Welcome to "Applying Number"!
Ever sat in a math lesson and wondered, "When am I actually going to use this?" Well, this chapter is the answer! We are stepping out of the textbook and into the real world. Whether you are checking if a "Buy One Get One Free" deal is actually a bargain, planning a travel itinerary, or converting your holiday spending money, you are applying number.
Don't worry if you find word problems a bit tricky at first. We’re going to break these down into simple, logical steps that anyone can follow. Let’s get started!
1. Mastering Metric Units
In this course, we focus on metric units. These are great because they work in powers of 10, making them much easier to manage than older systems! You need to be comfortable with four main types of measurement: Length, Mass, Capacity, and Area/Volume.
Length, Mass, and Capacity
The most important thing here is knowing the "conversion factors" (how much of one unit fits into another). Here is a quick cheat sheet:
Length:
\( 1 \text{ centimetre (cm)} = 10 \text{ millimetres (mm)} \)
\( 1 \text{ metre (m)} = 100 \text{ centimetres (cm)} \)
\( 1 \text{ kilometre (km)} = 1000 \text{ metres (m)} \)
Mass (Weight):
\( 1 \text{ gram (g)} = 1000 \text{ milligrams (mg)} \)
\( 1 \text{ kilogram (kg)} = 1000 \text{ grams (g)} \)
\( 1 \text{ tonne (t)} = 1000 \text{ kilograms (kg)} \)
Capacity (Liquids):
\( 1 \text{ litre (l)} = 1000 \text{ millilitres (ml)} \)
\( 1 \text{ centilitre (cl)} = 10 \text{ millilitres (ml)} \)
How to convert easily:
- Big to Small: When moving from a large unit (like km) to a smaller unit (like m), the number gets bigger. Multiply!
- Small to Big: When moving from a small unit (like ml) to a larger unit (like l), the number gets smaller. Divide!
Memory Aid: Think of a Kilo as a "King" - he is worth 1,000 of his subjects! Whenever you see "kilo-", think 1,000.
Area and Volume Units (The Tricky Part!)
This is where many students make a common mistake. If \( 1 \text{ m} = 100 \text{ cm} \), students often think \( 1 \text{ m}^2 = 100 \text{ cm}^2 \). This is not true!
Because Area is "length times width," you have to convert both dimensions.
\( 1 \text{ m}^2 = 100 \text{ cm} \times 100 \text{ cm} = 10,000 \text{ cm}^2 \)
For Volume:
\( 1 \text{ m}^3 = 100 \text{ cm} \times 100 \text{ cm} \times 100 \text{ cm} = 1,000,000 \text{ cm}^3 \)
Quick Review Box:
To convert Area, square the conversion factor. \( (100^2) \)
To convert Volume, cube the conversion factor. \( (100^3) \)
Key Takeaway: Always check if you are dealing with a standard measurement, an area, or a volume before you start multiplying or dividing!
2. Calculations with Money
Money math is just decimal math with a dollar sign (or pound, or euro) in front of it. In your exam, remember that money is usually written to 2 decimal places (e.g., $5.40, not $5.4).
Currency Conversion
To convert between different types of money, you use an exchange rate. For example, if \( \$1 = €1.15 \):
- To change Home Currency to Foreign Currency: Multiply by the rate.
Example: \( \$200 \times 1.15 = €230 \) - To change Foreign Currency back to Home Currency: Divide by the rate.
Example: \( €460 \div 1.15 = \$400 \)
Analogy: Imagine the exchange rate is a "bridge toll." To cross into the foreign country, you multiply your bags; to come back across the bridge, you divide them.
Did you know? Exchange rates change every second in the real world based on global news, but in your math exam, the rate will stay fixed for the whole question!
Key Takeaway: Check your answer! If 1 dollar is worth more than 1 euro, you should end up with more euros than dollars when you convert.
3. Managing Time
Time is unique because it doesn't use the "Base 10" system. We don't have 100 minutes in an hour; we have 60. This is the #1 place where students lose marks!
12-Hour vs. 24-Hour Clock
- 24-Hour Clock: Starts at 00:00 (Midnight) and goes up to 23:59. It does not use am or pm.
- Conversion: To change pm times to 24-hour time, just add 12 to the hours.
Example: 4:30 pm becomes 16:30.
Calculating Time Intervals
If a train leaves at 14:45 and arrives at 17:20, how long was the journey?
Step-by-step method:
1. Count the minutes to the next hour: 14:45 to 15:00 = 15 mins.
2. Count the full hours: 15:00 to 17:00 = 2 hours.
3. Add the remaining minutes: 17:00 to 17:20 = 20 mins.
4. Total = 2 hours and 35 minutes.
Common Mistake to Avoid: Don't try to use your calculator for time like a normal decimal. \( 2.5 \text{ hours} \) is 2 hours and 30 minutes, not 2 hours and 50 minutes!
Key Takeaway: When working with time, always bridge to the nearest hour rather than trying to do a big subtraction calculation.
4. Real-Life Math (Domestic and Community)
This section of the syllabus asks you to use your brain for everyday scenarios. These questions often involve multiple steps. You might see questions about:
- Household Bills: Calculating the cost of electricity based on units used.
- Shopping: Comparing "Best Value" deals. Is a 500g box for $4 better than a 750g box for $5.50? (Tip: Find the price for 100g for both to compare!)
- Cooking: Adjusting a recipe for 4 people to serve 10 people.
The "Unit Method" for Best Value
If you are confused about which deal is better, find the cost per 1 unit.
Example:
Deal A: 3 bars of soap for $2.40 (\( \$2.40 \div 3 = \$0.80 \text{ per bar} \))
Deal B: 5 bars of soap for $3.50 (\( \$3.50 \div 5 = \$0.70 \text{ per bar} \))
Deal B is better!
Key Takeaway: In "Everyday Life" questions, read the story carefully. Often, the math is simple addition or multiplication, but the "story" tells you which numbers to use.
Summary: The "Applying Number" Checklist
Before you finish a question in this chapter, ask yourself:
- Is it Metric? (m, kg, l - keep it in powers of 10).
- Is it Money? (Round to 2 decimal places if needed).
- Is it Time? (Remember the "Rule of 60").
- Does it make sense? (If you calculate that a loaf of bread costs $450.00, you’ve probably multiplied where you should have divided!)
You've got this! These are the math skills that will help you long after your exams are over.