Chapter 14 · ICSE Class 5 Math

Unitary Method

Find the value of ONE unit first, then scale up. Drag the sliders to see cost-per-unit problems solve themselves.

The Unit Rate Machine
₹5 per pen
6 pens cost ₹30
₹30
6

Try it: keep quantity the same and raise total cost — see the per-unit price rise too.

The unitary method: finding the cost of one item, then scaling up Three steps showing that 5 pens cost 50 rupees, so 1 pen costs 10 rupees, and therefore 8 pens cost 80 rupees 5 pens ₹50 ÷5→ 1 pen ₹10 ×8→ 8 pens ₹80 First find the cost of 1, then scale up to what you need
14.1

What is the unitary method?

The unitary method is a way of solving problems by first finding the value of a single unit (one item, one hour, one kilometre), then multiplying to find the value of any other number of units.

Why it matters — Once you know the price of ONE apple, you can find the cost of any number of apples — the unitary method is the tool behind almost every "how much for..." question.
14.2

Solving cost problems

1Finding the cost of one item

If 5 notebooks cost ₹150, find the cost of 1 notebook. Divide: 150 ÷ 5 = ₹30 per notebook

2Scaling up to a new quantity

Using the same rate, find the cost of 8 notebooks. Multiply: 30 × 8 = ₹240

Watch out — Always find the cost of ONE unit first (divide), then multiply for the new quantity. Skipping the "find one unit" step is the most common mistake in unitary method problems.
14.3

Converting between time formats

12-hour to 24-hour

Add 12 to PM hours (except 12 PM itself): 3:00 PM becomes 15:00.

24-hour to 12-hour

Subtract 12 from hours above 12, and label as PM: 18:30 becomes 6:30 PM.

1Converting 12-hour to 24-hour

Convert 7:45 PM to 24-hour format. Add 12 to the hour: 7 + 12 = 19. 19:45

2Converting 24-hour to 12-hour

Convert 21:15 to 12-hour format. Subtract 12: 21 − 12 = 9, and it's after noon so it's PM. 9:15 PM

14.4

Finding elapsed time

1Time between two clock readings

A train leaves at 9:15 AM and arrives at 11:40 AM. How long is the journey? From 9:15 to 11:15 is 2 hours, then 11:15 to 11:40 is 25 more minutes. 2 hours 25 minutes

2Elapsed time across noon

A movie starts at 11:30 AM and ends at 1:50 PM. From 11:30 AM to 1:30 PM is 2 hours, then 1:30 PM to 1:50 PM is 20 more minutes. 2 hours 20 minutes

Practice

Exercises

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Assess

Sample tests

Two 20-mark, 30-minute tests. Reveal answers question by question.