1. Stating the problems: We need to evaluate each arithmetic expression and solve for the missing numbers in the equations. 2. For the first set of expressions, we use the order of operations (PEMDAS/BODMAS): parentheses first, then multiplication/division from left to right. 3. Calculate each expression step-by-step: - $5 \times (5 + 4) = 5 \times 9 = 45$ - $(18 + 12) \div 3 = 30 \div 3 = 10$ - $7 \times (13 - 4) = 7 \times 9 = 63$ - $(42 - 14) \div 7 = 28 \div 7 = 4$ - $72 \div (5 + 4) = 72 \div 9 = 8$ - $24 \div (8 - 2) = 24 \div 6 = 4$ - $(14 - 7) \times (6 + 3) = 7 \times 9 = 63$ - $(32 + 10) \div (19 - 13) = 42 \div 6 = 7$ 4. For the second set, solve for the missing numbers: - Let the missing number be $x$ in $(x - 8) \times 9 = 45$ Step 1: Divide both sides by 9: $$\cancel{9} \times (x - 8) = \frac{45}{\cancel{9}}$$ $$x - 8 = 5$$ Step 2: Add 8 to both sides: $$x = 5 + 8 = 13$$ - Let the missing number be $y$ in $(y + 9) \div 10 = 10$ Step 1: Multiply both sides by 10: $$\frac{\cancel{(y + 9)}}{\cancel{10}} \times 10 = 10 \times 10$$ $$y + 9 = 100$$ Step 2: Subtract 9 from both sides: $$y = 100 - 9 = 91$$ - Let the missing number be $a$ in $a \times (6 + 2) = 80$ Step 1: Simplify parentheses: $$a \times 8 = 80$$ Step 2: Divide both sides by 8: $$\cancel{8} \times a = \frac{80}{\cancel{8}}$$ $$a = 10$$ - Let the missing number be $b$ in $b \div (16 - 9) = 6$ Step 1: Simplify parentheses: $$b \div 7 = 6$$ Step 2: Multiply both sides by 7: $$\frac{\cancel{b}}{\cancel{7}} \times 7 = 6 \times 7$$ $$b = 42$$ 5. Final answers: - $(x - 8) \times 9 = 45 \Rightarrow x = 13$ - $(y + 9) \div 10 = 10 \Rightarrow y = 91$ - $a \times (6 + 2) = 80 \Rightarrow a = 10$ - $b \div (16 - 9) = 6 \Rightarrow b = 42$