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What is Substitution (replacing a letter with a number)?
Grade Level:
Class 4
All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry
Definition
What is it?
Substitution means replacing something with another thing. In Maths, it often means replacing a letter (called a variable) with a specific number. This helps us find the value of an expression or solve a problem.
Simple Example
Quick Example
Imagine you have a formula for how much chai costs: Cost = 10 rupees + C. If C stands for the number of cups of chai, and you want to buy 3 cups, you would substitute '3' for 'C'. So, Cost = 10 rupees + 3. This is incorrect logic for the example, as it leads to 13 rupees for 3 cups of chai. A better example would be: Cost = 10 rupees * C. If C = 3 cups, then Cost = 10 * 3 = 30 rupees.
Worked Example
Step-by-Step
Let's find the value of the expression '5 + x' if x = 7.
1. Look at the expression: 5 + x.
2. We are given that x has a value of 7.
3. Substitute (replace) the letter 'x' with the number '7'.
4. The expression becomes: 5 + 7.
5. Now, calculate the sum: 5 + 7 = 12.
6. So, the value of the expression '5 + x' when x = 7 is 12.
Why It Matters
Substitution is a fundamental skill used in almost all STEM fields. Engineers use it to calculate forces, scientists use it in formulas, and even finance experts use it to predict market trends. Mastering substitution helps you solve complex problems in future studies and real-world careers.
Common Mistakes
MISTAKE: Forgetting the operation (like multiplication) when substituting. E.g., for '3y' and y=5, writing '35' instead of '3 x 5'. | CORRECTION: Remember that a number next to a letter means multiplication. So, '3y' means '3 multiplied by y'.
MISTAKE: Substituting the wrong number for the wrong letter in expressions with multiple letters. E.g., for 'a + b' where a=2, b=3, writing '3 + 2' instead of '2 + 3'. | CORRECTION: Carefully match each letter with its given number value before replacing.
MISTAKE: Not following the order of operations (BODMAS/PEMDAS) after substituting. E.g., for '2 + 3x' and x=4, doing (2+3) then multiplying by 4. | CORRECTION: Always follow BODMAS/PEMDAS. Do multiplication/division before addition/subtraction after you substitute the numbers.
Practice Questions
Try It Yourself
QUESTION: If 'p = 9', what is the value of 'p - 4'? | ANSWER: 5
QUESTION: Find the value of '2m + 5' if 'm = 6'. | ANSWER: 17
QUESTION: If 'a = 10' and 'b = 3', what is the value of 'a / b + 2'? | ANSWER: 10/3 + 2 = 3.33 + 2 = 5.33 (approx)
MCQ
Quick Quiz
What is the value of 'x + 15' if 'x = 8'?
158
23
7
815
The Correct Answer Is:
B
To find the value, you replace 'x' with '8'. So, the expression becomes 8 + 15, which equals 23. Options A and D incorrectly combine the numbers, and C subtracts instead of adds.
Real World Connection
In the Real World
When you use a mobile data calculator online, you often enter how many GB you use (a number) into a formula that calculates your bill. Or, when a cricket coach calculates a player's strike rate, they substitute the runs scored and balls faced into a formula. This is substitution in action!
Key Vocabulary
Key Terms
SUBSTITUTION: Replacing a letter with a number | VARIABLE: A letter that represents an unknown number | EXPRESSION: A mathematical phrase that can contain numbers, variables, and operations (like 5 + x) | VALUE: The number result after calculation
What's Next
What to Learn Next
Great job understanding substitution! Next, you can learn about 'Evaluating Algebraic Expressions'. This builds directly on substitution by applying it to more complex expressions with multiple operations and variables, preparing you for algebra.
