Vocabulary notes
value of the place – helyérték
is worth – egyenlő
a Latin word meaning – egy latin eredetű szó, amely jelentése
to distinguish from –megkülönböztet vmitől
a decimal point – pont a tizedes törtekben
improper fraction – áltört
integer – egész szám
a common denominator – közös nevező
vulgar fraction – közönséges tört
mixed number – kevert/vegyes tort, szám
proper fraction –valódi/valós tört
Exercises
I. Answer the following questions on the text:
1. What sign is used to separate the units from the tenths column?
2. What are the figures on the left of the decimal point called?
3. What are the figures on the right of the decimal point called?
4. What language does the word «fraction» come from?
5. What does the denominator show?
6. What does the numerator show?
7. How is bringing several fractions to a common denominator done?
II.
Read
the following numbers: 5.83;
96.79; 245.361; 0.02; 0.5;
;
;
;
;
1
;
1
.
III. Write your own examples of different types of fractions and read them in English. Lesson 10 mathematical sentences
In all branches of mathematics you need to write many sentences about numbers and mathematical statements.
A mathematical sentence is one in which a fact or completed idea is expressed.
There are two types of mathematical sentences:
An open sentence is a sentence which contains a variable.
"x + 2 = 8" is an open sentence. The variable is "x".
"It's a polygon." is an open sentence with the variable "It's."
A closed sentence, or statement, is a mathematical sentence which can be judged to be true or false. A closed sentence, or statement, has no variables.
"5 + 4 = 9" is a true closed sentence, or statement.
"A pentagon has exactly 4 sides" is a false closed sentence, or statement.
"An isosceles triangle has two congruent sides" is a true mathematical sentence.
"10 + 4 = 15" is a false mathematical sentence.
For example, you may be asked to write an arithmetic sentence that includes two numerals which may name the same number or even different numbers. Suppose that for your sentence you choose the numerals 8 and 11-3 which name the same number. You can denote this by writing the following arithmetic sentence 11-3=8, which is a true sentence.
Suppose that you choose the numerals 9+6 and 13 for your sentence. If you use the equal sign (=) between the numerals you will get the following sentence 9 – 6 = 13, which is not true but false.
As a matter of fact there is nothing incorrect or wrong about writing a false sentence. In fact, in some mathematical proofs it is essential to use false sentences.
It is important to be able to determine whether mathematical sentences are true or false. There exist the following properties of equality, which help us to do so:
Reflexive: a = a
Symmetric: if a = b, then b = a.
Transitive: if a = b and b = c, then a = c.
The relation of equality between two numbers satisfies these basic axioms for the numbers a, b and c.
Using mathematical symbols, we are constantly building a new language. In many respects it is more concise and direct than our everyday language. But if we are going to use this mathematical language correctly we must have a very good understanding of the meaning of each symbol used.
Drawing a short line across the = sign (equality sign) we change it to non-equality sign. This symbol implies either of the two things, namely: is greater than or is less than. The sign of non-equality in a sentence 3 + 4 ≠ 6 merely tells us that the numerals 3 + 4 and 6 name different numbers. If we are interested to know which of the two numerals is greater we use the conventional symbols meaning less than (<) or greater than (>). These are inequality symbols or ordering symbols because they indicate order of numbers.
The signs which express equality or inequality (=, ≠, >, <) are called relation symbols because they indicate how two expressions are related.