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Exercise 15

Simplify:

1. [tex]\(12 + \frac{9}{3}\)[/tex]
2. [tex]\(16 \times \frac{8}{4}\)[/tex]
3. [tex]\(23 - 8 \times 2\)[/tex]
4. [tex]\(\frac{32}{8} + 4 \times 6 - 2\)[/tex]
5. [tex]\(100 - \frac{72}{8} + 4 \times 3\)[/tex]
6. [tex]\(30 + \frac{75}{15} \times 4 - 18\)[/tex]
7. [tex]\(8 \times 6 + \frac{24}{6} - 18\)[/tex]
8. [tex]\(56 - \frac{36}{4} \times 2 + 7\)[/tex]
9. [tex]\(\frac{56}{14} \times 3 - \frac{10}{5} + 1\)[/tex]
10. [tex]\(198 - \frac{42 \times 15}{5} + 6\)[/tex]
11. [tex]\(105 \times \frac{14}{7} + 6 - 1\)[/tex]
12. [tex]\(17 + \frac{34}{17} \times 5 - 20\)[/tex]

Use of Brackets



Answer :

GinnyAnswer
Let's go through each expression step-by-step, ensuring we simplify properly according to the order of operations (PEMDAS/BODMAS rules: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Simplification Steps

1. Simplify [tex]\( 12 + 9 \div 3 \)[/tex]
- First, perform the division: [tex]\( 9 \div 3 = 3 \)[/tex]
- Then, add: [tex]\( 12 + 3 = 15 \)[/tex]

Result: [tex]\( 15.0 \)[/tex] (since division results in a float)

2. Simplify [tex]\( 16 \times 8 \div 4 \)[/tex]
- Perform multiplication first: [tex]\( 16 \times 8 = 128 \)[/tex]
- Then, division: [tex]\( 128 \div 4 = 32 \)[/tex]

Result: [tex]\( 32.0 \)[/tex]

3. Simplify [tex]\( 23 - 8 \times 2 \)[/tex]
- Perform multiplication first: [tex]\( 8 \times 2 = 16 \)[/tex]
- Then, subtraction: [tex]\( 23 - 16 = 7 \)[/tex]

Result: [tex]\( 7 \)[/tex]

4. Simplify [tex]\( 32 \div 8 + 4 \times 6 - 2 \)[/tex]
- Perform division first: [tex]\( 32 \div 8 = 4 \)[/tex]
- Then, multiplication: [tex]\( 4 \times 6 = 24 \)[/tex]
- Then, the addition: [tex]\( 4 + 24 = 28 \)[/tex]
- Finally, subtraction: [tex]\( 28 - 2 = 26 \)[/tex]

Result: [tex]\( 26.0 \)[/tex]

5. Simplify [tex]\( 100 - 72 \div 8 + 4 \times 3 \)[/tex]
- Perform division first: [tex]\( 72 \div 8 = 9 \)[/tex]
- Then, multiplication: [tex]\( 4 \times 3 = 12 \)[/tex]
- Then, subtraction: [tex]\( 100 - 9 = 91 \)[/tex]
- Finally, addition: [tex]\( 91 + 12 = 103 \)[/tex]

Result: [tex]\( 103.0 \)[/tex]

6. Simplify [tex]\( 30 + 75 \div 15 \times 4 - 18 \)[/tex]
- Perform division first: [tex]\( 75 \div 15 = 5 \)[/tex]
- Then, multiplication: [tex]\( 5 \times 4 = 20 \)[/tex]
- Then, addition: [tex]\( 30 + 20 = 50 \)[/tex]
- Finally, subtraction: [tex]\( 50 - 18 = 32 \)[/tex]

Result: [tex]\( 32.0 \)[/tex]

7. Simplify [tex]\( 8 \times 6 + 24 \div 6 - 18 \)[/tex]
- Perform multiplication first: [tex]\( 8 \times 6 = 48 \)[/tex]
- Then, division: [tex]\( 24 \div 6 = 4 \)[/tex]
- Then, addition: [tex]\( 48 + 4 = 52 \)[/tex]
- Finally, subtraction: [tex]\( 52 - 18 = 34 \)[/tex]

Result: [tex]\( 34.0 \)[/tex]

8. Simplify [tex]\( 56 - 36 \div 4 \times 2 + 7 \)[/tex]
- Perform division first: [tex]\( 36 \div 4 = 9 \)[/tex]
- Then, multiplication: [tex]\( 9 \times 2 = 18 \)[/tex]
- Then, subtraction: [tex]\( 56 - 18 = 38 \)[/tex]
- Finally, addition: [tex]\( 38 + 7 = 45 \)[/tex]

Result: [tex]\( 45.0 \)[/tex]

9. Simplify [tex]\( 56 \div 14 \times 3 - 10 \div 5 + 1 \)[/tex]
- Perform division first: [tex]\( 56 \div 14 = 4 \)[/tex]
- Then, another division: [tex]\( 10 \div 5 = 2 \)[/tex]
- Then, multiplication: [tex]\( 4 \times 3 = 12 \)[/tex]
- Then, subtraction: [tex]\( 12 - 2 = 10 \)[/tex]
- Finally, addition: [tex]\( 10 + 1 = 11 \)[/tex]

Result: [tex]\( 11.0 \)[/tex]

10. Simplify [tex]\( 198 - 42 \times 15 \div 5 + 6 \)[/tex]
- Perform multiplication first: [tex]\( 42 \times 15 = 630 \)[/tex]
- Then, division: [tex]\( 630 \div 5 = 126 \)[/tex]
- Then, subtraction: [tex]\( 198 - 126 = 72 \)[/tex]
- Finally, addition: [tex]\( 72 + 6 = 78 \)[/tex]

Result: [tex]\( 78.0 \)[/tex]

11. Simplify [tex]\( 105 \times 14 \div 7 + 6 - 1 \)[/tex]
- Perform multiplication first: [tex]\( 105 \times 14 = 1470 \)[/tex]
- Then, division: [tex]\( 1470 \div 7 = 210 \)[/tex]
- Then, addition: [tex]\( 210 + 6 = 216 \)[/tex]
- Finally, subtraction: [tex]\( 216 - 1 = 215 \)[/tex]

Result: [tex]\( 215.0 \)[/tex]

12. Simplify [tex]\( 17 + 34 \div 17 \times 5 - 20 \)[/tex]
- Perform division first: [tex]\( 34 \div 17 = 2 \)[/tex]
- Then, multiplication: [tex]\( 2 \times 5 = 10 \)[/tex]
- Then, addition: [tex]\( 17 + 10 = 27 \)[/tex]
- Finally, subtraction: [tex]\( 27 - 20 = 7 \)[/tex]

Result: [tex]\( 7.0 \)[/tex]

These are the detailed steps to achieve the simplified answers: [tex]\( (15.0, 32.0, 7, 26.0, 103.0, 32.0, 34.0, 45.0, 11.0, 78.0, 215.0, 7.0) \)[/tex].

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