Questions & Answers: "Arithmetic Expressions"

The correct option is 92. According to the order of operations (BODMAS/PEMDAS), we first perform multiplication and division from left to right, and then addition and subtraction from left to right.\n1. Perform multiplication: $18 \times 5 = 90$.\n2. Perform division: $20 \div 4 = 5$.\n3. The expression becomes: $90 - 5 + 7$.\n4. Perform subtraction: $90 - 5 = 85$.\n5. Perform addition: $85 + 7 = 92$.\nIncorrect options arise from violating the order of operations, such as performing subtraction before division or multiplication.

The correct option is 15. We follow the BODMAS/PEMDAS rule.\n1. Innermost parentheses: $15 \div (-3) = -5$.\n2. The expression inside the square bracket becomes: $10 + (-5) = 10 - 5 = 5$.\n3. The expression now is: $25 - [5] \times 2$.\n4. Perform multiplication: $5 \times 2 = 10$.\n5. Finally, perform subtraction: $25 - 10 = 15$.\nIncorrect options result from errors in integer arithmetic (e.g., sign errors in division or addition) or incorrect application of the order of operations, such as performing subtraction or addition before multiplication.

The correct option is -295 m.\n1. Represent the initial depth below sea level as a negative integer: -250 m.\n2. A rise of 75 m means adding 75: $-250 + 75$.\n3. A dive of 120 m means subtracting 120: $-120$.\n4. The arithmetic expression is: $-250 + 75 - 120$.\n5. Evaluate the expression:\n $-250 + 75 = -175$.\n $-175 - 120 = -295$.\nSo, the final depth is -295 m, meaning 295 m below sea level.\nIncorrect options arise from errors in representing 'below sea level' as a negative integer, or incorrect application of addition and subtraction rules for integers, especially when dealing with 'rise' and 'dive'.

The correct option is 22.\nThe given expression is $30 - 6 \times 2 + 4$. According to the BODMAS/PEMDAS rule, multiplication should be performed before addition or subtraction.\n1. Perform multiplication: $6 \times 2 = 12$.\n2. The expression becomes: $30 - 12 + 4$.\n3. Now perform subtraction and addition from left to right: $30 - 12 = 18$.\n4. Finally, perform addition: $18 + 4 = 22$.\nThe student's answer of 52 results from performing operations from left to right without respecting the order of operations ($30 - 6 = 24$, then $24 \times 2 = 48$, then $48 + 4 = 52$). Option 14 would result from doing addition before subtraction ($30 - (12+4)$).

The correct option is 4. We apply the BODMAS/PEMDAS rule.\n1. Innermost parentheses: $(8 - 4) = 4$.\n2. Inside the square bracket, perform multiplication first: $(-3) \times 2 = -6$.\n3. Complete the square bracket: $[-6 - 4] = -10$.\n4. The expression becomes: $60 \div [-10] + 10$.\n5. Perform division: $60 \div (-10) = -6$.\n6. Finally, perform addition: $-6 + 10 = 4$.\nIncorrect options arise from errors such as incorrect signs for integer operations (e.g., option 16 forgets the negative sign for $60 \div (-10)$) or incorrect application of the order of operations (e.g., option -34 results from ignoring the brackets for division).

According to the order of operations (BODMAS/PEMDAS - Brackets, Orders, Division/Multiplication, Addition/Subtraction):

1. Division: $18 \div 3 = 6$
2. Multiplication: $5 \times 2 = 10$ The expression becomes: $6 + 10 - 4$
3. Addition: $6 + 10 = 16$
4. Subtraction: $16 - 4 = 12$ Thus, the correct value of the expression is $12$. Options A, C, and D are incorrect as they do not follow the proper order of operations.

Following the order of operations:

1. Multiplication: $12 \times (-2) = -24$
2. Division: $10 \div 5 = 2$ The expression transforms to: $(-5) + (-24) - 2$
3. Now perform addition and subtraction from left to right: $-5 - 24 = -29$ $-29 - 2 = -31$ Therefore, the correct value is $-31$. Options B, C, and D result from incorrect application of integer rules or order of operations.

We simplify the expression by working from the innermost brackets outwards:

1. Innermost parenthesis: $(6 - 4) = 2$ The expression becomes: $5 \times [10 - (8 - 2 \times 2)]$
2. Multiplication inside parenthesis: $2 \times 2 = 4$ The expression becomes: $5 \times [10 - (8 - 4)]$
3. Subtraction inside parenthesis: $(8 - 4) = 4$ The expression becomes: $5 \times [10 - 4]$
4. Subtraction inside square bracket: $[10 - 4] = 6$ The expression becomes: $5 \times 6$
5. Final Multiplication: $5 \times 6 = 30$ Thus, the simplified value is $30$. Other options result from errors in the order of operations, especially with brackets.

Let's track the changes in the number of passengers:

• Started with: $60$
• At first stop: 15 got off ($-15$), 7 got on ($+7$). Current passengers: $60 - 15 + 7$
• At second stop: 10 got off ($-10$), 12 got on ($+12$). Final passengers: $60 - 15 + 7 - 10 + 12$ This matches the expression in option A. Now, let's calculate the result: $60 - 15 = 45$ $45 + 7 = 52$ $52 - 10 = 42$ $42 + 12 = 54$ The final number of passengers is $54$. Therefore, option A is correct as both the expression and the result are accurate. The other options have incorrect expressions or incorrect calculations based on the given information.

Let's evaluate each option using the order of operations:

• Option A: $20 - 5 \times 2$ Multiplication first: $5 \times 2 = 10$ Then subtraction: $20 - 10 = 10$. Since $10 \neq 30$, statement A is false.
• Option B: $15 \div 3 + 4$ Division first: $15 \div 3 = 5$ Then addition: $5 + 4 = 9$. Since $9 = 9$, statement B is true.
• Option C: $10 + 8 \div 2$ Division first: $8 \div 2 = 4$ Then addition: $10 + 4 = 14$. Since $14 \neq 9$, statement C is false.
• Option D: $2 \times (5 + 3)$ Parenthesis first: $5 + 3 = 8$ Then multiplication: $2 \times 8 = 16$. Since $16 \neq 13$, statement D is false. Therefore, only statement B is true.

According to the order of operations (BODMAS/PEMDAS):

1. Multiplication and Division are performed before Addition and Subtraction. $2 \times 6 = 12$ $10 \div 5 = 2$ The expression becomes: $15 - 12 + 2$
2. Perform Addition and Subtraction from left to right. $15 - 12 = 3$ $3 + 2 = 5$ Therefore, the correct answer is 5. Options 26, 17, and 3 are incorrect as they result from not following the correct order of operations.

Following the order of operations (BODMAS/PEMDAS):

1. First, solve the operation inside the Brackets: $7 - 4 = 3$ The expression becomes: $18 \div 3 \times 2 + 5$
2. Next, perform Division and Multiplication from left to right: $18 \div 3 = 6$ The expression becomes: $6 \times 2 + 5$ $6 \times 2 = 12$ The expression becomes: $12 + 5$
3. Finally, perform Addition: $12 + 5 = 17$ Therefore, the correct answer is 17. The other options are incorrect due to misapplication of BODMAS, such as performing addition before multiplication or division.

Let's evaluate the expression step-by-step using BODMAS/PEMDAS, paying attention to integer rules:

1. Solve the operation inside the Brackets first: $8 - 12 = -4$ The expression becomes: $-5 \times (-4) + 20 \div (-4)$
2. Perform Multiplication and Division from left to right: $-5 \times (-4) = 20$ (Product of two negative integers is positive) $20 \div (-4) = -5$ (Division of a positive by a negative integer is negative) The expression becomes: $20 + (-5)$
3. Perform Addition: $20 + (-5) = 20 - 5 = 15$ Therefore, the value of the expression is 15. Incorrect options would arise from errors in integer arithmetic or order of operations.

Let's break down the earnings and expenses:

• Monday's earning: Rs. 250
• Tuesday's spending: Rs. 120 (This is a negative earning or expense)
• Wednesday's earning: Double the amount spent on Tuesday, which is $2 \times 120 = 240$ Rs. The arithmetic expression for the net earning is: $250 - 120 + 2 \times 120$ Now, apply the order of operations (BODMAS/PEMDAS):

1. Perform Multiplication: $2 \times 120 = 240$ The expression becomes: $250 - 120 + 240$
2. Perform Subtraction and Addition from left to right: $250 - 120 = 130$ $130 + 240 = 370$ Therefore, the net earning over these three days is Rs. 370. The other options are incorrect, likely due to errors in forming the expression or in the calculation steps.

We need to evaluate each expression using the order of operations (BODMAS/PEMDAS):

1. Expression A: $20 - 5 \times 2 + 4$ $20 - 10 + 4$ (Multiplication first) $10 + 4$ (Subtraction then Addition from left to right) $= 14$ (Not 10)

2. Expression B: $(15 - 5) \times 2 \div 2$ $10 \times 2 \div 2$ (Brackets first) $20 \div 2$ (Multiplication then Division from left to right) $= 10$ (This is 10)

3. Expression C: $30 \div (2 + 3) \times 1$ $30 \div 5 \times 1$ (Brackets first) $6 \times 1$ (Division then Multiplication from left to right) $= 6$ (Not 10)

4. Expression D: $40 \div 8 + 3 \times 2$ $5 + 6$ (Division and Multiplication first) $= 11$ (Not 10)

Therefore, only expression B simplifies to 10.

According to the order of operations (BODMAS/PEMDAS), multiplication is performed before addition and subtraction. First, calculate $3 \times 4 = 12$. The expression becomes $15 - 12 + 2$. Next, perform operations from left to right: $15 - 12 = 3$. Finally, $3 + 2 = 5$. Thus, the correct answer is 5.

First, solve the operation inside the parenthesis: $6 - 8 = -2$. The expression becomes $(-5) \times (-2) + 10$. Next, perform multiplication: $(-5) \times (-2) = 10$. Finally, perform addition: $10 + 10 = 20$. Thus, the correct answer is 20.

Follow the BODMAS/PEMDAS rule. First, solve the bracket: $10 - 2 = 8$. The expression is now $24 \div 4 + 5 \times 3 - 8$. Next, perform division and multiplication from left to right: $24 \div 4 = 6$ and $5 \times 3 = 15$. The expression becomes $6 + 15 - 8$. Finally, perform addition and subtraction from left to right: $6 + 15 = 21$, then $21 - 8 = 13$. So, the correct answer is 13.

The phrase 'sum of 15 and 10' translates to $(15 + 10)$. The phrase 'product of 7 and 3' translates to $(7 \times 3)$. The instruction 'Subtract A from B' means to write $B - A$. Therefore, 'Subtract the product of 7 and 3 from the sum of 15 and 10' translates to $(15 + 10) - (7 \times 3)$. Option A correctly represents this.

Follow the BODMAS/PEMDAS rule for nested brackets, working from the innermost outwards:

1. Innermost parenthesis: $(10 \div 2 - 3) = (5 - 3) = 2$.
2. Curly braces: $\{6 + 2\} = 8$.
3. Square brackets: $[18 - 8] = 10$.
4. Finally, perform the multiplication: $10 \times 4 = 40$.
   Thus, the correct answer is 40.