SEVENTH GRADE / MATHEMATICS / TEST 18.104.22.168
The order of operations is similar to stack or last-in-first-out memories. The later defined/used
operations are done/evaluated earlier. That means evaluation of powers, division and multiplication and subtraction and summation
is the correct order.
Paranthesis are blocks and are to be evaluated first in order to be able to continue.
7-7=0 ; - 8:2 - 8:2 = -8 ; 8+8 = 16.
Looking at the paranthesis we record (17-8:2x4+64:8) is bit uneasy. The result of 8:2x4 differs
depending of the order of operations having equal priorities. Usually extra paranthesis are used but her we will evaluate the
operations according to yehir order in print/script and we will adopt evaluating the division first:8:2x4=16.
(7-8:2+64:8)=11; (7+8:2-4x2)=3; (17-8:2x4+64:8)=9; (7+18:2-4:2)=14.
"Between" means here that the limits are excluded. It is usually better to cite this exclusion
because language gets sometimes vauge.
The denominator (in both cases) is greater than the numerator, try to see at a glance .
Just expand by 1000 ... It will then be much easier to see .
If we consider the equality AxB=24, the minimal sum for A+B will be (-24)+(-1)=-25. Integers having a
definite sum will have max. product when they are closest and/besides integers do contain negative wholes.
Since AxB = 24, B=24/A is valid. replace and get (24/A)xC=48, i.e. C=2xA. ry1 makes use of this
The least values are A=1 and B=3, whereas the greatest ...
Least B/A değeri if greatest A and least B; similarly ...
The first addition implies C=0 .
The second addition implies A+B=10 and B=1 .
If A-B>0, take the greatest A+B under A-B=1.
If A-B<0 ... And compare the reults.
The question is already answered if A and B are positive integers. The least numerator is to be
attained in case B>A in which case the result is negatve integer if A+B>0.
Let A=-1 . B should be among 2 and 9. The least value if B=2 .
Let A=-2 . B should be among 3 and 9. olmalıdır. Values: -5, -6/2, ... , -11/7
Let A=-8 olsun. B should be 9 olmalıdır. Value: -17 .
That is a preperation for coordinate systems; have please a look at ry1 .
Even powers of integers are whole (natural) numbers .
b can not be equal to or grater than 5, because ... .
5!=5x4x3x2x1 . 0! is defined to be 1.
5! = 5 x 4! i.e. 5!-4! = 4x4! .
[1+1/(1+2/S)]=3 i.e. 1/(1+2/S)=2 i.e. 1+2/S=1/2 i.e. 2/S=-1/2 .
The first equation means 5xA = 3xB, i.e. 6xA = 3xB +A ve 6xA + B = ... .