Class 7 Maths Chapter 2 HOTS Question Answers - Arithmetic Expressions

Q1: A shop sells notebooks at ₹15 each and pens at ₹10 each. Arjun buys 3 notebooks and 2 pens, while Priya buys 2 notebooks and 4 pens. Write an expression for the total amount they spend together, identify its terms, and evaluate the total cost.

Ans: Step 1: Write the expression for Arjun's purchase
Arjun buys 3 notebooks at ₹15 each and 2 pens at ₹10 each.
Cost for Arjun = (3 × 15) + (2 × 10).
Step 2: Write the expression for Priya's purchase
Priya buys 2 notebooks at ₹15 each and 4 pens at ₹10 each.
Cost for Priya = (2 × 15) + (4 × 10).
Step 3: Write the total expression
Total amount = Arjun's cost + Priya's cost
= [(3 × 15) + (2 × 10)] + [(2 × 15) + (4 × 10)].
Step 4: Identify the terms
Rewrite the expression by grouping:
= (3 × 15) + (2 × 10) + (2 × 15) + (4 × 10).
Terms: 3 × 15, 2 × 10, 2 × 15, 4 × 10.
Step 5: Evaluate the expression
Calculate each term:
3 × 15 = 45
2 × 10 = 20
2 × 15 = 30
4 × 10 = 40
Total = 45 + 20 + 30 + 40 = 135.

Q2: Evaluate the expression 48 − (12 × 2) + 16 ÷ 4 by identifying its terms and applying the correct order of operations. Explain why brackets are crucial in this expression.

Ans: Step 1: Identify the terms
The expression is 48 − (12 × 2) + 16 ÷ 4.
Rewrite subtraction as addition of the inverse:
48 + (−(12 × 2)) + (16 ÷ 4).
Terms: 48, −(12 × 2), 16 ÷ 4.
Step 2: Evaluate inside brackets and perform division/multiplication
Inside brackets: 12 × 2 = 24, so −(12 × 2) = −24.
Division: 16 ÷ 4 = 4.
Expression becomes: 48 + (−24) + 4.
Step 3: Add the terms
48 + (−24) = 48 − 24 = 24.
24 + 4 = 28.
Step 4: Importance of brackets
Without brackets, the expression 48 − 12 × 2 + 16 ÷ 4 would be evaluated using the order of operations (multiplication/division before addition/subtraction)
12 × 2 = 24, 16 ÷ 4 = 4.
48 − 24 + 4 = 24 + 4 = 28 (same result in this case).

However, if interpreted as (48 − 12) × 2 + 16 ÷ 4, the result would differ:
48 − 12 = 36, 36 × 2 = 72, 16 ÷ 4 = 4, 72 + 4 = 76.

Brackets ensure the intended grouping, avoiding any mistake.

Q3: Compare the expressions 123 + 56 and 124 + 54 using '<', '>', or '=' without computing their values. 

Ans: Step 1: Analyze the expressions
First expression: 123 + 56.
Second expression: 124 + 54.
Step 2: Reasoning without computation
Imagine two people, Anil and Bela, collecting marbles.
Anil starts with 123 marbles and adds 56 more.
Bela starts with 124 marbles (1 more than Anil) and adds 54 more (2 less than Anil).
Initially, Bela has 1 more marble. However, Anil gains 2 more marbles than Bela (56 − 54 = 2).
Net effect: Anil's total marbles = Bela's initial advantage (1) + Anil's gain (2) = 1 + 2 = 3 more than Bela.
Thus, 123 + 56 > 124 + 54.

Q4: A bakery sells cakes for ₹200 each and cookies for ₹10 each. A family buys 2 cakes and 15 cookies, then gives a ₹50 tip. Write an expression for the total cost, identify its terms, and calculate the amount.

Ans: Step 1: Write the expression
Cost of 2 cakes = 2 × 200.
Cost of 15 cookies = 15 × 10.
Tip = 50.
Total cost = (2 × 200) + (15 × 10) + 50.
Step 2: Identify terms
Terms: 2 × 200, 15 × 10, 50.
Step 3: Evaluate
2 × 200 = 400.
15 × 10 = 150.
50 = 50.
Total = 400 + 150 + 50 = 600.
The expression is (2 × 200) + (15 × 10) + 50, with terms 2 × 200, 15 × 10, 50. 
The total cost is ₹600.

Q5: Show that 4 × (12 + 8) equals 4 × 12 + 4 × 8 using the distributive property. Then, evaluate both expressions to confirm they yield the same value.

Ans: 
Step 1: Apply distributive property
The distributive property states: a × (b + c) = a × b + a × c.
For 4 × (12 + 8):
4 × (12 + 8) = 4 × 12 + 4 × 8.
Step 2: Evaluate both expressions
Left: 4 × (12 + 8) = 4 × 20 = 80.
Right: 4 × 12 + 4 × 8 = 48 + 32 = 80.
Step 3: Confirmation
Both expressions yield 80, confirming the distributive property.