1.5 Calculate using metric units of length
You may need to carry out calculations with length. This may require you to convert between metric units, either before you carry out the calculation or at the end.
Fran is putting up bunting. She has three lengths of bunting, measuring 160 cm, 240 cm and 95 cm. How many metres of bunting does she have?
All of the units are given in centimetres, so you can add them together:
165 cm + 240 cm + 95 cm = 500 cm
The question asks for the answer in metres, so you need to convert 500 cm into metres:
500 cm ÷ 100 = 5 m
So Fran will have 5 m of bunting.
Example: Length of shelves
Dixie wants to put up a shelf in an alcove. The alcove is 146 cm wide. She has a plank of wood that is 2 m long. How much wood will she have left over?
The plank of wood is in metres, so you need to convert this into centimetres:
2 m × 100 = 200 cm
200 cm – 146 cm = 54 cm
So Dixie will have 54 cm left over.
Now try the following activity.
Activity 7: Carrying out calculations with length
Calculate the answers to the following problems without using a calculator. You may double-check your answers with a calculator if you need to. Remember to check your answers once you have completed the questions.
- You are making Christmas cards for a craft stall. You want to add a bow, which takes 10 cm of ribbon, to each card. You plan to make 50 cards. How many metres of ribbon do you need?
- You want to make a garden planter that measures 1.5 m by 60 cm. How much wood will you need to buy? (Hint: you will need two planks of each length to make the planter.)
- Sally is making a pair of curtains. Each curtain requires 1.8 m of fabric plus 20 cm each for hemming. How many metres of fabric will she need?
- John wants to put shelving in his garage to hold storage boxes. Each storage box is 45 cm wide and John wants to be able to put four boxes on each shelf. He has seen some shelves that are 2 m wide. Would they be suitable?
You will have found it useful to refer to the metric conversion diagram for this activity.
- First you need to work out how many centimetres of ribbon you need:
- 10 × 50 = 500 cm
- 500 ÷ 100 = 5 m
- The measurements for the planters are in different units, so you need to convert everything into centimetres or metres first. The question does not specify whether your answer needs to be in centimetres or metres, so either will be OK.
Using Method 1, converting to centimetres, note that the length of the planter is 1.5 m:
- 1.5 × 100 = 150 cm
- 150 cm + 60 cm + 150 cm + 60 cm = 420 cm
- 60 ÷ 100 = 0.6 m
- 1.5 m + 0.6 m + 1.5 m + 0.6 m = 4.2 m
- The measurements for the curtains and the hem are given in different units. The question asks for the answer in metres, so you need to convert everything into metres first:
- 20 cm ÷ 100 = 0.2 m
- 1.8 m + 1.8 m + 0.2 m + 0.2 m = 4.0 m (4 m)
- The measurements for the storage boxes and shelves are given in different units, so you need to convert everything into centimetres or metres first. The question does not specify whether your answer needs to be in centimetres or metres, so either will be OK.
Using Method 1, converting to centimetres, the shelves are 2 m wide. First you need to convert this to centimetres:
- 2 m × 100 = 200 cm
- 45 cm × 4 = 180 cm
So the shelves would be suitable.
Using Method 2, converting to metres, the shelves are already in metres, but the boxes measure 45 cm.
- 45 cm ÷ 100 = 0.45 m
- 0.45 m × 4 = 1.80 m (1.8 m)
- 45 cm × 4 = 180 cm
- 180 cm ÷ 100 = 1.80 m (1.8 m)
Throughout this section you have looked at measuring and calculating length. You have used different metric measurements, such as millimetres, centimetres, metres and kilometres. You can now:
- measure and understand the sizes of objects
- understand different units of length
- convert between different units of length
- carry out calculations with length.