Module 10 fractions

Texts

BT1 Fractions, their meaning and types

ST1 Addition, subtraction, multiplication and division of fractions

ST2 Fractions

I.Робота в парах. Прочитайте і перекладіть наступні інтернаціональні слова.

annex component decimal denominator directive distance equivalent horizontal indicator letter

line mixer numerator reduction separator show start type vertical

II. Робота в парах. Прочитайте та запам’ятайте наступні англійські слова. Порівняйте їх з українськими, які мають той же корінь.

annex	анексувати, приєднувати
component	компонент
cross	крос, перетинати
decimal	децимальний, десятковий
denominator	деномінатор, знаменник
directive	директивний
distance	дистанція, відстань
equivalent	еквівалент
horizontal	горизонтальний
indicator	індикатор, показник
letter	літера, буква
line	лінія
mixer	міксер
numerator	нумератор, чисельник
reduction	редукція
separator	сепаратор, відокремлювач
show	шоу, показ
start	старт, початок
type	тип
vertical	вертикальний

III. Прочитайте наступні слова та запам’ятайте їх значення.

common	[`ko mən]	звичайний
fraction	[`fræ k∫ən]	дріб
improper	[im`propə ]	неправильний
integer	[`intid3ə ]	ціле число
mixed	[mikst]	мішаний
nought	[no:t]	нуль
proper	[`propə]	правильний
unit	[`ju:nit]	одиниця
whole	[houl]	цілий
zero	[`ziərou]	нуль

IV. Прочитайте англійські дієприкметники. Виберіть український еквівалент.

A

placed reduced crossed checked mixed

мішаний перевірений скорочений перекреслений розташований

B

called changed obtained carried

змінений одержаний перенесений названий

C

indicated divided separated denoted added

поділений відображений доданий відділений показаний

V. Прочитайте подані приклади. Зверніть увагу на читання дробу в множині.

1/10 – one tenth; 3/10 – three tenth; 7/5 – seven fifths

1, 3, 7 – numerators

10, 10, 5 – denominators

2 1/3 – two and one third

0, 5 – zero and five tenths

- zero point five

- point five

3, 05 – three and five one hundredths

- three point zero five

VI. Прочитайте базовий текст №1 (BТ1) та перекладіть його.

FRACTIONS, THEIR MEANING AND TYPES

1. Fraction is a part of unit, such as ½, ¾ etc.

2. It indicates that something has been cut or divided into a number of equal parts.

3. In a fraction the upper and lower numbers are called the terms of fraction.

4. The horizontal line separating the two numbers in each fraction is called the fraction line.

5. The top term or the term above the fraction line is called the numerator, the bottom or the term below the fraction line is called the denominator.

6. The denominator shows into how many parts a unit is divided.

7. The numerator shows how many of these parts are taken.

8. In the fraction 3/5 the number 5 is the denominator, it shows that a unit is divided into 5 equal parts; the number 3 is the numerator, it shows that only 3 of 5 equal parts are taken.

9. A common fraction is a number that has the numerator and the denominator represented by numbers placed the one above, and the other below a horizontal line. 3/7 is a common fraction.

10. A proper fraction is one in which the denominator is greater than the numerator. 1/3, 7/9, 11/21 are proper fractions because their numerators are smaller than the denominators.

11. An improper fraction is one in which the numerator is greater than the denominator.

12. A mixed number is an integer (a whole number) together with a fraction, such as 2 1/3, 7 11/13 etc.

13. Fractions in which the denominators are 10, 100, 1000 etc. are called decimal fractions.

14. In a decimal fraction the fractional part is divided from the integer (the whole number) by a point, e. g. 0, 5; 3, 5; 7, 05 etc.

VII. Дайте відповіді на наступні запитання.

1. What is a fraction?

2. What are the terms of a fraction?

3. What does the denominator show?

4. What does the numerator show?

5. Types of fractions (common, decimal).

6. Proper and improper fractions.

7. Mixed numbers.

8. What is a decimal fraction?

9. How is the decimal fraction 0,5 read?

10. What is two and 35 in the decimal fraction 2,35?

VIII. Прочитайте додатковий текст №1 (SТ 1), звертаючи увагу на виділену в тексті спеціальну лексику уроку.

ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF FRACTIONS

COMMON FRACTIONS. To add fractions having the same denominator (like fractions) add their numerators and write the sum over the common denominator (do not add the denominators). Reduce the resulting fraction to the lowest terms.

To add fractions having different denominators (unlike fractions) the fractions must be changed to equivalent fractions which have the same or common denominator. The least number which must be a common denominator, for example, of 2/3 and 3/5 is 15. 15 is the least common denominator, or the lowest common denominator of 2/3 and 3/5. The least common denominator is sometimes denoted by the letters L.C.D.

To subtract fractions having the same denominator subtract the numerators and write the difference over the common denominator (do not subtract the denominators).

To subtract fractions having different denominator first change the fractions to equivalent fractions having a common denominator. To subtract the fractions when they have a common denominator, subtract the numerators and write the difference over the denominator.

To multiply a mixed number and a fraction: 1) reduce the fraction to its lowest terms; 2) change the mixed number to an improper fraction; 3) multiply the two numerators to obtain the numerator of the answer; 4) multiply the denominators to obtain the denominator of the answer; 5) reduce the fraction obtained when possible. Reduction can be done by dividing a numerator and the denominator by the same number. The numbers that are divided are crossed out, and the quotients are written as the new numerator and the new denominator.

To divide a whole number by a fraction, multiply the whole number by the denominator of the fraction and divide the result by the numerator of the fraction.

DECIMAL FRACTIONS. Decimal fractions are added in the same way that the whole numbers are added. Since only like decimal fractions can be added, that is hundredths to hundredths, and tenths to tenths, the addends are arranged in a vertical column with the decimal point directly below one another, all the way down and down to the answer.

Problem: Find the sum of the following numbers: 2.23, 4.8, 9 and 0.067.

Annex zeroes and arrange numbers in columns 2.230

4.800

9.000

0.067

16.097 answer

In subtracting decimal fractions we must write decimal fractions so that the decimal point of the minuend, subtrahend and remainder are below each other. Zeroes should be annexed so that both minuend and subtrahend are carried out to the same number of places. Check the answer in the same way that you check the subtraction of whole numbers.

In multiplying a decimal fraction or mixed decimals multiply as you do whole numbers. Then, starting at the right, mark off as many decimal places in the product as they are in the multiplier and multiplicand together.

To divide a number by 10 or any power of 10, move the decimal point in the dividend as many placed to the left as there are zeroes in the divisor. Add zeroes when needed.

X. Прочитайте та перекладіть додатковий текст №2(SТ 2).

FRACTIONS

There are three methods of dealing with fractions:

1 – by expressing each fraction as the sum of fractions with unit numerators, e.g. 5/6 =1/2 + 1/3

2 – by dividing the unit into sub-units which are given special names, e.g. the foot is divided into twelve parts and each twelfth part is called an inch;

3 – by using fractions whose denominators are powers of the same number, e.g. 3/3 = 7/10 + 5/100

The Egyptians used the first method and developed a high degree of skill in it. The second method, was used by Romans, who divided their pound, their foot and one of their coins into twelfth these fractions called unciae, from which we get the words inch and ounce. The third method dates back to the Babylonians, who used fractions with denominators which were powers of 60; the Greeks also used this method in scientific work.

It was not until Simon Stevin (1548 -1620) published his essay on decimal fractions in 1585 that the third method, with denominators which are all powers of ten< became generally adopted. Stevin was an important government official in he Netherlands in the time of the struggle against Spain. Many authors had used decimal fractions in particular problems, and the decimal point first appeared in print as early as in 1494, but Stevin was the originator of general rules for the use of decimal fractions.

XI. Анотуйте додаткові тексти № 1, 2(SТ 1, 2) англійською та українською мовами.

XII. Підготуйте повідомлення про одного з відомих математиків.