NUMERACIÓN II -5TO Y 6TO ARITMÉTICA-.pdf

numeracion

1. TEMA: NUMERACÍÓN II
Aritmética

2. NUMERACÍÓN II
CAMBIO DE BASE
CASO 2: DE BASE 10 A BASE DIFERENTE DE 10




NUMERACIÓNII
CASO I: DE BASE DIFERENTE DE 10 A BASE 10
Por descomposición polinómica
Convertir 234
5 a base 10
234
5=2×5
2
+3×5+4
=50+15+4
=69
Por divisiones sucesivas
Convertir 346 a base 6
346 6
4 576
3 96
3 1
346=1334
6
234
5=69

3. NUMERACÍÓN II
CASO3: DE BASE DIFERENTE DE 10 A BASE DIFERENTE DE 10
Convertir 231
5 a base 7
A base 10
=50+15+1
=66
A base 7
3 9
66 7
7
2 1
231
5=123
7
231
5=2×5
2
+3×5+1
PROPIEDAD:
1�
1�
1??????. . .
1??????
(??????)
= x +a+b+c+……+n
Ejemplo:
12
1416
8
=8+2+4+6=20

4. NUMERACÍÓN II
2.-Calcule � +b+c si:
���
(8)=1236
(7)
1.- Calcule � +b+c+d
Si ����
(5)=298
298 5
3 59 5
4 11 5
1 2
����
(5)=2143
(5)
�+b+c+d=2+1+4+3=10
RESOLUCIÓN
�=2 b=1 c=4 d=3
1236
(7)= 1×7
3
+2×7
2
+3×7+6
=343+98+21+6
=468
468 8
4 58 8
2 7
���
(8)=724
(8)
� +b+c=7+2+4=13
RESOLUCIÓN
� =7 b=2 c=4

5. NUMERACÍÓN II
3.-El menor numeral de 3 cifras diferentes de la
base nueve, expresarlo en el sistema senario
4.-De las siguientes igualdades, halle m+n
23�
(9)=27�
(�) ���
(8)=1611
(�)
102
(9) � ���� 6
83 6
5 13 6
1 2
102
(9)=215
(6)
RESOLUCIÓN:
102
(9)= 1×9
2
+0×9+2=83
7< n<9
n=8
6< m<8
m=7
m+n=7+8=15
RESOLUCIÓN:

6. NUMERACÍÓN II
5.-Calcule &#3627408462;
2
+1
Si &#3627408462;&#3627408462;&#3627408462;&#3627408462;
(4)=170
6.-Halle a+b, si se cumple
&#3627408462;1&#3627408463;
(9)=1142
(7)

&#3627408462;×4
3
+&#3627408462;×4
2
+&#3627408462;×4+&#3627408462;=170
64 &#3627408462;+16&#3627408462;+4&#3627408462;+ &#3627408462;=170
85 &#3627408462;=170
&#3627408462;=2
&#3627408462;
2
+1=2
2
+1=5
RESOLUCIÓN:
1142
(7)=1 × 7
3
+1×7
2
+4×7+2
=343+49+28+2
=422
422 9
8 46
9
1 5
&#3627408462;1&#3627408463;
(9)=518
(9)
&#3627408462;=5 b=8
&#3627408462;+&#3627408463;=5+8=13
RESOLUCIÓN:

7. NUMERACÍÓN II
7.-Calcule x si
11
12
13
1516
(??????)
=37
(8)
8.-Calcule &#3627408462;
3
−&#3627408462;
2
11
1&#3627408462;
12
1??????13
1??????14
1??????(25)
=&#3627408462;&#3627408462;
(2&#3627408462;)

X+1+2+3+5+6=3∙8+7
X+17=31
X=14
RESOLUCIÓN:
25+1+ &#3627408462; +2+ &#3627408462; +3+ &#3627408462; +4+ &#3627408462; = &#3627408462;∙2&#3627408462;+ &#3627408462;
35+4&#3627408462;=2&#3627408462;
2
+&#3627408462;
35=2&#3627408462;
2
-3&#3627408462;
&#3627408462;=5
&#3627408462;
3
−&#3627408462;
2
= 5
3
−5
2
=125 - 25=100
RESOLUCIÓN:

8. NUMERACÍÓN II
9.-Si el numeral
(&#3627408462;+1)(&#3627408462;−1)(&#3627408462;−2) &#3627408466;&#3627408480;&#3627408481;á &#3627408466;&#3627408485;&#3627408477;&#3627408479;&#3627408466;&#3627408480;&#3627408462;&#3627408475;&#3627408465;&#3627408476; &#3627408466;&#3627408475; &#3627408463;&#3627408462;&#3627408480;&#3627408466; 4,
expresarlo en base 6
10.-Determine el valor &#3627408475; si se cumple

3&#3627408462;&#3627408463;
(7)=5&#3627408464;&#3627408465;
(&#3627408475;)
&#3627408462;=2
(&#3627408462;+1)(&#3627408462;−1)(&#3627408462;−2)
(4) =310
(4)
310
(4) en base 6
310
(4)= 3× 4
2
+1×4+0=52
52 6
4 8 6
2 1
310
(4)=124
(6)
RESOLUCIÓN:
5< n<7
n=6
RESOLUCIÓN:

9. NUMERACÍÓN II
11.- El número 1002 de la base 4.¿En que base se escribe
como 123?
12.-Calcule &#3627408462;
2
+ &#3627408462; si
1&#3627408462;
12
1??????
15
1??????13
(16)
=14
14
14
(5??????)
1002
(4)=123
(??????)
1∙4
3
+0∙4
2
+0∙4+2= 1∙&#3627408485;
2
+2∙&#3627408485; +3
64+2 = &#3627408485;
2
+2&#3627408485; +3
66 = &#3627408485;
2
+2&#3627408485; +3
63=&#3627408485;
2
+2&#3627408485;
X=7
RESOLUCIÓN:
16+ &#3627408462; +2+ &#3627408462; +5+ &#3627408462; +3=5&#3627408462; + 4+ 4+ 4
26+3&#3627408462; =5&#3627408462; +12
14=2&#3627408462;
a =7
&#3627408462;
2
+ &#3627408462; =7
2
+ 7=56
RESOLUCIÓN:

10. NUMERACÍÓN II
13.-Si se cumple que 2&#3627408462;&#3627408463;&#3627408464;
(7)=3254
(&#3627408475;)
Calcule a+b+c+n

14.-Siendo que &#3627408485;&#3627408486;&#3627408487;&#3627408485;
(8)=1043
(11)
Calcule xyz
5< n<7
n=6
2&#3627408462;&#3627408463;&#3627408464;
(7)=3254
(6)
3254
(6)=3×6
3
+2×6
2
+5×6+4=754
754 7
2&#3627408462;&#3627408463;&#3627408464;
(7)=2125
(7)
&#3627408462; +b+c+n=1+2+5+6=14
5 1077
2 15
7
1 2
RESOLUCIÓN:
&#3627408462;=1 b=2 c=5
1043
(11)=1 × 11
3
+0×11
2
+4×11+3=1378
1378 8
2 172 8
4 21
8
5 2
&#3627408485;&#3627408486;&#3627408487;&#3627408485;
(8)=2542
(8)
xyz=2∙5 ∙ 4=40
RESOLUCIÓN:
x=2 y=5 z=4

11. NUMERACÍÓN II
15.-Halle a+n si se cumple que
(&#3627408475;−1)(&#3627408475;
3
)(&#3627408475;+2)
(9)=&#3627408462;&#3627408462;&#3627408462;
(12)
n=2
184
(9)= &#3627408462;&#3627408462;&#3627408462;
(12)
184
(9)=1×9
2
+8×9+4=157
157 12
1 13
12
1 1
184
(9)=111
(12)=&#3627408462;&#3627408462;&#3627408462;
(12)
&#3627408462; =1
&#3627408462; +n=1+2=3
RESOLUCIÓN

12. NUMERACÍÓN II

13. ¡Muchas Gracias!