Units and converting units

There are 10 mm in 1 cm.

$15 \times 10 = 150$ mm

There are 60 minutes in an hour.

$140 = 60 + 60 + 20$, so it is 2 hours 20 minutes.

There are $1000$ ml in a litre.

$5000 \div 1000 = 5$ litres.

There are 100 cm in 1 m.

$800 \div 100 = 8$ m

There are 100 cm in 1 m.

$7 \times 100 = 700$ cm

There are 100 cm in 1 m, so $9 \times 100 = 900$ cm.

There are 1000 g in 1 kg.

$4000 \div 1000 = 4$ kg

There are 10 mm in 1 cm.

$40 \times 10 = 400$ mm

There are 10 mm in 1 cm.

$53 \times 10 = 530$ mm

There are 100 cm in 1 m, so $3 \times 100 = 300$ cm.

Add the 2 hours first: 8.05 am → 10.05 am.

Then add 40 minutes: 10.05 am → 10.45 am.

There are 100 cm in 1 m, so divide by 100.

$300 \div 100 = 3$ metres

There are 60 minutes in an hour.

$180 \div 60 = 3$ hours

There are 1000 g in 1 kg, so divide by 1000.

$1756 \div 1000 = 1.756$ kg

There are 1000 metres in a kilometre.

$4 \times 1000 = 4000$ metres

1 km = 1000 m

$1.5 \times 1000 = 1500$ metres.

(a) 1 cm = 10 mm, so $35 \times 10 = 350$ mm

(b) 1 litre = 1000 ml, so $7700 \div 1000 = 7.7$ litres

(c) 1 kg = 1000 g, so $0.32 \times 1000 = 320$ g

Change 6 cm to metres: $6 \div 100 = 0.06$ m.

$1.88 + 0.06 = 1.94$ m (or $188 + 6 = 194$ cm).

There are 100 cm in 1 m, so divide by 100.

$530 \div 100 = 5.3$ m

3 hours is $3 \times 60 = 180$ minutes.

$\frac14$ of an hour is $15$ minutes.

$180 + 15 = 195$ minutes

1 litre = 1000 ml, so 3 litres = 3000 ml.

$3000 - 700 = 2300$ ml

$3\frac{1}{4}$ hours $= 3$ hours 15 minutes.

14 10 back 3 hours is 11 10; back 15 more minutes is 10 55.

8:30 am + 1 h 45 min = 10:15 am

Rest 15 min: 10:30 am

85 min = 1 h 25 min, so 10:30 + 1 h 25 min = 11:55 am

11:55 am is before noon, so yes.

(a) $3 \times 60 = 180$ minutes, and $196 - 180 = 16$.

So 196 minutes is 3 hours 16 minutes.

(b) Speed = distance ÷ time, so the speed is $\frac{x}{2}$ miles per hour.

105 minutes = 1 hour 45 minutes.

Film ends: 14 30 + 1 h 45 min = 16 15

At the bus stop: 16 15 + 20 min = 16 35

16 35 is before 16 45, so yes, with 10 minutes to spare.

(a) Read across from 40 km on the scale: about 25 miles.

(b) $40 \div 10 = 4$, then $4 \times 6 = 24$ miles.

(c) 24 is close to 25, but the rule gives a slightly smaller answer.

$1\frac{1}{4}$ hours $= 60 + 15 = 75$ minutes

1 hour 25 minutes $= 60 + 25 = 85$ minutes

Difference $= 85 - 75 = 10$ minutes

Four blocks: $4 \times 650 = 2600$ g

Total: $3$ kg $= 3000$ g

Last block: $3000 - 2600 = 400$ g

(a) From 07 15 to 07 22 is 7 minutes.

(b) The 07 22 train reaches London at 09 00.

07 22 to 08 00 is 38 minutes; 08 00 to 09 00 is 1 hour.

Journey time: 1 hour 38 minutes (98 minutes).

(a) 1 kg = 1000 g, so $4560 \div 1000 = 4.56$ kg.

(b) 1 m = 1000 mm, so $7.3 \times 1000 = 7300$ mm.

1 litre = 1000 ml, so 1.5 litres = 1500 ml.

$1500 + 250 = 1750$ ml, which is 1750 ml (or 1.75 litres).

$8 \times 45 = 360$ minutes

$360 \div 60 = 6$ hours

$12\text{ kg} = 12000\text{ g}$

Food per day $= 3 \times 105 = 315$ g; per week $= 315 \times 7 = 2205$ g

$12000 \div 2205 = 5.44...$, so the bag lasts 5 complete weeks.

(a) 07 20 to 08 00 is 40 minutes, then 08 00 to 08 09 is 9 more: 49 minutes.

(b) She reaches Blackrod at $08\,00 + 7 = 08\,07$, so she catches the 08 09 bus.

That bus reaches Bolton at 08 58, and $08\,58 + 15 = 09\,13$.

09 13 is before 09 20, so yes.

(a) T-shirts: $3 \times 25 = 75$

Total with the jacket: $60 + 75 + 80 = 215$

$215 > 200$, so no, he is 15 dollars short.

(b) Round the rate down: $0.749 \approx 0.7$

$60 \times 0.7 = £42$. This is already an underestimate and is more than £40, so he is wrong.

$850 \times 18.53 = 15\,750.5$ rand

$15\,750.5 \div 200 = 78.7525$

Only whole notes count, so 78 notes.

Convert each limit to cm ($\times 2.54$):

- height: $22 \times 2.54 = 55.88$ cm (bag 50 cm, fine)
- width: $14 \times 2.54 = 35.56$ cm (bag 40 cm, too wide)
- depth: $9 \times 2.54 = 22.86$ cm (bag 20 cm, fine)

The bag is too wide, so Chris cannot take it.

1 m = 100 cm, so a 1 m by 1 m square is 100 cm by 100 cm.

$100 \times 100 = 10\,000$ cm²

Gallons: $560 \div 34.5 = 16.231...$

Litres: $16.231... \times 4.55 = 73.855...$

Cost: $73.855... \times 1.08 = £79.76$

Paris: $1980 \div 1.34 = £1477.61$

New York: $2250 \div 1.52 = £1480.26$

London: £1480

The cheapest is Jardins of Paris.

Put every price in pounds.

Paris: $1980 \div 1.34 = £1477.61$

New York: $2250 \div 1.52 = £1480.26$

London: £1480

The lowest is Jardins of Paris.

Change the London price to francs: $3.50 \times 1.25 = 4.375$ francs for 200 g.

Zurich price for 200 g: $7.20 \div 360 \times 200 = 4.00$ francs.

$4.00 < 4.375$, so Zurich is better value.

(a) Field B: $700 \times 2000 = 1\,400\,000\text{ m}^2$

B per person: $1\,400\,000 \div 6750 = 207.4...$

A per person: $80\,000 \div 425 = 188.2...$

Difference: $207.4 - 188.2 = 19.17... \approx 19\text{ m}^2$

(b) A square metre is $100\text{ cm} \times 100\text{ cm} = 10\,000\text{ cm}^2$, so $300\text{ cm}^2 = 0.03\text{ m}^2$.

Spain in £: $27 \times 0.85 = 22.95$, so per litre $22.95 \div 18 = 1.275$.

Wales: $8 \times 4.5 = 36$ litres, so per litre $40.80 \div 36 = 1.133...$

£1.13 < £1.275, so petrol is cheaper in Wales. Sam is not correct.

(a) $1\text{ m}^3 = 100^3 = 1\,000\,000\text{ cm}^3$, so $8000 \div 1\,000\,000 = 0.008\text{ m}^3$

(b) $180$ km $= 180\,000$ m, and 1 hour $= 3600$ s

$180\,000 \div 3600 = 50$ m/s

1 cm $= 10$ mm, so $1\text{ cm}^3 = 10 \times 10 \times 10 = 1000\text{ mm}^3$.

$37 \times 1000 = 37\,000\text{ mm}^3$