43
7
8
153.
8-rasmdan
foydalanib,
2
3
5
__
aralash sonni noto‘g‘ri kasrga aylantiring.
O
0
1
2
3
2
3
5
__
X
154.
Sonni noto‘g‘ri kasr ko‘rinishida ifodalang: a) 3
5
8
__
; b) 2 49
__
;d) 12 17
25
__
; e) 12
55
87
__
.
155.
Qo‘shishni bajaring va natijani aralash son ko‘rinishida ifodalang:
a) 3
5
_
+ 4
5
_
; b) 9
12
__
+ 14
12
__
; d) 78
_
+
5
8
_
; e) 13
25
__
+ 14
25
__
; f) 13
19
__
+ 11
19
__
+ 7
19
__
.
156.
Kilometrda ifodalang: a) 6 km
200 m
; b) 18 km 750
m
; d) 11 km 925
m
.
157.
Avtomobil 250 km masofani 3 soatda bosib o‘tgan bo‘lsa, avtomobilning tezligini
toping. Javobni aralash son ko‘rinishida ifodalang.
158.
Ishchi 8 soatda 145 dona detal tayyorladi. U 1 soatda nechta detal tayyorlagan?
Javobni aralash son ko‘rinishida ifodalang.
Uyda bajaramiz
148.
Soatlarda ifodalang:
a) 2 soat 34 minut; b) 4 soat 43 minut; d) 6 soat 14 minut.
Namuna:
a) 2 soat 34 minut = (2 + 34
60
__
) soat = 2 34
60
__
soat.
149.
Oila bir haftada 12 kg kartoshka iste’mol qildi. Oila bir kunda o‘rtacha
necha
kilogramm kartoshka iste’mol qilganini toping. Javobni aralash son ko‘rinishida
ifodalang.
150.
Uzunligi 2 9
15
__
m bo‘lgan sim, har biri 1
15
__
m bo‘lgan bo‘laklarga bo‘lindi. Nechta
bo‘lak sim hosil bo‘ldi?
151.
7-rasmdan foydalanib, noto‘g‘ri kasrni aralash son ko‘rinishida yozing.
7
2
__
= 3 1
2
__
;
19
8
__
= __________;
a)
b)
21
4
__
= __________;
11
3
__
= __________.
d)
e)
152.
Olim: “Bo‘yim
9
6000
____
km,
vaznim esa
2
50
__
tonna”, – deb aytdi. U adashmayap-
timi?
http://eduportal.uz
44
Aralash sonlarni qo‘shish va ayirish bu amallarning xossalari asosida bajariladi.
1-misol.
2
2
5
_
va 1 1
5
_
sonlari yig‘indisini toping.
Yechish:
2
2
5
_
= 2 +
2
5
_
va 1 1
5
_
= 1 + 1
5
_
bo‘lgani uchun (1-rasm)
2
2
5
_
+ 1 1
5
_
= 2 +
2
5
_
+ 1 + 1
5
_
= 2 + 1 +
2
5
_
+ 1
5
_
= 3 + 3
5
_
= 3 3
5
_
.
Bu qisqacha quyidagi ko‘rinishda yoziladi (2-rasm):
2
2
5
__
+
1
1
5
__
=
3
3
5
__
+
+
2-misol.
2
4
5
_
va 1
2
5
_
sonlarning ayirmasini toping.
Yechish:
(3-rasm)
2
4
5
_
–
1
2
5
_
=
2
+ 4
5
_
–
(1
+
2
5
_
)
=
2
+
4
5
_
–
1
–
2
5
_
=
(2
–
1)
+
( 4
5
_
–
2
5
_
)
=
1
+
2
5
_
=
1
2
5
_
.
Bu qisqacha quyidagi ko‘rinishda yoziladi (4-rasm):
2
4
5
__
–
1
2
5
__
=
1
2
5
__
–
–
Aralash sonlarni qo‘shishda (ayirishda) ularning butun va kasr qismlari alohida-
alohida qo‘shiladi (ayriladi).
Ba’zida aralash sonlarni qo‘shishda kasr qismlar yig‘indisi noto‘g‘ri kasr bo‘lishi
mumkin. Bunday hollarda noto‘g‘ri kasrning butun qismi ajratiladi va butun qismlar
yig‘indisiga qo‘shiladi. (5-rasm)
3-misol.
1 34
_
+ 1
2
4
_
= 2
5
4
_
= 2 +
5
4
_
= 2 + 1 14
_
= 2 + 1 + 14
_
= 3 1
4
_
.
+
=
Ba’zida, aralash sonlarni ayirishda
kamayuvchining kasr qismi, ayriluvchining
kasr qismidan kichik bo‘lishi mumkin. Bunday hollarda 1 butun “maydalanadi”.
ARALASH SONLARNI QO‘SHISH VA AYIRISH
48
1
3
+
=
2
–
=
4
5
http://eduportal.uz
45
Buni quyidagi misolda tushuntirish mumkin:
4-misol.
Ayirmani hisoblang:
3 13
_
– 1
2
3
_
.
1
3
_
<
2
3
_
. Demak, kamayuvchining bitta butunini maydalaymiz (6-rasm)
:
3 13
_
= 2 + 1 + 13
_
= 2 + 1 13
_
= 2 + 43
__
= 2 43
__
.
=
Endi ayirmani hisoblaymiz (7-rasm)
: 2
4
3
__
– 1
2
3
_
= 1
2
3
_
.
Bu
qisqaroq
5
2
9
_
– 2
4
9
_
= 4 11
9
__
– 2
4
9
_
= 2 79
_
ko‘rinishda yoziladi.
Butun sondan kasr son ayrilayotganda ham xuddi shunday yo‘l tutiladi, ya’ni
1 butun “maydalanadi”. Buni quyidagi misollarda tushuntirish mumkin (8-rasm)
:
5-misol.
3 –1 34
_
= 2 44
__
– 1 34
_
= 1 14
_
.
=
6
Mashq qilamiz
159.
(Og‘zaki) Hisoblang va yig‘indini qanday topganingizni tushuntiring.
a) 2 13
_
+ 1;
b) 3
2
3
_
+ 2; d) 4 + 2
2
5
_
; e) 3 1
5
_
+
2
5
_
.
160.
Yig‘indini toping.
a) 1 1
12
__
+ 2 1
12
__
;
b) 3
5
9
_
+ 1 19
_
;
d) 4
2
9
_
+ 1 19
_
;
e) 3 38
_
+ 1 18
_
.
N
amuna:
Yuqorida yechilgan 1-misol.
161.
Yig‘indini toping va natijani aralash son ko‘rinishida tasvirlang:
a) 38
_
+ 78
_
;
b) 6
11
__
+ 8
11
__
;
d)
2
3
_
+
2
3
_
;
e) 11
12
__
+ 7
12
__
.
Namuna:
Yuqorida yechilgan 3-misol.
162.
Yig‘indini toping.
a) 3 1
2
_
+ 1
2
_
;
b) 34
_
+ 1 14
_
;
d) 4 13
_
+ 1
2
3
_
;
e) 2 38
_
+ 3
5
8
_
.
Namuna:
Yuqorida yechilgan 3-misol.
163.
Yig‘indini toping.
a) 1
5
_
+
2
5
_
+ 7;
b) 18
_
+ 2 + 38
_
;
d) 10 + 18
_
+ 38
_
; e)
5
1
13
__
+ 4
13
__
+
5
13
__
.
7
8
http://eduportal.uz
46
164.
Yig‘indini toping.
a) 3
1
11
__
+ 2
3
11
__
;
b) 6
5
7
_
+ 9 17
_
;
d) 3 7
13
__
+ 2
5
13
__
.
165.
Yig‘indini toping.
a) 5 13
_
+
2
3
_
;
b)
5
7
_
+ 1
2
7
_
;
d) 5 1
5
_
+ 2 4
5
_
;
e) 1 34
_
+ 5 14
_
.
166.
Yig‘indini toping.
a) 49
_
+
2
9
_
+ 1;
b) 4
11
__
+ 3 + 3
11
__
;
d) 1
5
12
__
+ 1
12
__
+ 1
12
__
;
e) 12 +
5
6
_
+ 16
_
.
167.
Yig‘indini toping.
a) 3
8
17
__
+ 2
13
17
__
;
b) 6
9
14
__
+ 2
13
14
__
;
d) 1
5
7
_
+ 1 67
_
;
e) 5 78
_
+ 3 38
_
.
Namuna:
Yuqorida yechilgan 2-misol.
Uyda bajaramiz
Mashq qilamiz
168.
Yig‘indini toping.
a)
5
4
5
_
+ 2
2
5
_
;
b) 2 7
16
__
+ 2 3
16
__
;
d) 10
5
8
_
+ 1 38
_
;
e)
5
3
5
_
+ 3 4
5
_
.
Namuna:
Yuqorida yechilgan 3-misol.
169.
(Og‘zaki) Ayirmani toping:
a) 3 1
2
_
– 2
;
b)
5
2
3
_
– 4;
d)
5
7
9
_
– 3;
e) 12 14
_
– 9.
170.
(Og‘zaki) Butunni “maydalash” usuli bilan ayirmani hisoblang:
a) 1 – 1
2
_
;
b) 1 –
2
5
_
;
d) 1 – 13
_
;
e) 1 – 3
10
__
.
N
amuna:
Yuqorida yechilgan 5-misol.
171.
Ayirmani toping:
a) 3 – 13
_
;
b) 6 – 37
_
;
d) 4 – 19
_
;
e) 8 –
2
3
_
.
Namuna:
Yuqorida yechilgan 5-misol.
172.
Ayirmani toping:
a)
5 – 2
1
2
_
;
b) 6 – 1 1
2
_
;
d) 6 – 3
2
5
_
;
e) 4 – 2 3
5
_
.
Namuna:
Yuqorida yechilgan 5-misol.
173.
Paroxodning turg‘un suvdagi tezligi 22 km/h.
Daryo oqimining tezligi esa
2
2
3
_
km/h, paroxodning oqimga qarshi tezligini toping.
http://eduportal.uz
47
179.
Ayirmani toping:
a)
5
2
3
_
–
1
3
_
;
b) 7
5
8
_
–
1
8
_
; d) 4
5
7
_
–
3
7
_
;
e) 10 89
_
–
2
9
_
.
180.
Ayirmani toping:
a) 6 34
_
– 2
1
4
_
;
b) 4 78
_
– 2
1
8
_
; d) 3
2
5
_
– 1 1
5
_
;
e) 9
2
11
__
– 8 1
11
__
.
Namuna:
Yuqorida yechilgan 2-misol.
181.
Ayirmani toping:
a) 1
5
9
_
–
8
9
_
;
b) 1 1
12
__
–
5
12
__
;
d) 8 37
_
– 5
5
7
_
;
e) 4 18
_
– 1
5
8
_
.
Namuna:
Yuqorida yechilgan 4-misol.
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