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a) 2/3 + 7/2 - 7/3
2 - 7 + 7 - 5 + 7
----- ----- ----- = ------- ------
3 3 2 3 2
2.(-5) + 3.7 - 10 + 21 11
---------------- = ---------------- = -------
6 6 6
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
5/8 + (2/5 : 4/15)
5 + [ 2 . 15 ]
------ ------ ------
8 [ 5 4 ]
5 + 30 (:10)
------- -----
8 20 (:10)
5 + 3 1.5 + 4.3 5 + 12 17
----- ----- = ------------- = ------------ = -------
8 2 8 8 8
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
(2/3 + 3/2) : (1/2 - 2/5)
[ 2 + 3 ] [ 1 - 2 ]
----- ----- : ----- ------
[ 3 2] [ 2 5 ]
[ 2.2 + 3.3 ] : [ 5.1 - 2.2]
---------------- ------------
[ 6 ] [ 10 ]
[ 4 + 9 ] : [ 5 - 4] 13 : 1
-------- -------- = ------ ------
[ 6 ] [ 10 ] 6 10
13 . 10 130 (:2) 65
----- ------- = -------- = ------
6 1 6 (:2) 3
***************************************
d)
1/2 + 7/8 . 2/14
1 + 7 . 2
----- ------ -------
2 8 14
1 + 7 (:7) . 2 (:2)
------ ----- -----
2 14 (:7) 8 (:2)
1 + 1 . 1 1 + 1 4 + 1 5
------ ---- ----- = ----- ----- = ---------- = -------
2 2 4 2 8 8 8
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e)
5/3 + 2/5 : 4/3
5 + 2 . 3
------ ----- -------
3 5 4
5 + 6 (:2) 5 3
----- ------ = ------ + ------
3 20 (:2) 3 10
10.5 + 3.3 50 + 9 59
---------------- = ----------- = --------
30 30 30
****************************************
f)
1/10 : 15/30 - 2/5
1 . 30 - 2
----- ------- -----
10 15 5
1 . 2 - 2
------ -----
10 5
2 (:2) - 2 1 - 2 - 1
------- ------- = ----- ----- = --------
10 (:2) 5 5 5 5
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
g)
1/6 - 2/3 + 7/2
1 - 2 + 7 1.1 - 2.2 + 3.7 1 - 4 + 21
----- ---- ------- = ---------------------- = ---------------
6 3 2 6 6
22 - 4 18
--------- = ------- = 3
6 6
*******************************
h)
7/8 - 2/9 - 1/18
7 - 2 - 1 9.7 - 8.2 - 1.4 63 - 16 - 4
------ ---- ----- = -------------------- = -----------------
8 9 18 72 72
63 - 20 43
----------- = -------
72 72
***************************
Obs.: (mmc: 8,9,18) = 72
8,9,18: 2
4,9,9: 2
2,9,9: 2
1,9,9: 3
1,3,3: 3
-----------------
1,1,1 = 2³.3² = 8.9 = 72
2 - 7 + 7 - 5 + 7
----- ----- ----- = ------- ------
3 3 2 3 2
2.(-5) + 3.7 - 10 + 21 11
---------------- = ---------------- = -------
6 6 6
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
5/8 + (2/5 : 4/15)
5 + [ 2 . 15 ]
------ ------ ------
8 [ 5 4 ]
5 + 30 (:10)
------- -----
8 20 (:10)
5 + 3 1.5 + 4.3 5 + 12 17
----- ----- = ------------- = ------------ = -------
8 2 8 8 8
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
(2/3 + 3/2) : (1/2 - 2/5)
[ 2 + 3 ] [ 1 - 2 ]
----- ----- : ----- ------
[ 3 2] [ 2 5 ]
[ 2.2 + 3.3 ] : [ 5.1 - 2.2]
---------------- ------------
[ 6 ] [ 10 ]
[ 4 + 9 ] : [ 5 - 4] 13 : 1
-------- -------- = ------ ------
[ 6 ] [ 10 ] 6 10
13 . 10 130 (:2) 65
----- ------- = -------- = ------
6 1 6 (:2) 3
***************************************
d)
1/2 + 7/8 . 2/14
1 + 7 . 2
----- ------ -------
2 8 14
1 + 7 (:7) . 2 (:2)
------ ----- -----
2 14 (:7) 8 (:2)
1 + 1 . 1 1 + 1 4 + 1 5
------ ---- ----- = ----- ----- = ---------- = -------
2 2 4 2 8 8 8
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e)
5/3 + 2/5 : 4/3
5 + 2 . 3
------ ----- -------
3 5 4
5 + 6 (:2) 5 3
----- ------ = ------ + ------
3 20 (:2) 3 10
10.5 + 3.3 50 + 9 59
---------------- = ----------- = --------
30 30 30
****************************************
f)
1/10 : 15/30 - 2/5
1 . 30 - 2
----- ------- -----
10 15 5
1 . 2 - 2
------ -----
10 5
2 (:2) - 2 1 - 2 - 1
------- ------- = ----- ----- = --------
10 (:2) 5 5 5 5
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
g)
1/6 - 2/3 + 7/2
1 - 2 + 7 1.1 - 2.2 + 3.7 1 - 4 + 21
----- ---- ------- = ---------------------- = ---------------
6 3 2 6 6
22 - 4 18
--------- = ------- = 3
6 6
*******************************
h)
7/8 - 2/9 - 1/18
7 - 2 - 1 9.7 - 8.2 - 1.4 63 - 16 - 4
------ ---- ----- = -------------------- = -----------------
8 9 18 72 72
63 - 20 43
----------- = -------
72 72
***************************
Obs.: (mmc: 8,9,18) = 72
8,9,18: 2
4,9,9: 2
2,9,9: 2
1,9,9: 3
1,3,3: 3
-----------------
1,1,1 = 2³.3² = 8.9 = 72
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