Simplify the following expressions: a) 7 + (15 - 6) b) 6 x (5 + 4) c) 4(2 + 6) + 4 - 3(9 - 7) d) 32 / (14 - 6) x 3 e) 40 / 5 (16 - 48 / 4) f) 35 - \15 - (19 + 5) / 3\

here are the solutions for the remaining questions.

4. Let's simplify.

a) $7 + (15 - 6)$

Step 1: Perform the operation inside the parentheses.

$$7 + 9$$

Step 2: Perform the addition.

$$16$$ $$\boxed{16}$$

b) $6 \times (5 + 4)$

Step 1: Perform the operation inside the parentheses.

$$6 \times 9$$

Step 2: Perform the multiplication.

$$54$$ $$\boxed{54}$$

c) $4(2 + 6) + 4 - 3(9 - 7)$

Step 1: Perform operations inside the parentheses.

$$4(8) + 4 - 3(2)$$

Step 2: Perform multiplications.

$$32 + 4 - 6$$

Step 3: Perform addition and subtraction from left to right.

$$36 - 6$$

Step 4: Perform the subtraction.

$$30$$ $$\boxed{30}$$

d) $32 \div (14 - 6) \times 3$

Step 1: Perform the operation inside the parentheses.

$$32 \div 8 \times 3$$

Step 2: Perform the division.

$$4 \times 3$$

Step 3: Perform the multiplication.

$$12$$ $$\boxed{12}$$

e) $40 \div 5 (16 - 48 \div 4)$

Step 1: Perform the division inside the parentheses.

$$40 \div 5 (16 - 12)$$

Step 2: Perform the subtraction inside the parentheses.

$$40 \div 5 (4)$$

Step 3: Perform the division.

$$8 (4)$$

Step 4: Perform the multiplication.

$$32$$ $$\boxed{32}$$

f) $35 - \{15 - (19 + 5) \div 3\}$

Step 1: Perform the operation inside the innermost parentheses.

$$35 - \{15 - 24 \div 3\}$$

Step 2: Perform the division inside the curly braces.

$$35 - \{15 - 8\}$$

Step 3: Perform the subtraction inside the curly braces.

$$35 - 7$$

Step 4: Perform the subtraction.

$$28$$ $$\boxed{28}$$

g) $62 + 2 \{56 \div (4 \times 2) - 5\}$

Step 1: Perform the operation inside the innermost parentheses.

$$62 + 2 \{56 \div 8 - 5\}$$

Step 2: Perform the division inside the curly braces.

$$62 + 2 \{7 - 5\}$$

Step 3: Perform the subtraction inside the curly braces.

$$62 + 2 \{2\}$$

Step 4: Perform the multiplication.

$$62 + 4$$

Step 5: Perform the addition.

$$66$$ $$\boxed{66}$$

h) $5 \{13 + 12 \div 3 (2 \times 2)\}$

Step 1: Perform the operation inside the innermost parentheses.

$$5 \{13 + 12 \div 3 (4)\}$$

Step 2: Perform the division inside the curly braces.

$$5 \{13 + 4 (4)\}$$

Step 3: Perform the multiplication inside the curly braces.

$$5 \{13 + 16\}$$

Step 4: Perform the addition inside the curly braces.

$$5 \{29\}$$

Step 5: Perform the multiplication.

$$145$$ $$\boxed{145}$$

i) $39 - 4 \{16 \div (7 - 3)\} - 23$

Step 1: Perform the operation inside the innermost parentheses.

$$39 - 4 \{16 \div 4\} - 23$$

Step 2: Perform the division inside the curly braces.

$$39 - 4 \{4\} - 23$$

Step 3: Perform the multiplication.

$$39 - 16 - 23$$

Step 4: Perform subtractions from left to right.

$$23 - 23$$

Step 5: Perform the subtraction.

$$0$$ $$\boxed{0}$$

j) $25 - [90 - 5 \{9 - (14 - 12)\}]$

Step 1: Perform the operation inside the innermost parentheses.

$$25 - [90 - 5 \{9 - 2\}]$$

Step 2: Perform the subtraction inside the curly braces.

$$25 - [90 - 5 \{7\}]$$

Step 3: Perform the multiplication inside the square brackets.

$$25 - [90 - 35]$$

Step 4: Perform the subtraction inside the square brackets.

$$25 - 55$$

Step 5: Perform the subtraction.

$$-30$$ $$\boxed{-30}$$

k) $55 \div 11 [120 \div 2 \{4 + (10 + 5 - 7)\}]$

Step 1: Perform operations inside the innermost parentheses.

$$55 \div 11 [120 \div 2 \{4 + (15 - 7)\}]$$ $$55 \div 11 [120 \div 2 \{4 + 8\}]$$

Step 2: Perform the addition inside the curly braces.

$$55 \div 11 [120 \div 2 \{12\}]$$

Step 3: Perform division and multiplication inside the square brackets from left to right.

$$55 \div 11 [60 \times 12]$$ $$$$