Class 7 Exam > Class 7 Notes > Mathematics (Ganita Prakash) Class 7 - New NCERT > Practice Questions: Expression using Letter-Number
Practice Questions: Expression using Letter-Number | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download
Q1:Anita is 6 years older than her brother Vikram. If Vikram is 10 years old, how old is Anita?
Sol:
Anita’s age = Vikram’s age + 6
= 10 + 6
= 16 years
Q2: A store sells mangoes at ₹30 each and bananas at ₹10 each. What is the total cost of purchasing 4 mangoes and 3 bananas?
Sol:
Cost of 4 mangoes = 4 × ₹30 = ₹120
Cost of 3 bananas = 3 × ₹10 = ₹30
Total cost = ₹120 + ₹30 = ₹150
Q3: The perimeter of a square is calculated as 4 times the side length. If the side length is 8 cm, what is the perimeter?
Sol: Perimeter = 4 × side length
= 4 × 8
= 32 cm
Q4: A car travels at a speed of 15 km per hour. How far does it travel in 4 hours?
Sol:
Distance = Speed × Time
= 15 × 4
= 60 km
Q5:If y represents a number, what expression represents 5 more than three times the number?
Sol:
Three times the number = 3y
5 more than three times the number = 3y + 5
Q6: A garden hose is 12 meters long. An additional hose of length n meters is connected to it. Write an expression for the total length. If n = 5 meters, find the total length.
Sol:
Expression for total length = 12 + n
For n = 5 meters:
Total length = 12 + 5 = 17 meters
Q7: A bakery sells muffins at ₹25 each and brownies at ₹15 each. Write an expression for the total cost of buying m muffins and b brownies. Calculate the cost for 6 muffins and 2 brownies.
Sol:
Expression for total cost = 25m + 15b
For m = 6 and b = 2:
Total cost = (25 × 6) + (15 × 2) = 150 + 30 = ₹180
Q8: Simplify the expression: 6a + 3b - 2a + 5b - 9.
Sol:
Combine like terms:
= (6a - 2a) + (3b + 5b) - 9 =
= 4a + 8b - 9
Q9: In a quiz, a student earns 3x points for each correct answer and loses y points for each incorrect answer. Over three rounds, their scores are 3x - y, 2x - 2y, and 4x - 3y. Write and simplify an expression for the total score. If x = 4 and y = 2, calculate the total score.
Sol:
Total score = (3x - y) + (2x - 2y) + (4x - 3y)
= (3x + 2x + 4x) + (-y - 2y - 3y)
= 9x - 6y
For x = 4 and y = 2:
Total score = (9 × 4) - (6 × 2) = 36 - 12 = 24
Q 10: Subtract the expression 5x - 3y + 7 from 8x + 2y - 4. Evaluate the resulting expression if x = 3 and y = 2.
Sol:
Subtract: (8x + 2y - 4) - (5x - 3y + 7)
= (8x - 5x) + (2y - (-3y)) + (-4 - 7)
= 3x + 5y - 11
For x = 3 and y = 2:
Result = (3 × 3) + (5 × 2) - 11 = 9 + 10 - 11 = 8
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FAQs on Practice Questions: Expression using Letter-Number - Mathematics (Ganita Prakash) Class 7 - New NCERT
| 1. What is an expression using letter-number, and how is it used in mathematics? |  |
Ans.An expression using letter-number is a mathematical phrase that includes both letters (variables) and numbers. These expressions can represent values and relationships and are used in various mathematical operations such as addition, subtraction, multiplication, and division. For example, in the expression 3x + 5, x is a variable that can take different values, and the entire expression can be evaluated for different values of x.
| 2. How can I simplify expressions that involve letters and numbers? | |
Ans.To simplify expressions that contain letters and numbers, you should combine like terms, which are terms that have the same variable raised to the same power. For instance, in the expression 4x + 3x - 2, you can combine the like terms (4x and 3x) to get 7x - 2. Always remember to perform operations according to the order of operations (PEMDAS/BODMAS).
| 3. What are some common mistakes to avoid when working with letter-number expressions? | |
Ans.Common mistakes when working with letter-number expressions include forgetting to distribute correctly when using parentheses, misapplying the order of operations, and not combining like terms properly. Additionally, some students may confuse coefficients and constants, which can lead to errors in evaluation and simplification.
| 4. Can you provide an example of a real-world application of expressions using letter-number? | |
Ans.Expressions using letter-number are widely used in real-world applications such as finance, physics, and engineering. For example, in finance, if an individual earns a salary represented by the expression 50000 + 0.05x (where x is the number of years worked), this expression can help calculate total earnings over time. In this case, the variable helps model the relationship between time and income.
| 5. How do letter-number expressions relate to algebraic equations? | |
Ans.Letter-number expressions are foundational components of algebraic equations. An algebraic equation is formed when an expression is set equal to another expression or value, such as 3x + 5 = 20. Solving these equations involves finding the value of the variable that makes the equation true, which is a key concept in algebra. Understanding expressions helps to grasp how to manipulate and solve equations effectively.
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