2.7 Time, Money & Unit Conversion

Time, Money & Unit Conversion

Measures questions are where fluent children lose marks to carelessness rather than to difficulty. Every one of them can be done, and every one of them has a well-worn trap. Because the maths section runs for 25 minutes with no calculator, the goal here is a reliable method for each type rather than clever shortcuts.

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Time: The Only Base-60 System on the Paper

Every other number on the paper is base 10. Time is not, and the single most common error in 11+ maths is treating it as though it were.

Learn the fraction conversions as facts: 0.25 h = 15 min, 0.5 h = 30 min, 0.75 h = 45 min, ⅓ h = 20 min, ⅙ h = 10 min.

12-hour and 24-hour clocks

• Add 12 to any afternoon or evening time: 3:40 pm → 15:40.
• Midnight is 00:00 and midday is 12:00. The pair 12:15 am → 00:15 and 12:15 pm → 12:15 catches most children once.
• 24-hour times are written with four digits and no am/pm: 09:05, not 9:05 am.

Timetable and duration questions

Do not subtract the two times as if they were ordinary numbers. Count up in stages:

A coach leaves at 09:47 and arrives at 13:15. How long is the journey? 09:47 → 10:00 is 13 min. 10:00 → 13:00 is 3 h. 13:00 → 13:15 is 15 min. Total: 3 h 28 min.

The same method handles a journey crossing midnight, and it never produces the classic wrong answer of 3 h 68 min.

Calendar facts worth knowing cold

• Days in each month: 30 for September, April, June and November; 31 for the rest; February has 28, or 29 in a leap year.
• A leap year is divisible by 4, except century years, which must be divisible by 400. 2000 was a leap year; 1900 was not; 2100 will not be.
• A common year is 365 days = 52 weeks and 1 day, so a date moves forward one weekday each year, or two across a leap year.

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The Metric Conversion Ladder

Every metric conversion is a multiplication or division by a power of 10.

Also worth memorising: 1 cm = 10 mm, 1 tonne = 1,000 kg.

Direction check. Converting to a smaller unit gives a bigger number, so you multiply. Converting to a bigger unit gives a smaller number, so you divide. Saying that sentence out loud before writing prevents the most common conversion error.

2.4 km → m: metres are smaller, so multiply: 2.4 × 1,000 = 2,400 m. 750 ml → l: litres are bigger, so divide: 750 ÷ 1,000 = 0.75 l.

Area and volume are different. 1 m = 100 cm, but 1 m² = 100 × 100 = 10,000 cm², and 1 m³ = 1,000,000 cm³. Squaring the length factor for area and cubing it for volume is examined directly.

Imperial approximations

Some questions use everyday imperial units and give you the conversion, but these approximations are useful sanity checks: 1 kg ≈ 2.2 lb, 1 litre ≈ 1.75 pints, 1 inch ≈ 2.5 cm, 5 miles ≈ 8 km.

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Money Without a Calculator

Work in pence. Decimal points are where marks are lost; whole pence are not.

Four pens at £1.35 and three notebooks at £2.20. How much change from £20? 4 × 135 = 540p. 3 × 220 = 660p. Total 1,200p = £12.00. Change = £8.00.

Rules that get tested:

• Always write money answers with two decimal places: £8.50, never £8.5.
• £0.07 is 7p, not 70p. Reading the second decimal place is a genuine trap.
• Change questions are subtractions from a round amount, so count up in the same way as time: from £12.65 to £20 is 35p to £13, then £7 to £20 → £7.35.

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Best Buy: Compare Unit Prices

Never compare pack prices; compare the cost of one unit, or the amount you get per pound.

Which is better value: 750 g of oats for £1.80, or 1.2 kg for £2.76? £1.80 ÷ 750 = 0.24p per gram. £2.76 ÷ 1,200 = 0.23p per gram. The 1.2 kg pack is better value.

Where the numbers divide awkwardly, scale to a common quantity instead: 750 g and 1.2 kg both go into 3 kg, so compare 4 × £1.80 = £7.20 against 2.5 × £2.76 = £6.90. Same conclusion, easier arithmetic.

Multi-buy offers need the same treatment. "Three for the price of two" at £1.50 each is £3.00 for 3, or £1.00 each; "30% off" at £1.50 is £1.05 each, so the percentage deal wins on unit price.