2.6 Numbers

2.6.1 Cardinal Numbers

Numbers as Nouns

The number system of Ayola is built up from number roots for the basic digits (0-9) and the following powers of ten: 100, 1000, and higher powers of 1000.

As illustrated in Table 2.6-1, when numbers are used as nouns, e.g. in mathematical formulas, counting, etc., they have the noun ending -o.

Table 2.6-1 Basic Number Roots and Noun Forms of Numbers

Number Root			Noun Form
nul-	-o		nulo	0
un-	-o		uno	1
dus-	-o		duso	2
tres-	-o		treso	3
kwar-	-o		kwaro	4
kwin-	-o		kwino	5
ses-	-o		seso	6
sep-	-o		sepo	7
oc-	-o		oco	8
nawf-	-o		nawfo	9
dec-	-o		deco	10

Numbers of two digits have the following form:

(<multiplier->) + -dec- + hyphen + (<addend->) + -o

where the optional multiplier root ranges from dus- to nawf- and the optional addend root ranges from un- to nawf-. The hyphen is used to separate the tens place from the units place. Examples of two-digit numbers are shown in Table 2.6-2.

Table 2.6-2 Examples Two-Digit Numbers

Numbers of more than two digits are formed in an analogous fashion to those of two digits where the multiplier root directly precedes the power-of-ten root and hyphens separate the units, tens, hundreds, thousands, etc. places.

Here are more examples of multi-digit number words:

Note that in some cases the multiplier root may in itself be complex, i.e. it contains multiple number roots, as in dec-ses-milo and dustcen-un-milo where the multiplier roots are dec-ses- and dustcen-un-, respectively.

Numbers as Quantifiers

Numbers may also occur before nouns in which case they act as quantifiers, that is, they specify the count of the objects denoted by the nouns they precede. In order to function as quantifiers number words must have the quantifier ending -a in Ayola.

dusa libroy	two books
kwina katsoy	five cats
kwartcena dolaroy	four hundred dollars
mila djaroy	one thousand years
kwara skarpoy	four shoes

Convention for the Use of Numerals vs. Words in Ayola Text

When one wishes to refer to numbers, e.g. in mathematical or scientific contexts, in dates, times, etc., one should write the numerals – not the number words. When one wishes to refer to quantity nouns, e.g. in descriptive phrases for quantifiers up to one hundred, one should write the quantifier words – not the numerals. For numbers above one hundred, one should write the numerals.

5 + 11 = 16	5 + 11 = 16
Dya adiconits 3 cwe 4.	He added 3 and 4.
Hodjo estats 19 Junio 2010.	Today is June 19, 2010.
Dze estats deca studentoy hire.	There are ten students here.
Tcena personoy venits.	One hundred people came.
Moy viadjits kwantu 3000 mayloy.	We traveled 3000 miles.

Note that when quantity words are used as numbers they are pronounced with the noun ending –o in Ayola. For example, 16: dec-seso; 2010: dusmil-deco. When they are used as quantifiers they are pronounced with the quantifier ending –a in Ayola. For example, 3000: tresmila.

Numbers as Multiplier Adverbs

The third part of speech ending which may be added to number roots is the adverb ending -e. The resulting words are multiplier adverbs which denote the multiple of a quantity in a comparative construction.

Djon estats duse vyela asu Brus. John is twice as old as Bruce.

Myo estits tcene dirsta asu vu! I was one-hundred times as thirsty as you!

2.6.2 Ordinal Numbers

Ordinal forms of numbers are formed by adding the suffix -t- to their cardinal roots and adding the appropriate word endings. Ordinal number words use the same hyphen rules as cardinal number words, that is, a hyphen is always used to separate the roots of the different digit places.

Like cardinal number roots, ordinal number words can take three part of speech endings, namely, the noun, adjective, and adverb endings.

Table 2.6-3 Examples of Ordinal Numbers

2.6.3 Fractions

The fractional forms of the number two are halfa (half of) for the quantifier, and halfo (half) for the number. In fractional forms of the numbers three and above, the numerator adopts the quantifier ending -a, while the denominator consists of a cardinal number root plus the suffix -tel- plus one of the noun endings -o or -oy.

una trestelo	one third	1/3
tresa kwarteloy	three quarters	3/4
sepa octeloy	seven eighths	7/8
una kwindectelo	one fiftieth	1/50
sepa tcenteloy	seven hundredths	7/100

When fractional forms of numbers are used to specify a fraction of something denoted by a noun or a name they must be linked to that noun or name with the part-whole

link je. Here are some examples:

halfa la viroy	half of the men
una trestelo je la studentoy	one third of the students
tresa kwarteloy je la oceano	three quarters of the ocean
una kwindectelo je Tero	one fiftieth of the Earth

2.6.4 Mathematical Connectives

Mathematical connectives connect the number words in mathematical statements. The six common elementary mathematical connectives are as follows:

pyu plus poa to the power of

mye minus sua sub (subscript)

mwa multipled by

dwi divided by

Here are some examples of their use:

Uno pyu uno eglats duso. One plus one equals two.

Kwino mye uno eglats kwaro. Five minus one equals four.

Duso mwa treso eglats seso. Two multiplied by three equals six.

Deco dwi duso eglats kwino. Ten divided by two equals five.

Duso poa kwaro eglats dec-seso. Two to the power of four equals sixteen.

Duso poa treso mwenats deco. Two to the power of three is less than ten.

Treso poa duso plusats oco. Three to the power of two is more than

eight.

x sua duso plusats x sua uno. x-sub-2 is greater than x-sub-1.

pyu and mye are also used in telling the time. For example:

Dwa estats duso pyu kwartelo. It is quarter past two.

La klaseo natcats atu deco mye kwartelo. The class starts at quarter to ten.

mwa and dwi are also used in expressing physical quantities. dwi is used in expressing rates and may be translated as ‘per’. For example:

Dya kondwirits reytu tcena kilomitroy dwi horo.

She drove at one hundred kilometers per hour.

La momentumo estats dusa kilogramo mwa mitroy dwi sekundo.

The momentum is two kilogram-meters per second.

2.6.5 Non-numerical Quantifiers and Adverbs

Non-numerical quantifiers denote the count of nouns they precede without denoting a specific number. They are divided into groups, namely, the countable quantifiers and the non-countable quantifiers.

Table 2.6-4 Countable and Non-countable Non-numerical Quantifiers

Here are some examples of their use:

Myo lergintats kelka libroy. I have read a few books.

Dya bibintits poka vino. He has drunk a little wine.

Multa myoza amikoy havats mutca moneo. Many of my friends have a lot of money.

Tuta caka padjo estats alba. All of each page is white.

Majorna la votoy votits proru dya. A majority of the voters voted for him.

2.6.6 Quantifier Modifiers

Quantifier modifiers are words which precede quantifiers and extend the scope of the quantifier. They function in a manner similar to the way in which adverbs modify adjectives, but are a distinct part of speech. They are derived from comparative quantity verbs by applying a –de ending to the root. Table 2.6-5 lists the seven comparative adverbs and their related quantifier modifiers.

Table 2.6-5 Comparative Quantity Adverbs and Quantifier Modifiers

Here are some examples of their use:

Quantifier modifiers may also be used before multiplier adverbs in a comparative construction.

2.6.7 Complex Adjectives Derived from Quantifiers

Quantifier roots may be combined with noun roots to form complex adjectives:

<quant-> + <noun-> + -y- + -a

Here are some examples:

unokulya one-eyed dusdecpuntya twenty-pointed

kwarfolya four-leafed dec-un-puntya eleven-pointed

duspyedya two-footed dusdec-un-puntya twenty-one-pointed

Note that when the quantifier root already has a hyphen another hyphen must be inserted after the root to form a break.

From these complex adjectives nouns may also be derived, e.g. unokulyo (one-eyed one), duspyedyo (two-footed one), kwarfolyo (four-leafed one), dusdecpuntyo (twenty-pointed one). Chapter 2.7 Adjectives will discuss how to derive nouns from adjectives in more detail.

Complex adjectives may also be formed by the combination of non-numerical quantifier roots and noun roots. Noun phrases using complex adjectives containing quantifier roots are always equivalent to a linked phrase. Most commonly, the link is javu (with, having as feature), in which case the noun root in the complex adjective is followed by the suffix -y-.

However, with adjectives referring to time the link can also be jenu (at, in) and jdumu (during), in which case the noun root in the complex adjective is followed by the suffix

-w-.

cakdjurnwa djurnalo	=	djurnalo janu caka djurno
daily newspaper		newspaper occurring on every day
tutnaktwa festo	=	festo jdumu tuta nakto
all-night party		party lasting all night

Exercises

Exercise 1

Write out the Ayola words for the numbers and symbols in the equations below.

1. 3 + 5 = 8

2. 6 – 1 + 9 = 14

3. 17 x 2 = 34

4. 15 + 20 = 35

5. 41 – 10 = 31

6. 88 x 3 = 264

7. 101 – 79 = 22

8. 266 / 133 = 2

9. 7853 + 914 = 8767

10. 55000 – 6400 = 48600

Exercise 2

Translate the following phrases by using the numbers as quantifiers and multiplier adverbs.

1. three streets

2. twice as young as

3. fifteen years

4. six times as new as

5. eighty-nine boys

6. one hundred times as tired as

7. seven hundred children

8. ten times as old as

9. forty hours per week

10. zero dollars

Exercise 3

Two brothers, Alex (Aleks) and Chris (Kris), each have different amounts of the things they ask for. If Alex asks for a lot of candy, Chris only gets a little. Tell what amounts Chris has based on the amounts that Alex has.

Example: Aleks havats kelka komputeroy.

 Kris havats multa komputeroy.

1. Aleks mandjats mutca cokolado.

2. Aleks vwelats tuta la torto.

3. Aleks donats poka deserto.

4. Aleks kukats multa legumoy.

5. Aleks bibats poka vino.

6. Aleks prenats kelka floroy.

7. Aleks bakats caka pitso.

8. Aleks havats multa amikoy.

9. Aleks trovats tuta la moneo.

10. Aleks lergats multa storioy.

Exercise 4

Translate the following phrases into Ayola.

1. the second daughter

2. the twenty-first president

3. the sixteenth friend

4. the eighty-ninth day

5. the three-hundredth anniversary

Exercise 5

Afrim never eats all of anything. Translate the portions he eats into Ayola.

1. ½ of the pie

2. ¾ of the sandwich

3. 5/8 of the pizza

4. 27/40 of the salad

5. 58/59 of the money

6. 91/100 of the bread

Exercise 6

What time is it? Write the time in Ayola text.

Exercise 7

Translate the phrases using the glossary or dictionary if necessary.

1. three busy streets

2. seventeen bottles of orange juice

3. one shopping mall

4. five beach chairs

5. first dance

6. It’s ten to ten.

7. It’s five after six.

8. ten per year

9. Two minus one equals one.

10. Three plus two equals five.

Exercise 8

Describe the items pictured by using complex adjectives consisting of a quantifier root and a noun root. Follow the model. Use the word box to help you.

kwina gambo  kwingambya monstro

1. tresa okulo

2. caka semano

3. una kavalo

4. mutca sukero

5. plura bambino

6. kwara macto

Exercise 9

Noun phrases containing complex adjectives which are formed by combining quantifier roots and noun roots are always equivalent to a linked phrase. Write the noun phrases you created in Exercise 8 as linked phrases. Be sure to use the appropriate links.

1. ____________________________

2. ____________________________

3. ____________________________

4. ____________________________

5. ____________________________

6. ____________________________