Measurement — Challenge
Every conversion is a multiplication by one. Write the unit you want on top, the unit you have on the bottom, and the wrong units cancel themselves.
What these problems cover
These questions use 9 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Base — The number being multiplied. In 53 the base is 5.
- Factor — A number that divides evenly into another.
- Parallel — Same slope, different intercept.
- Perpendicular — Slopes multiply to -1 — negative reciprocals.
- Trapezoid — A quadrilateral with exactly one pair of parallel sides.
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
- Height — The perpendicular distance from the base to the opposite corner.
Problem 1
How many metres are there in 2.5 kilometres?
- 25
- 250
- 2500
- 25000
- 0.0025
Worked answer
2500
One kilometre is 1000 metres, and the answer should be a larger number because metres are smaller units.
2.5· 1000 = 2500 metres.
Problem 2
How many minutes are there in 3 hours and 45 minutes?
- 185
- 225
- 245
- 345
- 375
Worked answer
225
Three hours is 3· 60 = 180 minutes.
Adding the extra 45 minutes gives 180+45 = 225 minutes.
Writing the time as 3.45 and multiplying by 100 would give 345, which treats minutes as hundredths rather than sixtieths.
Problem 3
A room measures 4 metres by 3 metres. Carpet costs $12 per square metre. What does it cost in dollars to carpet the room?
- $84
- $120
- $132
- $144
- $288
Worked answer
$144
The floor area is 4· 3 = 12 square metres.
At 12 dollars per square metre the cost is 12· 12 = 144 dollars.
Using the perimeter, 14 metres, would give 168 dollars and measures the wrong thing.
Problem 4
What fraction of 2 kilograms is 500 grams?
- 12
- 14
- 15
- 140
- 18
Worked answer
14
Put both quantities in the same unit: 2 kilograms is 2000 grams.
The fraction is 5002000 = 14.
Comparing 500 with 2 directly would give 14 of a thousand times too small.
Problem 5
How many millilitres are there in 1.2 litres?
- 12
- 120
- 600
- 1200
- 12000
Worked answer
1200
One litre is 1000 millilitres.
1.2· 1000 = 1200 millilitres.
Problem 6
How many hours does a journey of 180 kilometres take at a steady 60 kilometres per hour?
- 2
- 2.5
- 3
- 3.5
- 4
Worked answer
3
Time is distance divided by speed.
18060 = 3 hours.
Problem 7
How many feet are there in 72 inches?
- 4
- 6
- 8
- 12
- 864
Worked answer
6
There are 12 inches in a foot, and feet are the larger unit, so divide.
7212 = 6 feet.
Multiplying instead gives 864, which is far too many.
Problem 8
How many square centimetres are there in 3 square metres?
- 300
- 3000
- 30000
- 300000
- 30
Worked answer
30000
One metre is 100 centimetres, so one square metre is 100· 100 = 10,000 square centimetres.
3· 10,000 = 30,000 square centimetres.
Multiplying by only 100 gives 300 and forgets that area has two dimensions.
Problem 9
A recipe uses 250 millilitres of stock. How many such portions are there in 2 litres?
- 4
- 5
- 6
- 8
- 80
Worked answer
8
Convert to a common unit: 2 litres is 2000 millilitres.
2000250 = 8 portions.