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Exercise 16

Simplify:

1. [tex]20-\{18 \div(7-2+1)\}[/tex]

2. [tex]23-[6+\{8-(9-6)\}][/tex]

3. [tex]2[19-\{7+(12 \div 4)\}][/tex]

4. [tex]40-[12+\{16-(12 \div 3)\}][/tex]

5. [tex][\{(30-\overline{9-6}) \div 3\} \times 6+6][/tex]

6. [tex]12-[6 \div 3+\{8 \div 2(8-6)\}][/tex]

7. [tex][40 \div\{19-3(6-\overline{4-1})\}][/tex]

8. [tex][105 \div\{23+2(9-\overline{5-2})\}][/tex]



Answer :

GinnyAnswer
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]

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