1. Find a partner from the other group. Tell each other the information you read about one of the universities

2. Imagine you meet someone from Nigeria who wants to study at Donetsk National University. Tell him/her about your university and be ready to answer the questions about it

L earn mathematics in English

Read the text and do the following tasks

Fractions

5; 241; 74 are whole numbers or integers. ; ; 0.5; 0.102 are fractions. A fraction (from the Latin fractus, broken) is a number that represents part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or vulgar fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole. An example is , in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole.

A still later development was the fraction, now called simply a decimal, in which the denominator is a power of ten, determined by the number of digits to the right of a decimal separator, the appearance of which (e.g., a period, a raised period (•), a comma) depends on the locale). Thus for 0.75 the numerator is 75 and the denominator is 10 to the second power, i.e. 100, because there are two digits to the right of the decimal point. If 100 is divided by 3, the quotient is 33.33. In spoken English it is, ‘Thirty- three point three, three recurring’. If 100 is divided by 3, and the quotient is written 33.333, it is correct to three significant figures. If the quotient is written 33.33 it is correct to two significant figures.

A third kind of fraction still in common use is the percentage, in which the denominator is always 100. Thus 75% (read as “seventy five percent”) means .

Other uses of fractions are to represent ratios, and to represent division. Thus the fraction is also used to represent the ratio 3:4 (three to four) and the division 3 ÷ 4 (three divided by four).

In mathematics, the set of all common (vulgar) fractions is called the set of rational numbers, and is represented by the symbol Q.

Common (vulgar) fractions

A common fraction (or vulgar fraction) is a rational number written as one integer (the numerator) divided by another non-zero integer (the denominator) such as .

A common fraction is said to be a proper fraction if the absolute value of the numerator is less than the absolute value of the denominator, that is, if the absolute value of the entire fraction is less than 1; a common fraction is said to be an improper fraction if the absolute value of the numerator is greater than or equal to the absolute value of the denominator (e.g. ).

Task 1. Find the following information in the text

1. The origin of the word ‘fraction’.

2. Three types of fractions used today.

3. Another word for ‘common fraction’.

4. The definition of a proper fraction.

5. The definition of an improper fraction.

Task 2. Match number symbols with the correct written expression

Group A		Group B
	Three quarters	.9	Nine-thousandths
	Two-thirds	9.0	Ninety
	One-fifth	.009	Nine-tenth
	A quarter	0.09	Nine point oh
	One-tenth	90	Nine-hundredths
	Five-halves	9.009	Point one nine
	A third	.19	Nine point oh oh nine
Group C		Group D
.4	Point oh oh four	63	The negative of the cube root of six
4.0	Four point oh	1/63	Six to the third power
.004	Point four	√63	The square root of six cubed
.04	Forty	6-3	One over six to the third power
40	Point oh four		Six to the negative third power

Task 3. Listen to your teacher and complete the conversion of non-metric measures into their metric equivalents

1. One inch equals_____________________________________________

2. One foot quals______________________________________________

3. One yard equals ___________________________________________

4. One acre equals ___________________________________________

5. One mile equals ___________________________________________

6. One pint equals ___________________________________________

7. One gallon equals ______________________________________

8. One ounce equals ______________________________________

9. One pound equals ______________________________________

10. One stone equals __________________________________________

Unit 5