition and explain your prediction.

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Check the question, source, date and evidence before combining claims. Explore the World Knowledge research library.

Try it without the guide: Take one claim. Find the source best placed to support it, note its date, and state what remains uncertain. Return to your original question.

There is plenty of help, but independence is hard to see.

Check what the learner can understand and do after support is removed. Understand how education works.

Try it without the guide: Choose one small task the child has practised. Agree on a calm, brief attempt without prompts. Use what happens to choose one next step, then stop.

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