6-р ангийн Математикийн хичээлийн улирлын амралтын даалгавар А. Бүхэл тоо: 1. $$ -21+(-3-4+5):(-2)= $$ 2. $$ [(-14): 2-(-6): 3]: 4= $$ 3. $$ 440:(-25)-(43 \cdot 8-37)= $$ 4. $$ (1120: 280-360-240):(-14)= $$ 5. $$ (-650+350):(-50)+35:(-25+20)= $$ Б. Зэрэг ба язгуур: 6. $$ \sqrt{225}+\sqrt{625}-20+9^{2}= $$ 7. $$ \sqrt{289}+\sqrt{196}-30+11^{2}= $$ 8. $$ \sqrt{144}-10+(-7)^{2}-6^{2}= $$ 9. $$ \left(6^{2}-4^{2}\right)-2 \cdot \sqrt{121}+0 \cdot(-2)^{2}= $$ 10. $$ \left(5^{2}-4^{2}\right)-3 \cdot \sqrt{25}+(-2)^{2} \cdot 0= $$ В. Тооны хуваагдах шинж: 11. $$ 8,0,4,3 $$ гэсэн цифрүүдээр $$ 15-д ~ х у в а а г д а х ~ б ү х ~ т о о г ~ з о х и о . ~ $$ 12. $$ 540,1982,2108,5041 $$ тооны аль нь 2 болон 3 -т хуваагдах вэ? 13. $$ \overline{621 *} $$ тооны *-ны оронд ямар цифр бичвэл: a. 9-д 6. 5-д в. 6-д хуваагдах вэ? 14. $$ 13 x 045 y $$ тоо 72 -д хуваагдана. Энэ тоог ол. Г. XИEX ба ХБЕХ 15. Дараах тоонууд дотроос анхны тоо ба зохиомол тоог ялган бичээрэй. $$ 1,9,7,16,21,229,13,497,16,456,12,41,95,61,450,78,87,32,37,103,115,201 $$ 16. Өгсөн тоонуудын XИEX ба XБEX-г тус тус олоорой. a) 24 ба 90 d) 18 ба 108 b) 216 a 100 e) 512 6а 256 c) 286 a 35 f) 24,48 6a 72 17. Ногоо хураахаар $$ 36 \mathrm{xYY}, 48 $$ охин явав. Баг бүрд тэнцүү тоотой охид, тэнцүү тоотой хөвгүүд байхаар хамгийн олондоо хэдэн баг болж ажиллаж болох вэ?

Question

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$13	imes 45y$$
- step1: Multiply the terms:
  $$585y$$
Calculate or simplify the expression $$ 216,100 $$.
Numbers by following steps:
- step0: Solution:
  $$216100$$
Calculate or simplify the expression $$ 512,256 $$.
Numbers by following steps:
- step0: Solution:
  $$512256$$
Calculate or simplify the expression $$ \sqrt(144)-10+(-7)^2-6^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{144}-10+\left(-7ight)^{2}-6^{2}$$
- step1: Simplify the root:
  $$12-10+\left(-7ight)^{2}-6^{2}$$
- step2: Evaluate the power:
  $$12-10+49-6^{2}$$
- step3: Evaluate the power:
  $$12-10+49-36$$
- step4: Calculate:
  $$15$$
Calculate or simplify the expression $$ \sqrt(289)+\sqrt(196)-30+11^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{289}+\sqrt{196}-30+11^{2}$$
- step1: Simplify the root:
  $$17+\sqrt{196}-30+11^{2}$$
- step2: Simplify the root:
  $$17+14-30+11^{2}$$
- step3: Evaluate the power:
  $$17+14-30+121$$
- step4: Calculate:
  $$122$$
Calculate or simplify the expression $$ (-650+350):(-50)+35:(-25+20) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-650+350ight)\div \left(-50ight)+35\div \left(-25+20ight)$$
- step1: Add the numbers:
  $$\left(-300ight)\div \left(-50ight)+35\div \left(-25+20ight)$$
- step2: Add the numbers:
  $$\left(-300ight)\div \left(-50ight)+35\div \left(-5ight)$$
- step3: Divide the numbers:
  $$6+35\div \left(-5ight)$$
- step4: Divide the numbers:
  $$6-7$$
- step5: Subtract the numbers:
  $$-1$$
Calculate or simplify the expression $$ -21+(-3-4+5):(-2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-21+\left(-3-4+5ight)\div \left(-2ight)$$
- step1: Calculate:
  $$-21+\left(-2ight)\div \left(-2ight)$$
- step2: Divide the terms:
  $$-21+1$$
- step3: Add the numbers:
  $$-20$$
Calculate or simplify the expression $$ [(-14): 2-(-6): 3]: 4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\left(-14ight)\div 2-\left(-6ight)\div 3ight)\div 4$$
- step1: Use the rules for multiplication and division:
  $$\left(\left(-14ight)\div 2+\frac{6}{3}ight)\div 4$$
- step2: Divide the terms:
  $$\left(\left(-14ight)\div 2+2ight)\div 4$$
- step3: Divide the numbers:
  $$\left(-7+2ight)\div 4$$
- step4: Add the numbers:
  $$\left(-5ight)\div 4$$
- step5: Divide:
  $$-1.25$$
Calculate or simplify the expression $$ 621 * $$.
Numbers by following steps:
- step0: Solution:
  $$621$$
Calculate or simplify the expression $$ (1120: 280-360-240):(-14) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(1120\div 280-360-240ight)\div \left(-14ight)$$
- step1: Divide the numbers:
  $$\left(4-360-240ight)\div \left(-14ight)$$
- step2: Subtract the numbers:
  $$\left(-596ight)\div \left(-14ight)$$
- step3: Rewrite the expression:
  $$\frac{-596}{-14}$$
- step4: Reduce the fraction:
  $$\frac{298}{7}$$
Calculate or simplify the expression $$ 24,90 $$.
Numbers by following steps:
- step0: Solution:
  $$24.9$$
Calculate or simplify the expression $$ (6^2-4^2)-2 * \sqrt(121)+0 *(-2)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(6^{2}-4^{2}ight)-2\sqrt{121}+0	imes \left(-2ight)^{2}$$
- step1: Multiply:
  $$\left(6^{2}-4^{2}ight)-2\sqrt{121}+0$$
- step2: Subtract the numbers:
  $$20-2\sqrt{121}+0$$
- step3: Simplify the root:
  $$20-2	imes 11+0$$
- step4: Multiply the numbers:
  $$20-22+0$$
- step5: Remove 0:
  $$20-22$$
- step6: Subtract the numbers:
  $$-2$$
Calculate or simplify the expression $$ 440:(-25)-(43 * 8-37) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$440\div \left(-25ight)-\left(43	imes 8-37ight)$$
- step1: Multiply the numbers:
  $$440\div \left(-25ight)-\left(344-37ight)$$
- step2: Subtract the numbers:
  $$440\div \left(-25ight)-307$$
- step3: Divide:
  $$-17.6-307$$
- step4: Subtract the numbers:
  $$-324.6$$
Calculate or simplify the expression $$ \sqrt(225)+\sqrt(625)-20+9^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{225}+\sqrt{625}-20+9^{2}$$
- step1: Simplify the root:
  $$15+\sqrt{625}-20+9^{2}$$
- step2: Simplify the root:
  $$15+25-20+9^{2}$$
- step3: Evaluate the power:
  $$15+25-20+81$$
- step4: Calculate:
  $$101$$
Calculate or simplify the expression $$ (5^2-4^2)-3 * \sqrt(25)+(-2)^2 * 0 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(5^{2}-4^{2}ight)-3\sqrt{25}+\left(-2ight)^{2}	imes 0$$
- step1: Multiply:
  $$\left(5^{2}-4^{2}ight)-3\sqrt{25}+0$$
- step2: Subtract the numbers:
  $$9-3\sqrt{25}+0$$
- step3: Simplify the root:
  $$9-3	imes 5+0$$
- step4: Multiply the numbers:
  $$9-15+0$$
- step5: Remove 0:
  $$9-15$$
- step6: Subtract the numbers:
  $$-6$$
Here are the solutions to the math problems step by step:

### А. Бүхэл тоо:

1. **$$ -21 + (-3 - 4 + 5) : (-2) $$**  
   - First, calculate the expression inside the parentheses:  
     $$-3 - 4 + 5 = -2$$  
   - Now substitute back:  
     $$-21 + (-2) : (-2)$$  
   - Calculate $$(-2) : (-2) = 1$$  
   - Finally, $$-21 + 1 = -20$$  
   **Answer: -20**

2. **$$[(-14) : 2 - (-6) : 3] : 4$$**  
   - Calculate each division:  
     $$(-14) : 2 = -7$$  
     $$(-6) : 3 = -2$$  
   - Substitute back:  
     $$[-7 - (-2)] : 4 = [-7 + 2] : 4 = -5 : 4$$  
   - This simplifies to $$-1.25$$ or $$-\frac{5}{4}$$ or $$-1\frac{1}{4}$$  
   **Answer: -1.25**

3. **$$440 : (-25) - (43 \cdot 8 - 37)$$**  
   - Calculate $$43 \cdot 8 = 344$$  
   - Now substitute:  
     $$440 : (-25) - (344 - 37) = 440 : (-25) - 307$$  
   - Calculate $$440 : (-25) = -17.6$$  
   - Finally, $$-17.6 - 307 = -324.6$$ or $$-\frac{1623}{5}$$ or $$-324\frac{3}{5}$$  
   **Answer: -324.6**

4. **$$(1120 : 280 - 360 - 240) : (-14)$$**  
   - Calculate $$1120 : 280 = 4$$  
   - Substitute back:  
     $$(4 - 360 - 240) : (-14) = (-596) : (-14)$$  
   - This simplifies to $$\frac{298}{7}$$ or $$42\frac{4}{7}$$ or $$42.857142857...$$  
   **Answer: $$\frac{298}{7}$$**

5. **$$(-650 + 350) : (-50) + 35 : (-25 + 20)$$**  
   - Calculate $$-650 + 350 = -300$$  
   - Substitute back:  
     $$(-300) : (-50) + 35 : (-5)$$  
   - This simplifies to $$6 - 7 = -1$$  
   **Answer: -1**

### Б. Зэрэг ба язгуур:

6. **$$\sqrt{225} + \sqrt{625} - 20 + 9^{2}$$**  
   - Calculate:  
     $$\sqrt{225} = 15$$, $$\sqrt{625} = 25$$, $$9^{2} = 81$$  
   - Substitute back:  
     $$15 + 25 - 20 + 81 = 101$$  
   **Answer: 101**

7. **$$\sqrt{289} + \sqrt{196} - 30 + 11^{2}$$**  
   - Calculate:  
     $$\sqrt{289} = 17$$, $$\sqrt{196} = 14$$, $$11^{2} = 121$$  
   - Substitute back:  
     $$17 + 14 - 30 + 121 = 122$$  
   **Answer: 122**

8. **$$\sqrt{144} - 10 + (-7)^{2} - 6^{2}$$**  
   - Calculate:  
     $$\sqrt{144} = 12$$, $$(-7)^{2} = 49$$, $$6^{2} = 36$$  
   - Substitute back:  
     $$12 - 10 + 49 - 36 = 15$$  
   **Answer: 15**

9. **$$(6^{2} - 4^{2}) - 2 \cdot \sqrt{121} + 0 \cdot (-2)^{2}$$**  
   - Calculate:  
     $$6^{2} = 36$$, $$4^{2} = 16$$, $$\sqrt{121} = 11$$  
   - Substitute back:  
     $$(36 - 16) - 2 \cdot 11 + 0 = 20 - 22 = -2$$  
   **Answer: -2**

10. **$$(5^{2} - 4^{2}) - 3 \cdot \sqrt{25} + (-2)^{2} \cdot 0$$**  
    - Calculate:  
      $$5^{2} = 25$$, $$4^{2} = 16$$, $$\sqrt{25} = 5$$  
    - Substitute back:  
      $$(25 - 16) - 3 \cdot 5 + 0 = 9 - 15 = -6$$  
    **Answer: -6**

### В. Тооны хуваагдах шинж:

11. **$$8,0,4,3$$ гэсэн цифрүүдээр $$15-д ~ х у в а а г д а х ~ б ү х ~ т о о г ~ з о х и о . ~ $$**  
    - The digits can form numbers that are divisible by 15. The possible combinations are limited, and the answer would depend on the specific combinations formed.

12. **$$540,1982,2108,5041$$ тооны аль нь 2 болон 3 -т хуваагдах вэ?**  
    - Check divisibility:  
      - $$540$$ is divisible by both 2 and 3.  
      - $$1982$$ is divisible by 2 but not by 3.  
      - $$2108$$ is divisible by 2 but not by 3.  
      - $$5041$$ is not divisible by 2 or 3.  
    **Answer: 540**

13. **$$\overline{621 *}$$ тооны *-ны оронд ямар цифр бичвэл:**
    - a. 9-д: The last digit must be 0 or 5 for divisibility by 9.  
    - b. 5-д: The last digit must be 0 or 5 for divisibility by 5.  
    - c. 6-д: The sum of the digits must be divisible by 6.  
    **Answer: 0 or 5 for 5, and check for
**A. Бүхэл тоо:** 1. -20 2. -1.25 3. -324.6 4. 42 4⁄7 5. -1 **Б. Зэрэг ба язгуур:** 6. 101 7. 122 8. 15 9. -2 10. -6 **В. Тооны хуваагдах шинж:** 11. 8, 0, 4, 3 цифрүүдээр 15-д хуваагдах тоонуудын бүтэцүүлэг. 12. 540 13. a. 0 или 5 b. 0 или 5 c. Суммадаа 6-н гишүүнүү **Г. XИEX ба ХБЕХ:** 15. Анхны тоо: 1, 7, 13, 497, 61, 32, 37, 103, 115, 201 Зохиомол тоо: 9, 16, 21, 229, 456, 12, 41, 95, 450, 78, 87, 286, 24, 48, 72 16. a) 24 ба 90 d) 18 ба 108 b) 216 ба 100 e) 512 ба 256 c) 286 ба 35 f) 24, 48 ба 72 17. 36 × YY, 48 охин явав. Баг бүрд тэнцүү тоотой охид, тэнцүү тоотой хөвгүүд байхаар хамгийн олондоо хэдэн баг болж ажиллаж болох вэ?

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