Vocabulary Notes
term – tag, kifejezés
dividend – osztandó
partial dividend – részleges osztandó
divisor - osztó
quotient / answer – hányados
separate quotient – különálló hányados
remainder – maradék
actually – valójában
example – példa
cipher – 1) nulla (szám) 2) szimbólum; zéró
count out – ki/leszámolni
group of 7 cards – 7-es csoport
contain in – tartalmaz, magába foglal
a number of times – annyiszorosa
successive – következő
slash – ferde vonal, virgula
Exercises
I. Answer the following questions on the text:
1. What is the operation of division?
2. Is there always an exact answer to a division sum?
3. What is a remainder?
4. What is the number divided called?
5. What is the number by which the dividend is divided called?
6. What is the quotient?
II. Give the Ukrainian words for the words and word combinations. Use them in the sentences of your own:
equal numbers, to count out, exact answer, division sum, remainder, dividend
III. Divide the following numbers orally:
12 by 3; 40 by 5; 85 by 10; 116 by 4
Lesson 6 algebraic expression
An algebraic expression is an expression in which several numbers represented by letters (or by letters and figures) are connected by means of signs indicating the operations to which the numbers must be subjected and the order of these operations.
Such are,
for instance,
bc; cd; 2x +
1.
For the sake of brevity we may say «expression» instead of “algebraic expression”.
To evaluate an expression when the numerical values of the letters are given is to substitute the numerical equivalents for the letters and perform the operation indicated in the expression. Hence, the numerical value of the expression
bc
when a
=
225,
b =
4 and c
=
3 is
×4×3=4.5×12=54.
Order of operations. With regard to the order in which the operations indicated in an algebraic expression should be performed; it was agreed upon to perform operations of the higher order first, i. e. involution and devolution, then multiplication and division, and, finally addition and subtraction.
Thus, if
we have the expression 3a2b
-
+d.
We
must first perform the involution (square
the number and
cube
the number, then
the multiplication and division (multiply 3 by a2
and
the
result obtained we
multiply by b;
divide
b3
by
c)
and,
finally, we perform the subtraction and addition (subtract
from 3a2b
and
add d
to
the result).
Formula. If you write in algebraic language the law, “The area of a rectangle is equal to its length multiplied by its breadth” then you would write A = bl, where, A is standing for “the area of the rectangle”, b -for “its, breadth” and l for “its length”. This kind of statement is a formula. (A mathematical rule expressed in a set of numbers and letters.)
Vocabulary notes
the numbers must be subjected – a számokat alá kell vetni
the order of operations – a műveletek sorrendje
for the sake of brevity – az egyszerűség kedvéért
represent – jelöl, jelent
to evaluate an expression – kiértékelni egy kifejezést
hence – ennélfogva, innen
to square a number – négyzetre emelni egy számot
to cube a number – köbre emelni egy számot
the result obtained – a kapott eredmény
numerical equivalent / value– számbeli érték
with regard to the order – ami a sorrendet illeti
the law – szabály, törvény
involution – hatványozás
devolution – gyökvonás
rectangle – négyszög
area – terület, kerület