Practice Questions

Identify the terms in the expression $25 - 3 \times 7 + 10$.

List four different arithmetic expressions that have a value of 24.

Without performing the full calculation, justify why the expression 18 \times (100 - 2) must be equal to 18 \times 100 - 18 \times 2.

Create a plausible word problem that could be solved using the arithmetic expression 150 - (4 \times 15 + 3 \times 20).

Calculate the value of the expression $100 - (30 - 15)$ by first removing the brackets according to the rules.

A shopkeeper has 5 boxes of pens, and each box contains 12 pens. If he sells 8 pens from his total stock, write an arithmetic expression to represent the number of pens remaining and calculate the final quantity.

Calculate the value of the expression: $50 - 4 \times 8 + 15 \div 3$.

Formulate a single arithmetic expression to represent the total cost of 5 notebooks at ₹25 each, after receiving a discount of ₹10 on the total bill.

Apply the distributive property to fill in the blank and the box: $15 \times (20 - \_\_) = 15 \times 20 \ \Box \ 15 \times 8$. Then, calculate the value of the expression.

Define an arithmetic expression and provide one example.

State the commutative property of addition.

Apply brackets to the expression $24 - 10 + 4$ to make its value equal to 10.

Analyze the expression $12 - 3 \times 5 + 18 \div 2$ and list its terms.

Examine the following expressions and determine the relationship between them using '<', '>', or '='. Justify your answer by applying the distributive property, without calculating the final values. Expression A: $25 \times (18 - 7)$ Expression B: $25 \times 18 - 25 \times 9$

Ravi buys 3 notebooks for ₹25 each and 2 pens for ₹10 each. He pays the shopkeeper with a ₹100 note. Write a single arithmetic expression to calculate the change Ravi should receive, and then solve it.

Calculate the value of the expression: $36 + \frac{100}{5} - 2 \times (5+3)$

A library has 25 racks of books. The first 10 racks contain 40 books each. The remaining racks contain 30 books each. During a book fair, 50 books were issued (loaned out) from the library. Write a single arithmetic expression to represent the total number of books remaining in the library, and then calculate this number.

Compare the expressions $150 + 25$ and $148 + 27$ using '<', '>', or '=' without performing the full addition. Explain your reasoning.

Describe the steps to identify the terms in an expression containing subtraction, such as $42 - 11 + 5$.

Recall the associative property of addition and explain how it applies to the expression $(-8 + 5) + 10$.

Explain what the equality sign '=' represents in the statement $18 - 3 = 15$.

Explain the purpose of using brackets in an arithmetic expression. Use the expression $50 - (10 + 15)$ as an example.

Summarize the rule for removing brackets when they are preceded by a negative sign. Provide an example.

Explain why a standard order of operations is necessary when evaluating expressions. Use the expression $10 + 4 \times 3$ to illustrate your explanation.

Describe what 'terms' are in an arithmetic expression. Then, for each expression below, rewrite it as a sum and list its terms. (a) $32 - 15 + 6 \times 2$ (b) $150 - 9 \times 10 - 20$

Explain how subtraction can be understood as the addition of an inverse. Then, rewrite the expression $85 - 20 - 10$ purely as a sum of its terms. Finally, explain why the value of the expression does not change if you evaluate it as $85 - 10 - 20$.

Solve the expression $56 - (12 + 8 \times 2) + 10$. Show each step of your calculation.

Explain the distributive property of multiplication over addition. Then, write an expression for the following situation and show how the property applies: "For a school event, a teacher buys 8 packets of pens and 8 packets of pencils. A packet of pens costs ₹50 and a packet of pencils costs ₹30. What is the total amount spent?"

John was asked to solve the expression $100 - 20 \div 5 + 3$. His answer was 10. Analyze John's calculation to identify his mistake. Explain the error based on the 'order of operations'. Then, demonstrate the correct method and find the correct value.

A student claims that the expression 100 - (30 - 15) is equal to 100 - 30 - 15. Critique this claim and explain the error in reasoning.

Create an arithmetic expression using the numbers 4, 5, and 9 exactly once, along with any of the operations +, -, \times, \div and brackets, that evaluates to 1.

To calculate 49 \times 20, which expression is more efficient to evaluate mentally: 49 \times 20 directly, or (50 - 1) \times 20? Justify your choice.

Justify that subtraction is not associative by evaluating whether (20 - 10) - 5 is equal to 20 - (10 - 5). Propose a conclusion based on your findings.

A student evaluated the expression 12 + 8 \div 2 \times 3 and got the answer 30. Critique the student's method, identify the error, and provide the correct evaluation with justification.

Critique the statement: "The value of an expression does not change if we swap any two numbers." Justify your critique with one example where it holds true and one where it does not.

Design a real-world scenario for a school trip. Formulate a single, comprehensive arithmetic expression to calculate the total money to be collected from students. The scenario must include:

• A total of 120 students.
• A bus fee of ₹150 per student.
• An entry ticket fee of ₹50 per student.
• A school subsidy (discount) of ₹20 for each student.
• An additional flat collection of ₹1000 for miscellaneous group expenses. Finally, evaluate the expression.

Justify the property a - (b - c) = a - b + c. First, demonstrate it with the numerical example a=50, b=20, c=5. Second, formulate a real-world story involving money to explain why this property is logical.

Demonstrate two different real-life situations that can be represented by two different arithmetic expressions, but both expressions must have a final value of 40. For each situation, write the story, the corresponding expression, and show the calculation.

Summarize the reasoning used to compare expressions without full calculation. Use this reasoning to compare the following pairs with '>', '<', or '=' and explain your choice. (a) $250 + 105$ vs $252 + 103$ (b) $400 - 80$ vs $401 - 79$ (c) $18 \times (20 - 2)$ vs $18 \times 20 - 18 \times 2$

Identify which of the following expressions are equal to $7 \times (12+5)$ without calculating the final value. Explain your reasoning. (a) $7 \times 12 + 5$ (b) $7 \times 12 + 7 \times 5$ (c) $(12+5) \times 7$

A library has 5 shelves, and each shelf contains 120 books. On Monday, 30 books are issued. On Tuesday, twice the number of books issued on Monday are issued. Formulate a single expression for the number of books remaining and evaluate it.

Design two different arithmetic expressions that both evaluate to 20. Each expression must use the numbers 3, 4, and 8 exactly once and at least two different operations from +, -, \times, \div.

Analyze the following expressions and arrange them in ascending (increasing) order of their values. Justify your reasoning. (a) $50 - 15$ (b) $5 \times 9$ (c) $100 \div 2$ (d) $50 - 12$

Using the numbers 2, 3, 5, and 10 exactly once, along with any of the four basic operations (+, -, \times, \div) and brackets, create three distinct expressions that result in: a) The largest possible value. b) The smallest possible positive integer value. c) A value of 0. Justify your choice for the largest value.

Propose a rule to determine if the value of the expression A \times (B - C) will be positive, negative, or zero, where A, B, and C are integers. Justify your rule.