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).

Buck To … : Thursday, 29th December, 1977

I have just been awoken by Tiki at five minutes to seven as she was getting up to use the toilet. It is eight point five degrees Celsius according to 3BA, which is located at 1320 on the dial.

The cattle next-door are grazing right up to the boundary fence, some thirty-five metres distant from our window. A black one has its head through the fence feasting upon the rather long green lawn.

Tiki showered by twenty-one past the hour, just as The Hollies’ hit of 1969-’70, “He Ain’t Heavy He’s My Brother”, was commencing on 3BA. The house fire that was still smouldering when we passed the scene, at Warrenheip, at half past one yesterday afternoon, was mentioned on the “3BA News” at half past seven. The kitchen, bathroom, laundry and a bedroom were gutted. Firemen had required twenty minutes in order to control the blaze.

A maximum of just eighteen degrees is expected here today. Overnight rain has left our car wet, a fact we learned as we carried our bags to it in the dull, overcast chill. The young, blonde, surly attendant had been taking breakfast to another room and when ours did arrive, late, at twenty past eight, it contained only one compote of fruit and so she had to return with the other.

“I’d hate to get into an argument with her,” Tiki commented, “she’d probably scratch my eyes out!”

We departed at a quarter to nine and drove out past the Botanic Gardens and, six miles out of the city, the Dowling Forest Racecourse. Back roads conveyed us through Cheswick to Daylesford. I drove up Wombat Hill and we climbed the seventy-eight steps of the spiral staircase, inside the tower that stands atop it. Tiki was a little apprehensive of ascending the tower and then, conversely of descending from it, as well.

The drizzle that we’d experienced had stopped and the weather gradually began to warm. We decided to travel out to nearby Hepburn Springs where there is a bathhouse as well as areas which are occupied by spas. Some people were employing the use of cups to drink the naturally effervescent water, which ran from a pipe. The water contains iron, soda, magnesium, lime and sulphur. The consensus between those who were partaking of it appeared to be that the dominant taste was that of soda.

Farther up the slope we came upon a pump with an old Melburnian gentleman in close attendance. He told us of how he has been coming to Hepburn Springs for sixty years and of how the popularity of the place has dwindled. Once thousands of people would peregrinate there over the period that combines Christmas and the New Year.

I drove on to Castlemaine where the maroon –Tiki claims that it is a rusty colour — post office is as I remember it. I really tested Tiki’s patience as I unsuccessfully tried to find and retrace the dirt road taken by the chap, in a Ford ‘F-100’ utility, who, six years ago, supplied me with a lift that had conveyed us up to and along a hill that was in the vicinity of the Kalimna Reservoir and its adjoining parkland and from which, we had been afforded a view over the town of his birth.

Tiki drove on to Bendigo and it was quite warm when we stopped at the North Central Tourist Authority. We told the nice lady, who is in her forties, of how we had crossed “Fuckeye Creek” about eight miles prior to entering the city and she explained that the sign was supposed to read ‘Buckeye Creek’ and that the men who paint the names on such signs had made a mistake.

We parked the car on the hill above the Sacred Heart Cathedral. It was ten minutes to noon as we began our walk to Pall Mall. In doing so we passed the freshly painted Alexandra Fountain in the city’s centre. Searching for somewhere to have lunch, our choice became the Coles’ cafeteria.

Upon our return to the North Central Tourist Authority another pleasant lady informed us that only three caravan parks were in possession of on-site vans and, therefore, strongly advised us not to tarry as there had already been many such enquiries made. We departed in the same direction from whence we had entered the city and along the Calder Highway located the Central City Caravan Park, which has a swimming pool. Its office, however, was closed for lunch until a quarter to two. As this was thirty-five minutes henceforth, we opted to try and locate another of its counterparts, the Orana, which is out beyond Flora Hill and two and a half miles from town.

It didn’t take us long to learn that our tourist map lacked vital detail and as a consequence we frustratingly realised that we were doing little more than travelling around in circles. The only plus being that we did come upon what ostensibly appears to be an impressive project that involves a College of Advanced Education. I enquired of a gentleman at a B.P. petrol station as to the proximity of the caravan park and it appeared that we’d actually been close to it once before.

Having knocked on the door of the house within the caravan park’s grounds, a gentleman, who was clearly in the midst of eating his lunch, allocated to us the use of a large ‘Coronet’ van. I paid him the nine dollars without asking him for a receipt and once we had unloaded our belongings into the caravan we headed back into town to view the Central Deborah Goldmine, which is located just off High Street.

From where we parked our car in the sunshine, ‘Central Deborah’ appeared to be somewhat similar to Sovereign Hill, in Ballarat. This led us, instead, to walk into the centre of the city once more, again passing the Sacred Heart Cathedral. Trams run from the mine along High Street to a Chinese joss house on the other side of town. The vintage, maroon and open-sided means of transportation are known as “talking” trams because of the recorded commentary that describes points of interest along the way.

Tiki entered a fruit shop and soon learned that in Bendigo one buys such produce by weight and not by the actual number of articles selected. We walked down Pall Mall and through Rosalind Park to view the city from the observation tower that is made of poppet legs from a mine that was closed circa 1931. We returned to the ‘Galant’ via the fernery in Rosalind Gardens.

The weather was summery as I drove through town via McCrae and Napier streets, White Hills — where three teenagers died this week when the car in which they were travelling hit a tree — and Lake Weeroona. We sat beneath a shady tree on the lake’s bank. I read Ballarat’s “Courier”, which features yesterday’s house fire on its front page, before turning my attention to Melbourne’s “Sun”. In the meantime, Tiki’s attention was occupied by the children who were on various kinds of pedalo boats, that were for hire, in addition to a single rowing scull which was being shared alternately by a girl and a boy. Unfortunately, the water appeared to be extremely polluted.

Bendigo Golf Club beckoned, however, my keeness to play was not reflected in my score of fifty-three for the outward nine. Inconsistency marred my endeavours to post a respectable score for while I parred three holes, three sevens and an eight were also carded. Trees proved to be a regular source of frustration, especially on the par five seventh where I accumulated four strokes amongst them before my seven-iron bounced off the bridge over the creek and came to rest just short of the green in five. The eighth hole and the ninth tee are juxtaposed to Bendigo’s racecourse. To play the nine holes cost us more than we are used to paying: three dollars for me and two for Tiki.

It was a quarter to seven when we returned to our caravan. Once we had each showered in the clean communal facilities, we ate the fruit we’d bought this afternoon and drank cups of low-calorie lemonade.

The caravan creaks, even at the slightest of movements. There is a double bed at one end of the van and four single beds at the other. It is twenty past nine and Tiki is asleep behind the drawn screen. I am writing my diary at the long table that is designed to seat five. The caravan also possesses an impressive fridge by ‘Thorn’ and an electric stove by ‘Roden’. Our surroundings are really extremely quiet, which is a blessing.

There is now a youth hostel in Bendigo and it isn’t far from here. The city’s traffic lights display a green figure of a person for “Walk” and conversely a red figure to signal “Don’t walk”. Since I was last here, with my mother in January of 1970, Bendigo has experienced somewhat of a boom in its population and now has fifty-four thousand inhabitants. Some of its suburbs have names like Jobs Gully and Specimen Hill, that must surely date back to the days when the city was dependent upon mining?