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�� #1

�� 447. �� , �� :�) (1 - 4/7)/(1 + 4/7);...

�� #2

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447. �� , �� :

�) (1 - 4/7)/(1 + 4/7);

(1-4/7)/(1+4/7)=((1-4/7)�7)/((1+4/7)�7)=(1�7-4/7�7)/(1�7+4/7�7)=(7-(4�7)/7)/(7+(4�7)/7)=(7-4/1)/(7+4/1)=(7-4)/(7+4)=3/11

�) (3/4 + 1/8)/(3/4 - 1/8);

(3/4+1/8)/(3/4-1/8)=((3/4+1/8)�8)/((3/4-1/8)�8)=(3/4�8+1/8�8)/(3/4�8-1/8�8)=((3�8)/4+(1�8)/8)/((3�8)/4-(1�8)/8)=((3�2�4)/4+(1�8)/8)/((3�2�4)/4-(1�8)/8)=(6/1+1/1)/(6/1-1/1)=(6+1)/(6-1)=7/5=1 2/5

�) (1/2 + 1/3 + 1/4)/(1/3 - 1/6 - 1/12);

(1/2+1/3+1/4)/(1/3-1/6-1/12)=((1/2+1/3+1/4)�12)/((1/3-1/6-1/12)�12)=(1/2�12+1/3�12+1/4�12)/(1/3�12-1/6�12-1/12�12)=(12/2+12/3+12/4)/(12/3-12/6-12/12)=(6+4+3)/(4-2-1)=(10+3)/(2-1)=

=13/1=13

�) (2/5 - 3/10 + 11/15)/(1/2 + 2/3 - 1/6);

(2/5-3/10+11/15)/(1/2+2/3-1/6)=((2/5-3/10+11/15)�30)/((1/2+2/3-1/6)�30)=(2/5�30-3/10�30+11/15�30)/(1/2�30+2/3�30-1/6�30)=((2�30)/5-(3�30)/10+(11�30)/15)/(30/2+(2�30)/3-30/6)=

=((2�5�6)/5-(3�3�10)/10+(11�2�15)/15)/(15+(2�3�10)/3-5)=(12/1-9/1+22/1)/(15+20/1-5)=(12-9+22)/(15+20-5)=(3+22)/(35-5)=25/30=(5�5)/(5�6)=5/6

�) (1/5 � 1/9 � 1/11)/(2/5 � 2/9 � 2/11);

(1/5�1/9�1/11)/(2/5�2/9�2/11)=(1/5�5�1/9�9�1/11�11)/(2/5�5�2/9�9�2/11�11)=(5/5�9/9�11/11)/((2�5)/5�(2�9)/9�(2�11)/11)=(1�1�1)/(2�2�2)=(1�1)/(4�2)=1/8

�) (2/3 � 5/7 � 3/20)/(1/3 � 6/7 � 13/20);

(2/3�5/7�3/20)/(1/3�6/7�13/20)=(2/3�3�5/7�7�3/20�20)/(1/3�3�6/7�7�13/20�20)=((2�3)/3�(5�7)/7�(3�20)/20)/((1�3)/3�(6�7)/7�(13�20)/20)=(2�5�3)/(1�6�13)=(2�5�3)/(2�3�13)=5/13

�) (1 2/5 � 2 1/7)/(1 3/7 � 2 4/5);

(1 2/5�2 1/7)/(1 3/7�2 4/5)=((1�5+2)/5�(2�7+1)/7)/((1�7+3)/7�(2�5+4)/5)=(7/5�15/7)/(10/7�14/5)=(7/5�5�15/7�7)/(10/7�7�14/5�5)=((7�5)/5�(15�7)/7)/((10�7)/7�(14�5)/5)=(7�15)/(10�14)=(7�3�5)/(2�5�2�7)=3/4

�) (2 1/2 � 2 1/3 � 2 1/4)/(1 1/2 � 1 2/3 � 1 3/4).

(2 1/2�2 1/3�2 1/4)/(1 1/2�1 2/3�1 3/4)=((2�2+1)/2�(2�3+1)/3�(2�4+1)/4)/((1�2+1)/2�(1�3+2)/3�(1�4+3)/4)=(5/2�7/3�9/4)/(3/2�5/3�7/4)=(5/2�2�7/3�3�9/4�4)/(3/2�2�5/3�3�7/4�4)=((5�2)/2�(7�3)/3�(9�4)/4)/((3�2)/2�(5�3)/3�(7�4)/4)=(5�7�9)/(3�5�7)=9/3=3

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