P5 Rate: Unit Rate, Tables & Tiered Problems (Complete Guide)
Master P5 Rate with the Unitary Method — unit rate, two-step problems, table-based rates, and tiered pricing. Step-by-step worked examples for PSLE Math.
P5 Rate: The Complete Guide to Unit Rate, Tables & Tiered Problems
Rate is one of the most practical topics in P5 Math — it shows up in speed, pricing, postage, and even taxi fares. The secret weapon? Always find the value for 1 unit first. Let’s master it step by step.
What Is a Rate?
A rate compares two different quantities. It tells you how much of one thing corresponds to one unit of another.
You see rates everywhere in daily life:
| Rate | What It Means |
|---|---|
| 60 km per hour | 60 km for every 1 hour |
| $12 per hour | $12 for every 1 hour of work |
| 40 muffins per hour | 40 muffins baked every 1 hour |
| 32 litres per minute | 32 litres of water every 1 minute |
💡 The Magic Word: 'Per'
The word “per” means “for every 1”. Whenever you see “per” in a problem, you’re dealing with a rate. Think of it as a bridge connecting two different measurements.
Part 1: Finding the Unit Rate
The unit rate is the amount for exactly 1 unit. To find it, divide.
Formula:
Example 1: Baking Rate
A baker bakes 120 muffins in 3 hours. Find the baking rate in muffins per hour.
Step 1: Divide total muffins by total hours.
Answer: 40 muffins per hour
Example 2: Speed
A turtle crawls 450 cm in 9 minutes. What is its speed in cm per minute?
Step 1: Divide total distance by total time.
Answer: 50 cm per minute
Example 3: Pay Rate
Ali is paid $84 for working 7 hours. What is his hourly pay rate?
Step 1: Divide total pay by total hours.
Answer: $12 per hour
Quick Practice: Find the Unit Rate
| Problem | Unit Rate |
|---|---|
| 480 toys in 8 hours | 60 toys per hour |
| 60 litres in 5 minutes | 12 litres per minute |
| $150 for 6 kg | $25 per kg |
Part 2: Using Rate to Calculate
Once you know the unit rate, multiply to find larger amounts.
Formula:
Example 4: Earnings
Raju earns $12 per hour. How much does he earn in 8 hours?
Step 1: Multiply the rate by the number of hours.
Answer: $96
Example 5: Distance
A train travels at 90 km per hour. What distance does it cover in 4 hours?
Answer: 360 km
💡 The Two Core Operations
Finding the rate? → Divide (total ÷ units)
Using the rate? → Multiply (rate × units)
That’s really all there is to it!
Part 3: Two-Step Rate Problems (The Unitary Method)
Many PSLE problems don’t give you the unit rate directly. You need two steps:
- Step 1: Find the unit rate (divide)
- Step 2: Find the new amount (multiply or divide)
This is called the Unitary Method — and it’s the most important technique for rate problems.
Example 6: Fan Spins
A fan spins 300 times in 5 minutes. How many times does it spin in 2 minutes?
Step 1: Find the rate per minute.
Step 2: Find spins in 2 minutes.
Answer: 120 times
Example 7: Printer
A printer prints 400 flyers in 8 minutes. How many flyers does it print in 20 minutes?
Step 1: Find the rate per minute.
Step 2: Find flyers in 20 minutes.
Answer: 1000 flyers
Example 8: Finding Time
A bus travels 240 km in 4 hours. How long will it take to travel 420 km at the same speed?
Step 1: Find the speed.
Step 2: Find the time for 420 km.
Answer: 7 hours
Example 9: Price
5 kg of cherries cost $60. How much does 3 kg of cherries cost?
Step 1: Find the cost of 1 kg.
Step 2: Find the cost of 3 kg.
Answer: $36
Part 4: Table-Based Rate Problems
In real life, rates are often shown in tables — especially for postage and courier services. The key phrase to watch for is “up to”.
⚠️ 'Up to' Means 'Not More Than'
When a table says “Mass up to 50 g”, it means the rate applies for anything from just above the previous row to exactly 50 g. Always find the row where your value fits.
Example 10: Postage Table
Using the table below, find the cost to send a letter weighing 40 g.
| Mass up to | Postage Rate |
|---|---|
| 20 g | $2.00 |
| 50 g | $2.50 |
| 100 g | $3.00 |
Step 1: 40 g is more than 20 g but not more than 50 g.
Step 2: Use the “up to 50 g” row.
Answer: $2.50
Example 11: Courier Table
Find the cost to send a parcel of mass 3.5 kg.
| Mass up to | Charges |
|---|---|
| 2 kg | $20 |
| 5 kg | $40 |
| 8 kg | $55 |
Step 1: 3.5 kg is more than 2 kg but not more than 5 kg.
Step 2: Use the “up to 5 kg” row.
Answer: $40
Example 12: Two Letters
Find the total cost to send two letters: one 15 g and one 80 g.
| Mass up to | Postage Rate |
|---|---|
| 20 g | $2.00 |
| 50 g | $2.50 |
| 100 g | $3.00 |
Step 1: 15 g letter → up to 20 g → $2.00
Step 2: 80 g letter → up to 100 g → $3.00
Step 3: Total = $2.00 + $3.00 = $5.00
Answer: $5.00
Part 5: Tiered Rate Problems
Tiered rates are the trickiest type in P5 Rate. The price changes after a certain amount — like how a taxi charges differently for the first km versus the rest.
Strategy: Split the problem into portions, calculate each portion separately, then add.
Example 13: Bike Rental
Bike rental charges: First hour $5.00, every subsequent half hour $2.00. How much to rent for 2 hours?
Step 1: First hour = $5.00
Step 2: Remaining time = 2 - 1 = 1 hour = 2 half-hours
Step 3: Remaining cost = $2.00 × 2 = $4.00
Step 4: Total = $5.00 + $4.00 = $9.00
Answer: $9.00
Example 14: Electricity Bill
Electricity charges: First 100 units at $0.20 per unit, above 100 units at $0.30 per unit. A household uses 150 units. Calculate the bill.
Step 1: Split usage: 150 = 100 + 50
Step 2: First 100 units = $0.20 × 100 = $20.00
Step 3: Next 50 units = $0.30 × 50 = $15.00
Step 4: Total = $20.00 + $15.00 = $35.00
Answer: $35.00
Example 15: Indoor Playground
Indoor playground: 1st hour $10, subsequent half hour $4. Find the cost for playing from 3:00 pm to 5:30 pm.
Step 1: Find the duration: 3:00 pm to 5:30 pm = 2 hours 30 minutes
Step 2: First hour (3:00 - 4:00) = $10
Step 3: Remaining time = 1 hour 30 minutes = 3 half-hours
Step 4: Remaining cost = $4 × 3 = $12
Step 5: Total = $10 + $12 = $22
Answer: $22
Example 16: Taxi Fare
Taxi flag-down fare (1st km) is $4.00. Every additional 500 m is $0.30. Find the fare for a 6 km trip.
Step 1: First 1 km = $4.00
Step 2: Remaining distance = 6 - 1 = 5 km = 5000 m
Step 3: Number of 500 m blocks = 5000 ÷ 500 = 10
Step 4: Additional fare = $0.30 × 10 = $3.00
Step 5: Total fare = $4.00 + $3.00 = $7.00
Answer: $7.00
💡 Tiered Rate Checklist
For every tiered rate problem, follow these steps:
- Identify the first portion and its rate
- Calculate the remaining amount after the first portion
- Convert units if needed (hours to half-hours, km to metres)
- Calculate the cost for the remaining portion
- Add both portions together
Common Mistakes to Avoid
❌ Mistake 1: Forgetting to Find Unit Rate First
Many students try to jump straight to the answer. Always find the value for 1 unit first, then multiply or divide. The Unitary Method works every time!
❌ Mistake 2: Misreading 'Up To' Tables
A 40 g letter does NOT use the “up to 20 g” rate — it uses the “up to 50 g” rate. Always check: is my value within the range of this row?
❌ Mistake 3: Applying Tiered Rates to the Whole Amount
In tiered problems, the second rate only applies to the remaining portion, not the whole amount. Don’t multiply the total by the second rate!
⚠️ Mistake 4: Forgetting to Convert Units
In tiered problems, you might need to convert hours to half-hours or km to metres. A common error is counting 1.5 hours as 1 half-hour instead of 3.
Quick Reference: Rate Problem Types
| Problem Type | Strategy | Key Step |
|---|---|---|
| Find unit rate | Divide total by units | |
| Use unit rate | Multiply rate by target | |
| Two-step | Divide then multiply | Find for 1, then find for N |
| Table-based | Match value to correct row | Check “up to” ranges |
| Tiered rate | Split into portions | Calculate each portion separately |
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