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?

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions