Responder Os Exercícios Com Calculo
Anexos:
Soluções para a tarefa
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3
4)
3 . ( 2 + 8)
----- ---- -----
4 ( 3 15)
6 (:6) + 24 (:4) 1 + 6 15 + 12 27 (:3) 9
------- ------ = ------ ------ = ------------ = ----- = ------
12 (:6) 60 (:4) 2 15 30 30 (:3) 10
************************
5)
3 + 2 = 21 + 10 31
---- ---- ------------ = ------
5 7 35 35
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
1 + 1 + 1 6 + 4 + 3 13
---- --- ---- = -------------- = ---------
2 3 4 12 12
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
2 + a = 2b + 3a
------ ----- --------------------
3 b 3b
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
x + 3 4x + 3y
------ ----- = -------------
y 4 4y
**************************************
6)
a) 3 . 2 6
-------- = ---------
5 . 7 35
******************************
b)
1.1.1 1
------- = ------
2.3.4 24
*****************************
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
2 . a 2a
----- ----- = ---------
3 b 3b
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d) x.3 = 3x
----- -------
y.4 4y
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
7)
a)
3 . ( 8 + 5) 3.13 39
----- ---------- = ----------- = ------
4 ( 20 ) 80 80
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
3 ( 4x + 5y) 12x + 15y
----- ----------- = ---------------
4 20 80
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
a . (8 + 5) 13a
----- --------- = ----------
3 ( 20) 60
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
a ( 4a + 5b) 4a² + 5ab
----- . ------------ = ------------------
3 ( 20 ) 60
******************************************************
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
8) inverso:
a)
1994 = 1/1994
b)
1/13 = 13
c)
2/7 = 7/2
d)
7/2 = 2/7
e)
1/t = t
f)
3/b = b/3
g)
a/10 = 10/a
h)
n/m = m/n
**************************************
9) oposto:
a) 2/5 = - 2/5
b) - 3/7 = 3/7
c) a/8 = - a/8
d) 10/b = - 10/b
**************************************************
10)
a)
- 3 + x = 0
-----
5
x = 3/5
******************************
b)
2 + x = 0
----
7
x = - 2/7
**********************************
c)
- 20 + x = 0
-------
17
x = 20/17
***********************************
d)
a + x = 0
----
b
x = - a/b
**************************************
11)
a) - 3 . x = 1
------
5
x = 5 / (-3)
x = -5/3
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
2 . x = 1
-----
7
2x = 7
x = 7/2
******************************
c)
a . x = 1
----
5
x = 5/a
**************************
d)
2 . x = 1
-----
b
b = 2x
****************************
12)
a)
3 + 5 9 + 10
------- ----- -------------
3/4 + 5/6 4 6 12
------------- = ----------------- = -------------
2 2 2
19 . 1 19
----- ------- = ------
12 2 24
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
10 9 + 10
3 + ----- -----------
3 + 10/3 3 3 19 1 19
------------ = ------------ = --------------- = ----- . ---- = ------
2 2 2 3 2 6
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
x + 1 3x + 1 . 1 3x + 1
----- = ---------- ------ = -----------
3 3 2 6
-----------
2
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d) 2 + a 2b + 3a 2b + 3a 1
---- ----- ----------- ------------- . ------
3 b 3b = 3b 2
--------------- = --------------
2 2
= 2b + 3a
-------------
6b
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
13) multiplicação (a ordem dos fatores não altera o produto)
2 x 1 = 1 x 2
3 . ( 2 + 8)
----- ---- -----
4 ( 3 15)
6 (:6) + 24 (:4) 1 + 6 15 + 12 27 (:3) 9
------- ------ = ------ ------ = ------------ = ----- = ------
12 (:6) 60 (:4) 2 15 30 30 (:3) 10
************************
5)
3 + 2 = 21 + 10 31
---- ---- ------------ = ------
5 7 35 35
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
1 + 1 + 1 6 + 4 + 3 13
---- --- ---- = -------------- = ---------
2 3 4 12 12
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
2 + a = 2b + 3a
------ ----- --------------------
3 b 3b
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
x + 3 4x + 3y
------ ----- = -------------
y 4 4y
**************************************
6)
a) 3 . 2 6
-------- = ---------
5 . 7 35
******************************
b)
1.1.1 1
------- = ------
2.3.4 24
*****************************
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
2 . a 2a
----- ----- = ---------
3 b 3b
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d) x.3 = 3x
----- -------
y.4 4y
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
7)
a)
3 . ( 8 + 5) 3.13 39
----- ---------- = ----------- = ------
4 ( 20 ) 80 80
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
3 ( 4x + 5y) 12x + 15y
----- ----------- = ---------------
4 20 80
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
a . (8 + 5) 13a
----- --------- = ----------
3 ( 20) 60
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d)
a ( 4a + 5b) 4a² + 5ab
----- . ------------ = ------------------
3 ( 20 ) 60
******************************************************
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
8) inverso:
a)
1994 = 1/1994
b)
1/13 = 13
c)
2/7 = 7/2
d)
7/2 = 2/7
e)
1/t = t
f)
3/b = b/3
g)
a/10 = 10/a
h)
n/m = m/n
**************************************
9) oposto:
a) 2/5 = - 2/5
b) - 3/7 = 3/7
c) a/8 = - a/8
d) 10/b = - 10/b
**************************************************
10)
a)
- 3 + x = 0
-----
5
x = 3/5
******************************
b)
2 + x = 0
----
7
x = - 2/7
**********************************
c)
- 20 + x = 0
-------
17
x = 20/17
***********************************
d)
a + x = 0
----
b
x = - a/b
**************************************
11)
a) - 3 . x = 1
------
5
x = 5 / (-3)
x = -5/3
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
2 . x = 1
-----
7
2x = 7
x = 7/2
******************************
c)
a . x = 1
----
5
x = 5/a
**************************
d)
2 . x = 1
-----
b
b = 2x
****************************
12)
a)
3 + 5 9 + 10
------- ----- -------------
3/4 + 5/6 4 6 12
------------- = ----------------- = -------------
2 2 2
19 . 1 19
----- ------- = ------
12 2 24
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
10 9 + 10
3 + ----- -----------
3 + 10/3 3 3 19 1 19
------------ = ------------ = --------------- = ----- . ---- = ------
2 2 2 3 2 6
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
x + 1 3x + 1 . 1 3x + 1
----- = ---------- ------ = -----------
3 3 2 6
-----------
2
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
d) 2 + a 2b + 3a 2b + 3a 1
---- ----- ----------- ------------- . ------
3 b 3b = 3b 2
--------------- = --------------
2 2
= 2b + 3a
-------------
6b
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
13) multiplicação (a ordem dos fatores não altera o produto)
2 x 1 = 1 x 2
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