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Misollar yechish:
Tarqatma materiallar:
1. Natural sonlarni qo’shish.
1-variant.
1) 11182 + 415;
2) 746738 + 6579;
3) 316 + 7463;
4) 925 + 698;
5) 5455 + 4545;
6) 68083 + 77877;
7) 237 + 0;
8) 65254 + 2760;
9) 3214 + 4080;
10) 105 + 8998;
11) 93225 + 597975;
12) 624 + 59376.
2- variant.
1) 577 + 33853;
2) 2764 + 393002;
3) 492 + 100;
4) 743 + 7257;
5) 46866 + 4459;
6) 83642 + 3806358;
7) 1463 + 9977;
8) 24374 + 975626;
9) 54676 + 318;
10) 4510 + 1695;
11) 520530 + 25033;
12) 0 + 649.
3-variant.
1) 74524 + 68997;
2) 33000 + 4789;
3) 61479 + 629521;
4) 81228 + 615700;
5) 52204 + 47796;
6) 911 + 89089;
7) 3875 + 67679;
8) 79995 + 7206;
9) 30802 + 0;
10) 566 + 131;
11) 449 + 989804;
12) 736 + 340.
4-variant.
1) 0 + 477;
2) 3719 + 594281;
3) 1444 + 8556;
4) 3759 + 4220;
5) 79557 + 158474;
6) 83305 + 99897;
7) 34923 + 763002;
8) 2944 + 296;
9) 701 + 1699;
10) 671 + 89329;
11) 75812 + 150;
12) 87481 + 35765.
2. Natural sonlarni ayirish.
1-variant.
1) 80000 - 6917;
2) 50000 - 391;
3) 677966 - 6961;
4) 143900 - 6601;
5) 46594 - 45594;
6) 995485 - 995428;
7) 3889 - 0;
8) 2071 - 1375;
9) 23558 - 2589;
10) 10000 - 1330;
11) 759 - 421;
12) 100000 - 884.
2-variant.
1) 87948 - 39948;
2) 832581 - 832188;
3) 80000 - 4224;
4) 888964 - 28854;
5) 368 - 268;
6) 8922 - 4978;
7) 919200 - 7960;
8) 10000 - 393;
9) 10000 - 5482;
10) 3756064 - 27799;
11) 600000 - 2030;
12) 546179 - 0.
3-variant.
1) 496 - 295;
2) 6397389 - 34378;
3) 131 - 0;
4) 10000 - 8360;
5) 2000 - 119;
6) 20549 - 19579;
7) 400000 - 5876;
8) 9980414 - 9980119;
9) 3396942 - 29963;
10) 893900 - 1711;
11) 100000 - 3360;
12) 564723 - 155723.
4-variant.
1) 5000000 - 4051;
2) 736 - 568;
3) 62855 - 33855;
4) 697898 - 567697;
5) 10000 - 1689;
6) 1000000 - 4532;
7) 67103 - 2777;
8) 812649 - 0;
9) 476474 - 41302;
10) 759561 - 759476;
11) 30000 - 9251;
12) 888200 - 7994.
3. Natural sonlarni ko’paytirish.
1-variant.
1) 202 47;
2) 540 1;
3) 700 124;
4) 39 66;
5) 562 100;
6) 361 99;
7) 670 30;
8) 100 1000;
9) 45076 0;
10) 808 102;
11) 6 339;
12) 9676 43.
2-variant.
1) 124 10000;
2) 17 69;
3) 14848 1;
4) 70 940;
5) 2366 63;
6) 502 601;
7) 813 700;
8) 86 344;
9) 31 701;
10) 8 519;
11) 5554 0;
12) 1000 10.
3-variant.
1) 0 396333;
2) 10000 1835;
3) 806 803;
4) 100 1000;
5) 736 600;
6) 1 933;
7) 94 64;
8) 417 17;
9) 64 6169;
10) 561 3;
11) 205 26;
12) 50 390.
4-variant.
1) 77 73;
2) 809 37;
3) 6593 28;
4) 50 950;
5) 0 503912;
6) 73 641;
7) 303 404;
8) 6 175;
9) 1000 10000;
10) 591540 1;
11) 300 423;
12) 100 662932.
4. Natural sonlarni bo’lish.
1-variant.
1) 11889 : 1;
2) 299628 : 4;
3) 12312 : 72;
4) 0 : 866508;
5) 38504 : 8;
6) 216120 : 24;
7) 11249202 : 149;
8) 16500 : 50;
9) 327900 : 10;
10) 16941400 : 200;
11) 151040 : 32;
12) 2799688 : 904.
.2-variant.
1) 1328448 : 51;
2) 2502630 : 30;
3) 655200 : 900;
4) 0 : 681545;
5) 5313600 : 738;
6) 686736 : 342;
7) 241800 : 403;
8) 16640 : 1;
9) 54486 : 6;
10) 33340 : 10;
11) 19072 : 2;
12) 552968 : 818.
3-variant.
1) 308693 : 77;
2) 58852419 : 901;
3) 1587580 : 20;
4) 0 : 9757;
5) 156087 : 3;
6) 816860 : 158;
7) 2279541 : 67;
8) 507332 : 7;
9) 33137 : 1;
10) 11718400 : 800;
11) 3160200 : 458;
12) 260500 : 10.
.4-variant.
1) 77924 : 92;
2) 1473000 : 200;
3) 134067 : 67;
4) 203562 : 6;
5) 0 : 175003;
6) 206750 : 827;
7) 24390 : 30;
8) 16300 : 100;
9) 16311 : 1;
10) 1656750 : 705;
11) 22173905 : 445;
12) 133045 : 5.
Hisoblang:
EKUB(48, 72, 528); 3) EKUB(164, 541, 1271);
EKUK(24, 25, 1200); 4) EKUK(120, 360,420).
Qonuniyatlar asosida bajaring:
7950.
2. 1000124.
3. 39 + 79.
4. 72115.
5. a147b.
6. 8k900m.
7. 4s3x5p.
8. 14713 – 3147.
9. 2916 + 7116.
10. 852 – 552.
11. 6a – 2a.
12. 17m + 13m.
13. 5k – 5a.
14. 14k + 9k – 3k.
15. x + 5x.
16. 72y – 12y – y.
17. y – y.
18. 3x + 3x.
19. 2n + 7n + 3.
20. 6x – 6x + 5.
Kasr sonlarga oid aralash misollarni hisoblang:
Natural va kasr sonlarga oid aralash misollarni hisoblang:
1. 3/41 + 5.
2. 8/21 + 9,9.
3. 4 – 5/81.
4. 5/22 – 4.
5. 14/9 – 9.
6. 1 – 12/99.
7. 13/18 + 3/22.
8. 60/27 – 50/27.
9. 41/45 – 45.
10. 2 – 1/22.
11. 13/100 : 11/200.
12. 660/99 : 33.
13. 2/30,01.
14. 27/38 : 8.
15. 11/32 : 1/2.
16. 530/101.
17. 100035/86.
18. 12/21 : 100.
19. 9/371000.
20. 3/5 : 5/7.
Tenglamalarni yeching:
1. 1 : x = 1.
2. m : 4 = 0.
3. 6 : n = 1.
4. v : 1 = v.
5. m : 27 = 1.
6. 12 : x = 12.
7. x : 0 = 2.
8. 0 : y = 0.
9. 3m = 18.
10. x : 9 = 8.
11. 24x = 92 – 20.
12. 7n – 1 = 13.
13. (13 + 11)x = 48.
14. 3n – 12 = 18.
15. 40 – 4y = 8.
16. 6x – 21 = 9.
17. y(32 – 26) = 60.
18. 36 – 5x = 46 – 20.
19. 64 : 4 : x = 2.
20. 32 – 5x = 21 – 14.
Masalalar:
3 ta yashikda 38 kg anor bor. Birinchi yashikda ikkinchisiga qaraganda 4 kg kam, ammo uchinchisiga qaragancha 2 kg ko’p anor bor. Har bir yashikda necha kilogrammdan anor bor?
To’g’ri to’rtburchakning bo’yi 22 sm. Eni bo’yidan 4 sm qisqa. Perimetri shu to’g’ri to’rtburchakning perimetriga teng bo’lgan kvadratning yuzini toping.
Ketma-ket kelgan uchta natural sonning: 1) yig’indisi 3 ga; 2) ko’paytmasi 6 ga bo’linadi. Shu tasdiqning to’g’riligini ko’rsatuvchi 4 ta misol tuzing.
5. Darsga yakun yasash va baholash – darsning maqsadini yana bir bor eslatish va unga qanchalik erishilganligini o’quvchilar bilan birgalikda aniqlash. O’quvchilarning mavzu bo’yicha savollariga javob berish, ulaming o’zlashtirganlik darajasini aniqiash, darsning asosiy lahzalarini qayd qilish. Darsda faol qatnashgan o’quvchilarni tilga olish va baholash;
6. Uyga vazifa ________________________
Sana: «___» _____________ 201__ y.
Mavzu: KASR ASOSIY XOSSASI
Darsning maqsadi: Kasr asosiy xossasi haqida ma’lumot berish. Misollar bilan tushuntirish.
Darsning ko’rgazmali qurollari: ______________________________
Darsning borishi:
1. Tashkiliy qism – salom-alik qilish, davomatni tekshirish, zarur ko’rgazmali qurol va jihozlarni darsga hozirlash;
2. O’tilganlarni takrorlash va yangi mavzuni boshlashga hozirlik – yangi mavzu bilan bog’liq o’tilgan dars mavzularini takrorlash; o’quvchilarning yangi
mavzuni o’tishdan oldin bu mavzuga oid bilim darajalarini aniqiash, baholash
va yangi materialni o’zlashtirishga tayyorlash; yangi dars maqsadini tushuntirish;
3. Yangi mavzuni yoritish va Yangi mavzuni mustahkamlash:
Yuqoridagi rasmlarni daftaringizga chizib oling. Unda bir xil to’g’ri to’rtburchaklar ikkita, to’rtta va sakkiz ta teng bo’lakka bo’lingan.
Mos ravishda ularning va qismi bo’yalgan.
Rasmlardan to’g’ri to’rtburchaklarning qismi uning qismiga tengligi ravshan: = .
Shuningdek, to’g’ri to’rtburchaklarning qismi uning qismiga tengligi ham ko’rinib turibdi: = . Demak, = = .
va kasrlar ayni bir sonning turlicha yozilishidir.
Agar kasrning surat va maxrajini ayni bir natural songa ko’paytirilsa, kasrning qiymati o’zgarmaydi, avvalgisiga teng kasr hosil bo’ladi.
Bu xossa kasrning asosiy xossasi deyiladi.
Berilgan ixtiyoriy kasrga teng kasrlarni shu xossa yordamida hosil qilish mumkin.
tenglik kasrning asosiy xossasini ifodalaydi.
599. tengliklar nima uchun to’g’riligini tushuntiring:
1) ; 2) ; 3) ; 4) ?
600. kasrning surat va maxraji qanday songa ko’paytirilgan:
1) ; 2) ; 3) ; 4) ?
601. Quyidagi kasrlarni maxraji 24 bo’lgan kasr bilan almashtiring:
; ; ; ; ; ; ; .
602. Tomonlari 6 sm va 8 sm bo’lgan to’g’ri to’rtburchakni 6 ta teng bo’lakka bo’ling. Uning qismini bo’yang. Chizmadan foydalanib, ekanini ko’rsating.
5. Darsga yakun yasash va baholash – darsning maqsadini yana bir bor eslatish va unga qanchalik erishilganligini o’quvchilar bilan birgalikda aniqlash. O’quvchilarning mavzu bo’yicha savollariga javob berish, ulaming o’zlashtirganlik darajasini aniqiash, darsning asosiy lahzalarini qayd qilish. Darsda faol qatnashgan o’quvchilarni tilga olish va baholash;
6. Uyga vazifa ________________________
Sana: «___» _____________ 201__ y.
Mavzu: KASRLARNI QISQARTIRISH
Darsning maqsadi: Kasrlarni qisqartirish haqida ma’lumot berish. Misollar bilan tushuntirish.
Darsning ko’rgazmali qurollari: ______________________________
Darsning borishi:
1. Tashkiliy qism – salom-alik qilish, davomatni tekshirish, zarur ko’rgazmali qurol va jihozlarni darsga hozirlash;
2. O’tilganlarni takrorlash va yangi mavzuni boshlashga hozirlik – yangi mavzu bilan bog’liq o’tilgan dars mavzularini takrorlash; o’quvchilarning yangi
mavzuni o’tishdan oldin bu mavzuga oid bilim darajalarini aniqiash, baholash
va yangi materialni o’zlashtirishga tayyorlash; yangi dars maqsadini tushuntirish;
3. Yangi mavzuni yoritish va Yangi mavzuni mustahkamlash:
kasr uchun kasrning asosiy xossasiga ko’ra tengliklarni yozish mumkin. Bu tengliklarni quyidagicha yozib olaylik:
Demak, va kasrlarni ularga teng, lekin surat va maxraji kichikroq bo’lgan kasr bilan almashtirish mumkin ekan.
kasrning surat va maxraji umumiy ko’paytuvchi 8 ga ega: = shunga o’xshash:
tenglikni hosil qilish uchun kasrning surat va maxrajini umumiy ko’paytuvchi 8 ga bo’lish kerak. Buni kasrni qisqartirish deyiladi.
Surat va maxraji o’zaro tub son bo’lgan kasr qisqarmas kasr deyiladi.
Berilgan kasrdan qisqarmas kasrni hosil qilish uchun:
1-qadam. Kasrning surat va maxrajining EKUB topiladi.
2-qadam. Kasrning surat va maxraji shu EKUB ga bo’linadi.
612. Kasrlarni qisqartiring:
1) ; 2) ; 3) ; 4) ; 5) .
613. , , , , , , , kasrlarning surat va maxrajini 6 ga bo’ling. Hosil bo’lgan mos tengliklarni yozing.
614. Har bir kasrning surat va maxrajini ularning EKUB ga bo’ling:
, , , , , , , .
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