IDNLearn.com offers a user-friendly platform for finding and sharing answers. Discover in-depth answers to your questions from our community of experienced professionals.
Sagot :
Sure, let's simplify each expression step-by-step.
### 1. Simplify [tex]\(20 - \{18 \div (7-2+1)\}\)[/tex]
1. Simplify inside the parentheses first:
[tex]\[ 7 - 2 + 1 = 6 \][/tex]
2. Perform the division:
[tex]\[ 18 \div 6 = 3 \][/tex]
3. Subtract from 20:
[tex]\[ 20 - 3 = 17.0 \][/tex]
So, the result for the first expression is [tex]\(17.0\)[/tex].
### 2. Simplify [tex]\(23 - [6 + \{8 - (9 - 6)\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 9 - 6 = 3 \][/tex]
2. Subtract:
[tex]\[ 8 - 3 = 5 \][/tex]
3. Add:
[tex]\[ 6 + 5 = 11 \][/tex]
4. Subtract from 23:
[tex]\[ 23 - 11 = 12 \][/tex]
So, the result for the second expression is [tex]\(12\)[/tex].
### 3. Simplify [tex]\(2[19 - \{7 + (12 \div 4)\}]\)[/tex]
1. Perform the division inside the parentheses:
[tex]\[ 12 \div 4 = 3 \][/tex]
2. Add:
[tex]\[ 7 + 3 = 10 \][/tex]
3. Subtract from 19:
[tex]\[ 19 - 10 = 9 \][/tex]
4. Multiply by 2:
[tex]\[ 2 \times 9 = 18.0 \][/tex]
So, the result for the third expression is [tex]\(18.0\)[/tex].
### 4. Simplify [tex]\(40 - [12 + \{16 - (12 \div 3)\}]\)[/tex]
1. Perform the division inside the parentheses:
[tex]\[ 12 \div 3 = 4 \][/tex]
2. Subtract:
[tex]\[ 16 - 4 = 12 \][/tex]
3. Add:
[tex]\[ 12 + 12 = 24 \][/tex]
4. Subtract from 40:
[tex]\[ 40 - 24 = 16.0 \][/tex]
So, the result for the fourth expression is [tex]\(16.0\)[/tex].
### 5. Simplify [tex]\(\{[(30 - (9 - 6)) \div 3] \times 6 + 6\}\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 9 - 6 = 3 \][/tex]
2. Subtract:
[tex]\[ 30 - 3 = 27 \][/tex]
3. Divide by 3:
[tex]\[ 27 \div 3 = 9 \][/tex]
4. Multiply by 6:
[tex]\[ 9 \times 6 = 54 \][/tex]
5. Add:
[tex]\[ 54 + 6 = 60.0 \][/tex]
So, the result for the fifth expression is [tex]\(60.0\)[/tex].
### 6. Simplify [tex]\(12 - [6 \div 3 + \{8 \div 2(8 - 6)\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 8 - 6 = 2 \][/tex]
2. Multiply inside the braces:
[tex]\[ 2 \times 2 = 4 \][/tex]
3. Divide:
[tex]\[ 8 \div 4 = 2 \][/tex]
4. Divide 6 by 3:
[tex]\[ 6 \div 3 = 2 \][/tex]
5. Add:
[tex]\[ 2 + 2 = 4 \][/tex]
6. Subtract from 12:
[tex]\[ 12 - 4 = 8.0 \][/tex]
So, the result for the sixth expression is [tex]\(8.0\)[/tex].
### 7. Simplify [tex]\([40 \div \{19 - 3(6 - (4 - 1))\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 4 - 1 = 3 \][/tex]
2. Multiply inside the parentheses:
[tex]\[ 3 \times 3 = 9 \][/tex]
3. Subtract from 19:
[tex]\[ 19 - 9 = 10 \][/tex]
4. Divide 40 by 10:
[tex]\[ 40 \div 10 = 4.0 \][/tex]
So, the result for the seventh expression is [tex]\(4.0\)[/tex].
### 8. Simplify [tex]\([105 \div \{23 + 2(9 - (5 - 2))\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 5 - 2 = 3 \][/tex]
2. Multiply inside the parentheses:
[tex]\[ 2 \times 3 = 6 \][/tex]
3. Add:
[tex]\[ 23 + 6 = 29 \][/tex]
4. Divide 105 by 29:
[tex]\[ 105 \div 29 \approx 3.0 \][/tex]
So, the result for the eighth expression is [tex]\(3.0\)[/tex].
Thus, the simplified results are:
1. [tex]\(17.0\)[/tex]
2. [tex]\(12\)[/tex]
3. [tex]\(18.0\)[/tex]
4. [tex]\(16.0\)[/tex]
5. [tex]\(60.0\)[/tex]
6. [tex]\(8.0\)[/tex]
7. [tex]\(4.0\)[/tex]
8. [tex]\(3.0\)[/tex]
### 1. Simplify [tex]\(20 - \{18 \div (7-2+1)\}\)[/tex]
1. Simplify inside the parentheses first:
[tex]\[ 7 - 2 + 1 = 6 \][/tex]
2. Perform the division:
[tex]\[ 18 \div 6 = 3 \][/tex]
3. Subtract from 20:
[tex]\[ 20 - 3 = 17.0 \][/tex]
So, the result for the first expression is [tex]\(17.0\)[/tex].
### 2. Simplify [tex]\(23 - [6 + \{8 - (9 - 6)\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 9 - 6 = 3 \][/tex]
2. Subtract:
[tex]\[ 8 - 3 = 5 \][/tex]
3. Add:
[tex]\[ 6 + 5 = 11 \][/tex]
4. Subtract from 23:
[tex]\[ 23 - 11 = 12 \][/tex]
So, the result for the second expression is [tex]\(12\)[/tex].
### 3. Simplify [tex]\(2[19 - \{7 + (12 \div 4)\}]\)[/tex]
1. Perform the division inside the parentheses:
[tex]\[ 12 \div 4 = 3 \][/tex]
2. Add:
[tex]\[ 7 + 3 = 10 \][/tex]
3. Subtract from 19:
[tex]\[ 19 - 10 = 9 \][/tex]
4. Multiply by 2:
[tex]\[ 2 \times 9 = 18.0 \][/tex]
So, the result for the third expression is [tex]\(18.0\)[/tex].
### 4. Simplify [tex]\(40 - [12 + \{16 - (12 \div 3)\}]\)[/tex]
1. Perform the division inside the parentheses:
[tex]\[ 12 \div 3 = 4 \][/tex]
2. Subtract:
[tex]\[ 16 - 4 = 12 \][/tex]
3. Add:
[tex]\[ 12 + 12 = 24 \][/tex]
4. Subtract from 40:
[tex]\[ 40 - 24 = 16.0 \][/tex]
So, the result for the fourth expression is [tex]\(16.0\)[/tex].
### 5. Simplify [tex]\(\{[(30 - (9 - 6)) \div 3] \times 6 + 6\}\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 9 - 6 = 3 \][/tex]
2. Subtract:
[tex]\[ 30 - 3 = 27 \][/tex]
3. Divide by 3:
[tex]\[ 27 \div 3 = 9 \][/tex]
4. Multiply by 6:
[tex]\[ 9 \times 6 = 54 \][/tex]
5. Add:
[tex]\[ 54 + 6 = 60.0 \][/tex]
So, the result for the fifth expression is [tex]\(60.0\)[/tex].
### 6. Simplify [tex]\(12 - [6 \div 3 + \{8 \div 2(8 - 6)\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 8 - 6 = 2 \][/tex]
2. Multiply inside the braces:
[tex]\[ 2 \times 2 = 4 \][/tex]
3. Divide:
[tex]\[ 8 \div 4 = 2 \][/tex]
4. Divide 6 by 3:
[tex]\[ 6 \div 3 = 2 \][/tex]
5. Add:
[tex]\[ 2 + 2 = 4 \][/tex]
6. Subtract from 12:
[tex]\[ 12 - 4 = 8.0 \][/tex]
So, the result for the sixth expression is [tex]\(8.0\)[/tex].
### 7. Simplify [tex]\([40 \div \{19 - 3(6 - (4 - 1))\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 4 - 1 = 3 \][/tex]
2. Multiply inside the parentheses:
[tex]\[ 3 \times 3 = 9 \][/tex]
3. Subtract from 19:
[tex]\[ 19 - 9 = 10 \][/tex]
4. Divide 40 by 10:
[tex]\[ 40 \div 10 = 4.0 \][/tex]
So, the result for the seventh expression is [tex]\(4.0\)[/tex].
### 8. Simplify [tex]\([105 \div \{23 + 2(9 - (5 - 2))\}]\)[/tex]
1. Simplify inside the innermost parentheses:
[tex]\[ 5 - 2 = 3 \][/tex]
2. Multiply inside the parentheses:
[tex]\[ 2 \times 3 = 6 \][/tex]
3. Add:
[tex]\[ 23 + 6 = 29 \][/tex]
4. Divide 105 by 29:
[tex]\[ 105 \div 29 \approx 3.0 \][/tex]
So, the result for the eighth expression is [tex]\(3.0\)[/tex].
Thus, the simplified results are:
1. [tex]\(17.0\)[/tex]
2. [tex]\(12\)[/tex]
3. [tex]\(18.0\)[/tex]
4. [tex]\(16.0\)[/tex]
5. [tex]\(60.0\)[/tex]
6. [tex]\(8.0\)[/tex]
7. [tex]\(4.0\)[/tex]
8. [tex]\(3.0\)[/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.
