Part 1 — Lessons (45)
1. Decimals & Place Value
Decimals show parts smaller than one. After the point: tenths, hundredths, thousandths.
In 3.47: 3 ones, 4 tenths, 7 hundredths.
To compare, line up the decimal points: 0.5 is bigger than 0.45 (think 0.50 vs 0.45).
Try this: Which is larger, 0.7 or 0.68? (0.7.)
2. Sharing in a Ratio
What is a ratio?
A ratio compares quantities. The ratio 3:4 means for every 3 of one part there are 4 of another.
To share an amount in a ratio, first add the parts to find the total number of parts. Then divide the amount by the total to find the value of one part. Finally multiply.
Example: share $35 in the ratio 3:4. Parts = 3+4 = 7. Each part = $35 ÷ 7 = $5. The shares are 3×$5 = $15 and 4×$5 = $20.
3. Ratio & Proportion
A ratio compares amounts. If a recipe uses 2 cups flour to 1 cup sugar, the ratio is 2:1.
Keep ratios in proportion by multiplying both parts: 2:1 is the same as 4:2 and 6:3.
Try this: 3 pens cost $60. How much for 5 pens? (Each is $20, so 5 = $100.)
4. Average Speed
Speed, distance and time
Speed tells us how fast something moves. Average speed = distance ÷ time.
Example: a bus travels 240 km in 4 hours. Its average speed = 240 ÷ 4 = 60 km/h.
Remember to keep the units matching: kilometres with hours give km/h.
5. Working with Percentages
Percent means "out of 100." 50% = 50/100 = 1/2.
To find 10% of a number, divide by 10. 10% of 250 = 25. For 20%, double it = 50.
Tip: Find 10% first, then build up — it's faster than long multiplication.