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4.1 Solving problems involving measurements

4.1 Solving problems involving measurements

To solve problems involving measurements, you must know how to convert between the metric units.
You also need to know how to convert between units of time.
When you are working with measurements, you need to use skills such as #nding fractions and
percentages of amounts. You should be con#dent in multiplying and dividing by 10, 100 and 1000.
When you have to solve a problem in mathematics, follow these steps.
t Read the question very carefully.
t Go over it several times if necessary. Make sure you understand
what you need to work out, and how you will do it.
t Write down every step of your working. Set out each stage, clearly.
t Check that your answer is reasonable.
t Check your working to make sure you haven’t made any mistakes.

Worked example 4.1

a A rose gold necklace weighs 20 g. The necklace is made from 75% gold, 21% copper and 4% silver.
What is the mass of copper in the necklace?
b A bottle of medicine holds 0.3 litres.
The instructions on the bottle say: ‘Take two 5 ml spoonfuls four times a day.’
How many days will a full bottle of medicine last?

21
a 21% of 20 g = 100 × 20 First decide what you need to work out. Then write
down the calculation that you need to do.
= 4.2 g Work it out.
Check: 10% of 20 g = 2 g Check your answer is correct by using a different method.
1% of 20 g = 0.2 g
21% of 20 g = 2 + 2 + 0.2 = 4.2 g 9
Or: 21% is just less than 25%. You could also check your answer is reasonable by
1
25% of 20 g = of 20 g = 5 g comparing it with a common amount that is easy to
4

1
So 4.2 g is a reasonable answer. 9 calculate, such as 25%, or , in this case.
4
b Amount of medicine per day = 2 × 5 ml × 4 There are several steps in solving this problem.
= 40 ml Take it one step at a time. Start by using the
instructions on the bottle to work out how much
medicine is used each day.
0.3 litres = 300 ml Change the litres to millilitres so the units are the same.
300 ÷ 40 = 7.5 days Divide by 40 to work out the number of days the
medicine will last.
Check: 2 × 5 = 10, 10 × 4 = 40 ml per day Check by recalculating the amount needed per day.
7.5 × 40 = 300 ml 9 Use an inverse operation to check the number of days.
Or: In 7 days, total dose = 7 × 40 = 280 ml You could also check your answer by working out how
In 8 days, total dose = 8 × 40 = 320 ml much medicine would be used for 7 days and
So 7.5 days is a reasonable answer. 9 8 days.
This shows that 7.5 is a reasonable answer.

34 4 Length, mass, capacity and time