Resta Racionales

Vista previa del material en texto

Resta de racionales. 
Para restar fracciones como en el caso anterior se tiene que obtener 
el común denominador, obtener numeradores equivalentes y 
restarlas de acuerdo a las reglas de signos. 
Si son fracciones mixtas se convierten a fracciones impropias, y si 
son decimales se convierten a fracciones. 
 
-2 1/3 + 1 1/5 
-7/3+ 6/5 =
15
21
15
17
15
1835
−=
−
=
+− mcm= 15 
 
-1 1/3 +1 ¼ - 2.6= 
 
 -2 6/10 
-4/3 +5/4 –26/10 = 
60
412
60
161
60
1567580
−=
−
=
−+− mcm=60 
 
-1 1/3 + 2 ¼= 
-4/3 +9/4 =
12
11
12
2716
=
+− 
 
Ejercicio: Resuelve usando la recta numérica. 
a) –2 ¼ +1 1/3- 1 1/5=-9/4+ 4/3- 6/5 =- 127/60 = -2 7/60 
 
 
 
| | | | | | | 
-3 -2 -1 0 1 2 3 
 
 
b) –2 3/5 + 1 1/3 +1 ½= -13/5+4/3 + 3/2 =7/30 
 
 
 
| | | | | | | 
-3 -2 -1 0 1 2 3 
 
 
c) –3 1/6 +1 1/3- 1 ½ = -19/6 + 4/3 – 3/2 = -20/6 = -3 2/6= -3 1/3 
 
 
| | | | | | | | | | 
-4 -3 -2 -1 0 1 2 3 4 5 
 
d) – 2 ¾+ 1 3/7 + 1 ½ = -11/4+ 10/7 3/2 = 5/28 
 
 
| | | | | | | | | | 
-4 -3 -2 -1 0 1 2 3 4 5 
 
e) –2 3/5+ 2 1/10 + 1 1/12 = -13/5+21/10+13/12 =35/60 =7/12 
 
 
| | | | | | | | | | 
-4 -3 -2 -1 0 1 2 3 4 5 
 
Ejercicio de repaso resuelve las siguientes sumas y restas de 
números racionales. 
 
a) –3 ¼ + 2 1/3- 1 1/6 = -13/4+ 7/3 – 7/6 = -25/12 = -2 1/12 
b) –2 3/5 + 1 8/9 +1 2/3 = -13/5+ 17/9+5/3 = 43/45 
c) –5 4/7 + 2 1/5 + 1 ½ = -39/7 + 11/5 +3/2= -134/70 = -1 32/64 
d) –6 6/7+ 1 ¼ - 1 1/3 = -45/7+5/4-4/3= -537/84 = -6 33/84 
e) – 7 ½ + 1 1/3 – 1 1/5= -15/2+4/3-6/5=-221/30= -7 11/30 
f) –8 1/3-1 ¼ + 1 1/5= -543/60 = -9 3/60= -9 1/20 
g) –10 ½ -1 1/3 –1 1/7 = -545/42= -12 41/42 
h) –6 2/5 – 1 1/12 + 1 ¼ = -32/2-13/12+5/4=-190/12= -15 5/6 
i) – 8 1/3 –6 1/5 +1 1/6=-25/3-31/5+7/6=-401/30= -13 11/30 
j) –7 2/5 + 2 1/3 –1 1/3= -37/5+ 7/3- 4/3= -96/15 = - 6 6/15 
 
Ejercicio: 
 
a) [-(-2)-(-5)-(-3)(-2)-{-(-2)-(-4)}] = 
[-(-2)-(-5)-(-3)(-2)-{+2+4}] = 
[-(-2)-(-5)-(-3)(-2)-{+6}] = 
[ -(-2)-(-5)-(+6)+6]= 
[+2+5-6+6]= 
[13-6] = 7 
 
b) [-(-2)(-4)(-3)-{-(-2)-(-3)}] = 
[-(-2)(-4)(-3)-{+2+3}] = 
[-(-24)-5] = 
[24 – 5] = +19 
 
c) [ -(-2)-(-6)-(-3)-(-4)-{-(-3)(3)}] = 
[ - (-2)- (-6) –(-3) –(-4) – {3(3)}] = 
[+2+6+3+4-9] = 
[15 –9] = +6 
 
d)[-(-2)(-5)-(-6)-(-3)(2)-{-(-2)}] = 
[-(-2)(-5)-(-6)-(-3)(2)-{ +2}] = 
[-10+6+6-2] = 
[-12+12] = 0 
 
e)–[-(-2)-(-3)-(3)+(-4)-{-(-2)(4)}] = 
-[-(-2)-(-3)-(3)+(-4)-{-(-8)}] = 
-[-(-2)-(-3)-(3)+(-4)-{+8}] = 
-[+2 + 3 –3 - 4 –8] = 
-[-15+5] = 
-[-10] = +10 
 
Obtener el valor numérico de las siguientes expresiones: 
 a=2, b=3, x=1, c=-2, y=-3 
 
a)
)3)(2(2
)3)(1(4)3)(1(5
2
45 22 −+
=
+
ab
xybx = 
4
1
12
3
12
1215
)6(2
12)3)(1(5
==
−
=
− 
b) =+−+=+−+=++
)3)(4(3
9)2)(6(3)3(5
)3)(2(3
3)2)(3)(2(3)3)(1(5
3
35
2
22
2
22
ba
babcbx 
3
1
36
12
36
93615 −
=
−
=
+− 
 
c) =+−+=++
)3)(2(3
)2(2)3)(1(3)3)(2(5
3
235
2
)1
2ba
axyab x 
36
25
36
934
129(3
4930
)3)(4(3
)2(2)3(3)6(5
=
−
=
+−
=
+−+ 
 
d) =+=+
)2(2
)3)(1(4)1)(2(3
2
43 23
a
bxxa ab 
9
4
36
4
1224
4
)3)(1(4)1)(8(3
==
+
=
+ 
 
e) =+−=+−
)3)(2(2
)3)(2(4)3)(2(3
2
43
1
22
ba
abba
x 
1
12
12
12
2436
)6(2
24)12(3
)3)(2(2
)6(4)3)(4(3
−=
−
=
+−
=
+−
=
+− 
 
f) =
−
−+−
=
+−
)3)(1(3
)2)(2(2)3)(2(8
3
28 3122
xy
caba bx 
9
214
9
128
9
3296
9
)16(2)12(8
)3(3
)2)(8(2)3)(4(8
=
−
−
=
−
−−
=
−
−+−
=
−
−+− 
 
g) =++=++
)1)(2(2
4)1)(2(4)3)(2(2
2
442
23
232323
ab
ab
xa
xaba 
16
411
16
180
16
432144
16
432)72(2
)1)(8(2
4)1)(8(4)9)(8(2
==
++
=
++
=
++ 
Ejercicio: 
 
a) –[ -(-2)(-3)-(-5)-(-6)-(-3)(2)-{-(-2)(-3)}-(-2)] = 
-[-(-2)(-3)-(-5)-(-6)-(-3)(2)-{2(-3)}+2] = 
-[-(-2)(-3)-(-5)-(-6)-(-3)(2)-{-6}+2] = 
-[-6+5+6+6+6+2] = 
-[25-6] = 
-[19] = -19 
 
b)-[-(-5)-(-3)-(-2)-(-4)-(-5)-(-6)-{(-3)(4)(-2)}-(-2)] = 
-[-(-5)-(-3)-(-2)-(-4)-(-5)-(-6)-{24}+2] = 
-[ +5+3+2+4+5+6-24+2] = 
-[+27 -24] = 
-[+3] = -3 
 
c) – [-(-3)-(-5)-(-3)-(-2)-(-4)(2)-(-3)(-5)-{+6}] = 
-[-(-3)-(-5)-(-3)-(-2)-(-4)(2)-(-3)(-5)-6] = 
-[+3+5+3+2-(-8)-(15)-6] = 
-[3+5+3+2+8-15-6] = 
-[+21 –21] = 
-[0] = 0 
 
d) -[-(-3)(-4)(-5)-(-6)-(-3)]-[-(-3)(-2)-(-4)-(-5)-(-5)-(-3)-(-4)] = 
-[-(-60)+6+3]-[-(6)+4+5+5+3+4] = 
-[+60+6+3]- [-6+4+5+5+3+4] = 
-[69] – [21-6] = 
-[69]-[15] =-69 –15 =-84 
 
e) –[ -(-3)(-5)-(-6)-(-2)-(-6)-{(-2)-(-3)}-(-2)(-4)]-[-(-2)(-4)(-5)] = 
-[-(15)+6+2+6-{-2+3}-(8)]-[-(-40)] = 
-[-15+6+2+6 -(1)-8]-[+40] = 
-[-24+14]-[40] = 
-[-10]-[40] = 10- 40 = -30 
 
 
Ejercicio: 
a) 1.71068
3
5
=−=−+
x 
6108
3
5
+−=+
x 
8610
3
5
−+−=
x 
5x=(-10+6-8)3 
x=
5
36
5
)3(12 −
=
− 
 
b) 1563
2
8
=−+
x 
6153
2
8
+=+
x 
3615
2
8
−+=
x 
8x=(18)2 x=
2
9
8
36
= 
 
c) 4154
3
7
−=−+
x 
1544
3
7
+−=+
x 
4154
3
7
−+−=
x 
7x=(7)3 
x= 3
7
21
= 
 
d) 221178
4
5
=+−+
x 
711228
4
5
+−=+
x 
871122
4
5
−+−=
x 
5x=(10)4 
x= 8
5
40
= 
e) 101763
3
5
=+++
x 
176103
3
5
−−=+
x 
317610
3
5
−−−=
x 
5x= (-16)3 
x=
5
48− 
 
Ejercicio: elabora las siguientes conversiones de decimal a 
fracción, simplificando. 
 
a) 0.21 = 21/100+5/900=(189+5)/900 =194/900 = 97/450 
_
5
b) 0.25 = 2/10+54/990=(198+54)/990 = 252/990= 42/165 
_
4
c) 0.12 = 12/100+34/9900 =(1188+34)/9900 = 1222/9900 = 
611/4950 
__
34
d) 0.4 = 4/10+21/990 =(396+21)/990 = 417/990 =139/330 
__
21
e) 0.2 = 2/10+34/990 =(198+34)/990 = 232/990 = 116/495 
__
34
f) 0. = 2146/9999 
______
2146
 
Suma y ubica en la recta numérica. 
 
a) 2/5+4/3+1/6 = 57/30= 1 27/30= 1 9/10 
 
| l l l l | l l l l l | 
0 1 2 
 
b) 2 1/3+1 ¼+4/2 = 7/3+5/4+4/2 =67/12 = 5 7/12 
 
 
| l l l l l l | 
0 1 2 3 4 5 6 7 
 
c) 1/3+ 1/6+ 8/7 = 69/42 = 1 27/42 = 1 9/14 
 
 
| l l | l l | 
0 1 2 
 
d) 2 1/3+1 ¼ +3/5 =7/3+5/4+3/5=251/60 = 4 11/60 
 
 
| | | | | | 
0 1 2 3 4 5 
 
e) 1 ¼+2 1/3+1 1/6 =5/4+7/3+7/6 =57/12= 4 9/12 
 
 
| | | | | | | 
0 1 2 3 4 5 6