IV. Form derivatives from the following words and translate them into Hungarian:

digit, to separate, value, to suppose, possible, to use, to repeat, power, difficult, agreement, placement, element, identity, to exist, to expect, division, system, to observe

V. Find the following words and word combinations in the text. Guess their meanings. Make up your own sentences with them.

to be used in, may prove helpful, to be separated, to the left of, at the right, indefinitely, fractional numerals, simple pattern, to indicate, over and over again, this is also true, to lie on the same vertical line, proper place-value position

VI. Ask questions to which the following sentences could be answers.

1. The change of the order may affect the result.

2. On the right and on the left of the comma you see three digits.

3. He obtained the difference after he had subtracted the numeral.

4. The identity property is being considered by the students.

5. The value of the digit is defined by its position.

6. The given definition corresponds to the idea of uniqueness.

7. You may change 3.29 to 3.290 if it helps you to obtain the correct answer.

8. When you deal with decimal numbers you are to align the decimal points.

9. In the operation of multiplication it is the product of the numerator and the denominator that we actually find.

10. In the given example we have been trying to show the validity of these principles.

11. These digits are separated from 6 by a point.

12. All the points have been aligned on the vertical line.

Lesson 9 decimal and common fractions

Decimals. When you read from left to right in a whole number, the value of each place is just one-tenth as large as the value of the place before it, and ten times as big as the value of the place after it. In decimals the first place to the right after the units column is worth one-tenth of l or . The next place is worth one-tenth of or and so on. It is important to separate the units from the tenths column and this is done by using a decimal point. The number 34.76 is read aloud as “thirty four point seventy six”. The figures on the left of the decimal point 34 are whole numbers or integers and the figures on the right of the decimal point are decimal fractions (or decimals).

Fractions. Fraction comes from a Latin word meaning “to break” (ламати, розривати). In arithmetic the word fraction means a part, and the size of the part is shown by the numbers used. Fractions such as , , are called vulgar fractions to distinguish them from the “decimal fractions”.

In the fraction the 5 is called the denominator and shows that the whole is divided into fifths. The denominator is always the number below the line. The 3 is called numerator and shows how many parts of the whole are being taken. The numerator is always the number above the line.

The fraction (or , or and so on) is called a proper fraction as it is less than a whole “one”. The fractions and are called improper fractions as they are not less than a whole “one”.

The numbers 1 , 2 , 6 are called mixed numbers because they are mixtures of whole numbers and proper fractions. Mixed numbers can be changed to improper fractions by multiplying the whole number by the denominator and then adding on the numerator (6 = ).

Changing several fractions so that they have the same denominator is called bringing them to a common denominator, which must be a number into which the denominators of all the fractions in the sum will divide exactly.

The following example shows how this is done:

+ + = + + = = 1