Fractions

The mere mention of the word ‘fraction’ can fill a child’s thoughts with trepidation.

A fraction consists of a numerator and a denominator. In order to avoid confusion, I suggest that a child be told to associate the word ‘denominator’ and the word ‘downstairs’ — which, of course, has nothing to do with fractions — as both begin with the letter dee.

Via associating both words, the child should, therefore, remember that the denominator lies at the base of a fraction.

When the numerator is of a value that is less than the denominator, the fraction is known as a proper fraction. An example being a quarter: one as the numerator and four as the denominator.

However, when the fraction’s numerator is greater than its denominator it appears to be “top heavy” and in such an instance, is known as an improper fraction.

Two examples being six-fifths (six over five) and twenty-two sevenths (twenty-two over seven).

Improper fractions can be converted into what is known as a mixed numeral. A mixed numeral is simply a whole number and a proper fraction.

A mixed numeral can be obtained by dividing the smaller denominator into the larger numerator.

Using the above example of six-fifths, all we have to do to obtain the whole number is to divide the denominator, which in this case is five, into the numerator, six.

One should, therefore, be the whole number. Our remainder is one, as six, of course, is one more than five.

As a mixed numeral is composed of a whole number and a proper fraction all that is left to do is to place the remainder, which in this case is one, above the original denominator, five.

Our mixed numeral now reads as one (whole) and one fifth.

By following this same procedure, my second example: twenty-two sevenths becomes the mixed numeral, three (wholes) and one seventh.

Fractions 2

An proper fraction represents a part of a whole, that is, the numeral one.

A whole could be a cake, a pie or a bar of chocolate. Anything that can be cut or divided into equal pieces.

If we cut a cake into two equal pieces, we have divided it in half. Writing this as a proper fraction, we write one as the fraction’s numerator and two as its (“downstairs”) denominator.

Should we give one half of the cake to a friend. Our friend has been given one part out of two.

Therefore, the numerator informs us that our friend has one part of the cake and the denominator shows into how many equal parts the cake has been divided.

Three-quarters (written as three over four) shows possession of three equal parts out of a possible four. Seven-eighths (seven over eight), seven out of a total of eight equal parts.

Fractions 3

Any whole number can be expressed as a fraction by writing it over one.

The whole number, one hundred, becomes the numerator above a denominator of one.

The whole number, thirty, becomes the numerator above a denominator of one.

We can express a fraction as a percentage by multiplying it by one hundred over one.

If the fraction is three-fifths (three over five), we multiply it by one hundred over one to obtain its equivalent as a percentage.

Multiplying the numerators (in this case, three and one hundred) gives a numerator of three hundred.

Doing the same to the denominators (five and one) leaves us with a denominator of five.

As the short line or vinculum between a numerator and a denominator can act as the sign, division, we obtain three-fifths as a percentage by dividing our new numerator (three hundred) by the denominator (five).

Therefore, the fraction, three-fifths, expressed as a percentage, is sixty per cent (60%).

In order to express a fraction as a decimal, divide the denominator into the numerator.

In the case of, let’s say, three-quarters, we divide the denominator, four, into the numerator, three.

Three-quarters, as a decimal, is, therefore, nought point seven five (0.75).