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Sagot :
Sure, I can provide a detailed, step-by-step solution to each problem following the order of operations.
Lets solve each step by step:
### Problem 1:
[tex]\[ (2 \times 13) + (4 \times 6) + (3 \times (4 + 2)) \][/tex]
1. Start with the operations inside the parentheses:
- [tex]\( 2 \times 13 = 26 \)[/tex]
- [tex]\( 4 \times 6 = 24 \)[/tex]
- [tex]\( 4 + 2 = 6 \)[/tex]
- [tex]\( 3 \times 6 = 18 \)[/tex]
2. Then perform the additions:
- [tex]\( 26 + 24 + 18 = 68 \)[/tex]
So, the answer is [tex]\( 68 \)[/tex].
### Problem 2:
[tex]\[ 8^2 + 760 - 200 \][/tex]
1. Start with the exponentiation:
- [tex]\( 8^2 = 64 \)[/tex]
2. Then perform the additions and subtractions:
- [tex]\( 64 + 760 = 824 \)[/tex]
- [tex]\( 824 - 200 = 624 \)[/tex]
So, the answer is [tex]\( 624 \)[/tex].
### Problem 3:
[tex]\[ 3 - 7 \times 12 + 16 \div 4 \][/tex]
1. Start with the multiplication and division:
- [tex]\( 7 \times 12 = 84 \)[/tex]
- [tex]\( 16 \div 4 = 4 \)[/tex]
2. Then perform the additions and subtractions:
- [tex]\( 3 - 84 = -81 \)[/tex]
- [tex]\( -81 + 4 = -77 \)[/tex]
So, the answer is [tex]\( -77 \)[/tex].
### Problem 4:
[tex]\[ (-2,760 + (214 \times 2) + (156 \times 8)) + 4 \][/tex]
1. Start with the multiplications inside the parentheses:
- [tex]\( 214 \times 2 = 428 \)[/tex]
- [tex]\( 156 \times 8 = 1,248 \)[/tex]
2. Then perform the additions and subtractions inside the parentheses:
- [tex]\( -2,760 + 428 = -2,332 \)[/tex]
- [tex]\( -2,332 + 1,248 = -1,084 \)[/tex]
3. Finally, add 4:
- [tex]\( -1,084 + 4 = -1,080 \)[/tex]
So, the answer is [tex]\( -1,080 \)[/tex].
### Problem 5:
[tex]\[ 360 + 45 - 7 + 6^2 - -73 \][/tex]
1. Start with the exponentiation:
- [tex]\( 6^2 = 36 \)[/tex]
2. Then perform the additions and subtractions:
- [tex]\( 360 + 45 = 405 \)[/tex]
- [tex]\( 405 - 7 = 398 \)[/tex]
- [tex]\( 398 + 36 = 434 \)[/tex]
- [tex]\( 434 - (-73) = 434 + 73 = 507 \)[/tex]
So, the answer is [tex]\( 507 \)[/tex].
Bringing all the answers together:
1. [tex]\( (2 \times 13) + (4 \times 6) + (3 \times (4 + 2)) = 68 \)[/tex]
2. [tex]\( 8^2 + 760 - 200 = 624 \)[/tex]
3. [tex]\( 3 - 7 \times 12 + 16 \div 4 = -77 \)[/tex]
4. [tex]\( (-2,760 + (214 \times 2) + (156 \times 8)) + 4 = -1,080 \)[/tex]
5. [tex]\( 360 + 45 - 7 + 6^2 - -73 = 507 \)[/tex]
So, the final answers in sequence are:
68, 624, -77, -1080, 507
Lets solve each step by step:
### Problem 1:
[tex]\[ (2 \times 13) + (4 \times 6) + (3 \times (4 + 2)) \][/tex]
1. Start with the operations inside the parentheses:
- [tex]\( 2 \times 13 = 26 \)[/tex]
- [tex]\( 4 \times 6 = 24 \)[/tex]
- [tex]\( 4 + 2 = 6 \)[/tex]
- [tex]\( 3 \times 6 = 18 \)[/tex]
2. Then perform the additions:
- [tex]\( 26 + 24 + 18 = 68 \)[/tex]
So, the answer is [tex]\( 68 \)[/tex].
### Problem 2:
[tex]\[ 8^2 + 760 - 200 \][/tex]
1. Start with the exponentiation:
- [tex]\( 8^2 = 64 \)[/tex]
2. Then perform the additions and subtractions:
- [tex]\( 64 + 760 = 824 \)[/tex]
- [tex]\( 824 - 200 = 624 \)[/tex]
So, the answer is [tex]\( 624 \)[/tex].
### Problem 3:
[tex]\[ 3 - 7 \times 12 + 16 \div 4 \][/tex]
1. Start with the multiplication and division:
- [tex]\( 7 \times 12 = 84 \)[/tex]
- [tex]\( 16 \div 4 = 4 \)[/tex]
2. Then perform the additions and subtractions:
- [tex]\( 3 - 84 = -81 \)[/tex]
- [tex]\( -81 + 4 = -77 \)[/tex]
So, the answer is [tex]\( -77 \)[/tex].
### Problem 4:
[tex]\[ (-2,760 + (214 \times 2) + (156 \times 8)) + 4 \][/tex]
1. Start with the multiplications inside the parentheses:
- [tex]\( 214 \times 2 = 428 \)[/tex]
- [tex]\( 156 \times 8 = 1,248 \)[/tex]
2. Then perform the additions and subtractions inside the parentheses:
- [tex]\( -2,760 + 428 = -2,332 \)[/tex]
- [tex]\( -2,332 + 1,248 = -1,084 \)[/tex]
3. Finally, add 4:
- [tex]\( -1,084 + 4 = -1,080 \)[/tex]
So, the answer is [tex]\( -1,080 \)[/tex].
### Problem 5:
[tex]\[ 360 + 45 - 7 + 6^2 - -73 \][/tex]
1. Start with the exponentiation:
- [tex]\( 6^2 = 36 \)[/tex]
2. Then perform the additions and subtractions:
- [tex]\( 360 + 45 = 405 \)[/tex]
- [tex]\( 405 - 7 = 398 \)[/tex]
- [tex]\( 398 + 36 = 434 \)[/tex]
- [tex]\( 434 - (-73) = 434 + 73 = 507 \)[/tex]
So, the answer is [tex]\( 507 \)[/tex].
Bringing all the answers together:
1. [tex]\( (2 \times 13) + (4 \times 6) + (3 \times (4 + 2)) = 68 \)[/tex]
2. [tex]\( 8^2 + 760 - 200 = 624 \)[/tex]
3. [tex]\( 3 - 7 \times 12 + 16 \div 4 = -77 \)[/tex]
4. [tex]\( (-2,760 + (214 \times 2) + (156 \times 8)) + 4 = -1,080 \)[/tex]
5. [tex]\( 360 + 45 - 7 + 6^2 - -73 = 507 \)[/tex]
So, the final answers in sequence are:
68, 624, -77, -1080, 507
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