I am motivated to write this article because, in the past, I have come across supporters of metrication, some of whom with teaching experience, who say that only decimals should be taught rather than both fractions and decimals in elementary mathematics in school.

They say that only very simple fractions like halves and quarters should be dealt with and anything else, especially fractional arithmetic, be confined to more advanced levels and for the most able students.

Their contention is that time spent teaching fractions at an introductory level is only preparation for the teaching of non-metric units and so is a waste of time.

Before going any further I would like to clarify some terminology. ‘Fraction’ is a reference here to non-integral numbers (numbers that are not whole numbers) where the denominator is something other than a power of ten such as 2/3, 3/4 and so on. ‘Decimal’ is a reference to non-integral numbers which do have a denominator that is a power of ten and written using the point system like 3/10 written as 0.3, 25/100 written as 0.25 etc. Strictly speaking all non-integral numbers are fractions but the foregoing is sufficient for the purpose of this discussion.

I contend that learning fractions and the basic arithmetic methods is essential to understanding both numbers generally and the advantages of using decimals, and why the methods work.

As mentioned previously decimals are really fractions where the denominator is a power of ten. Decimals are easier to work with during adding or subtracting because the common denominator is simply the larger of the two and the numerator for the other operand only requires scaling up by a power of ten. The decimal point form enables the numbers to be handled arithmetically in the same way as whole numbers because only the numerators are required explicitly in the process.

It is difficult to see how this process can be properly understood without going through the fractional form and learning why two numbers have to be adjusted to having the same denominator so that they can added or subtracted using the numerators. It is equally difficult to see how the place value of digits to the right of the decimal point can be assimilated properly without reference to the notion of fractions and how they are summed to make up the overall quantity.

Having said this I fully acknowledge that decimals are sufficient for the purposes of measurement. Although it is true that not all fractions can be represented exactly with a finite number of digits in decimal form, all fractional quantities can be approximated to any chosen precision in decimal. This reflects perfectly the fact that all measurements, in whatever units, are themselves subject to some finite range of uncertainty so no information is lost when a sufficient number of digits are used. Furthermore it is much easier to determine and specify that range of uncertainty in decimal form than with fractions.

However this doesn’t mean we should surgically remove fractions from the early years of the curriculum. Measurement isn’t the only application and it would be a pity to lose an important part of the teaching of mathematics that helps to enrich and stimulate the developing mind.

I brought up the subject of ‘is 1/2 kg a valid measurement’ or some such, some time ago on these pages. Judging by the answers I got then it was ‘yes’. I tend to disagree, .5 kg or 500 g it is for me.

However, on the subject of fractions being taught in schools seems a rather strange question. Surely the teaching of vulgar fractions is a matter of arithmetic (or maths if you will), not one of measurement? A fraction is no more, nor less, than one number being divided by another using a standard divisor bar. It is un-separable from the wider application of using formulae using standard mathematical practice.

On a more basic level when I slice a pizza into two, I create two x half, not two x 50%, nor two x 0.5 pizzas. I consider that to be reasonable.

Fractions are fractions, decimals are decimals and they both go together, 1.375/2.4 is a fraction using decimals where each number is a decimal that needs to be divided one by the other.

How do the proponents of this idea define “simple fraction”? The speed of an LP record is 33 1/3 RPM. This has nothing to do with metric or imperial, but it is a very simple way of expressing a number that was once in widespread use, and has recently made a bit of a comeback. It becomes considerably less simple when expressed as a decimal. The reality is both have their place, and therefore both need to be learned and understood, as does the relationship between them. It’s a fundamental part of numerical literacy.