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Sagot :
Certainly! Let's break down and solve each mathematical expression step by step.
### Question 6: [tex]\(\{5(21 \div \overline{7-4})-30\}+2 \times 10 \div 5\)[/tex]
1. Start with the innermost parentheses:
[tex]\[ 7 - 4 = 3 \][/tex]
2. Substitute [tex]\(7 - 4\)[/tex] with 3:
[tex]\[ 5(21 \div 3) - 30 + 2 \times 10 \div 5 \][/tex]
3. Perform the division inside the parentheses next:
[tex]\[ 21 \div 3 = 7 \][/tex]
4. Substitute [tex]\(21 \div 3\)[/tex] with 7:
[tex]\[ 5 \times 7 - 30 + 2 \times 10 \div 5 \][/tex]
5. Perform the multiplication:
[tex]\[ 5 \times 7 = 35 \][/tex]
6. Substitute [tex]\(5 \times 7\)[/tex] with 35:
[tex]\[ 35 - 30 + 2 \times 10 \div 5 \][/tex]
7. Perform the multiplication and the division from left to right:
[tex]\[ 2 \times 10 = 20 \][/tex]
[tex]\[ 20 \div 5 = 4 \][/tex]
8. Substitute fully:
[tex]\[ 35 - 30 + 4 \][/tex]
9. Perform the subtraction and addition sequentially:
[tex]\[ 35 - 30 = 5 \][/tex]
[tex]\[ 5 + 4 = 9 \][/tex]
Therefore, the answer to Question 6 is:
[tex]\[ \boxed{9} \][/tex]
### Question 7: [tex]\(1-[1-\{1-\overline{1-1})\}]\)[/tex]
1. Start with the innermost operation:
[tex]\[ 1 - 1 = 0 \][/tex]
2. Substitute [tex]\(1 - 1\)[/tex] with 0:
[tex]\[ 1 - [1 - \{1 - 0\}] \][/tex]
3. Now simplify inside the curly brackets:
[tex]\[ 1 - 0 = 1 \][/tex]
4. Substitute [tex]\(1 - 0\)[/tex] with 1:
[tex]\[ 1 - [1 - 1] \][/tex]
5. Simplify inside the brackets:
[tex]\[ 1 - 1 = 0 \][/tex]
6. Substitute [tex]\(1 - 1\)[/tex] with 0:
[tex]\[ 1 - 0 \][/tex]
7. Simplify the final operation:
[tex]\[ 1 - 0 = 1 \][/tex]
Therefore, the answer to Question 7 is:
[tex]\[ \boxed{1} \][/tex]
### Question 6: [tex]\(\{5(21 \div \overline{7-4})-30\}+2 \times 10 \div 5\)[/tex]
1. Start with the innermost parentheses:
[tex]\[ 7 - 4 = 3 \][/tex]
2. Substitute [tex]\(7 - 4\)[/tex] with 3:
[tex]\[ 5(21 \div 3) - 30 + 2 \times 10 \div 5 \][/tex]
3. Perform the division inside the parentheses next:
[tex]\[ 21 \div 3 = 7 \][/tex]
4. Substitute [tex]\(21 \div 3\)[/tex] with 7:
[tex]\[ 5 \times 7 - 30 + 2 \times 10 \div 5 \][/tex]
5. Perform the multiplication:
[tex]\[ 5 \times 7 = 35 \][/tex]
6. Substitute [tex]\(5 \times 7\)[/tex] with 35:
[tex]\[ 35 - 30 + 2 \times 10 \div 5 \][/tex]
7. Perform the multiplication and the division from left to right:
[tex]\[ 2 \times 10 = 20 \][/tex]
[tex]\[ 20 \div 5 = 4 \][/tex]
8. Substitute fully:
[tex]\[ 35 - 30 + 4 \][/tex]
9. Perform the subtraction and addition sequentially:
[tex]\[ 35 - 30 = 5 \][/tex]
[tex]\[ 5 + 4 = 9 \][/tex]
Therefore, the answer to Question 6 is:
[tex]\[ \boxed{9} \][/tex]
### Question 7: [tex]\(1-[1-\{1-\overline{1-1})\}]\)[/tex]
1. Start with the innermost operation:
[tex]\[ 1 - 1 = 0 \][/tex]
2. Substitute [tex]\(1 - 1\)[/tex] with 0:
[tex]\[ 1 - [1 - \{1 - 0\}] \][/tex]
3. Now simplify inside the curly brackets:
[tex]\[ 1 - 0 = 1 \][/tex]
4. Substitute [tex]\(1 - 0\)[/tex] with 1:
[tex]\[ 1 - [1 - 1] \][/tex]
5. Simplify inside the brackets:
[tex]\[ 1 - 1 = 0 \][/tex]
6. Substitute [tex]\(1 - 1\)[/tex] with 0:
[tex]\[ 1 - 0 \][/tex]
7. Simplify the final operation:
[tex]\[ 1 - 0 = 1 \][/tex]
Therefore, the answer to Question 7 is:
[tex]\[ \boxed{1} \][/tex]
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