Substitution Class 6 ICSE — Maths Chapter 14
Substitution class 6 ICSE Maths teaches you to find an expression’s value by replacing each variable with a given number. This chapter from your Class 6 Mathematics book covers basic substitution, removing and inserting brackets, and evaluating expressions with powers and fractions. Read each section in order, then work through the exercises at the end of the chapter to test your understanding.
Download Substitution Class 6 ICSE Mathematics Chapter 14 PDF
Download the Substitution Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 7 pages, 4 sections, 10 questions.
What is inside Chapter 14
7 pages · 4 sections · 10 worked examples · 10 exercise questions
| Section | Title |
|---|---|
| 14.1 | BASIC CONCEPT |
| 14.3 | OPENING OR REMOVING A BRACKET |
| 14.4 | REMOVAL OF BRACKETS |
| 14.5 | INSERTING A BRACKET |
- EXERCISE 14(B): 0 questions
- EXERCISE 14(C): 2 questions
- REVISION EXERCISE (Chapter 14): 8 questions
14.1 BASIC CONCEPT
The value of an algebraic expression depends on the values of its variables. In 3x + 2, the variable is x. Change x, and the expression’s value changes too.
Substitution is the process of finding an expression’s value by replacing each variable with a given number. This builds on earlier work in your Class 6 ICSE Maths book, where you learned to handle variables. The CISCE board’s official website publishes the full Mathematics curriculum for this class.
Take x = 4 and y = 2. Evaluate 3x + 2y, 2x^2, and \frac{x + y}{x - y}.
First: 3x + 2y = 3 \times 4 + 2 \times 2 = 12 + 4 = 16. For the power: 2x^2 = 2 \times 4^2 = 2 \times 16 = 32. The exponent applies only to x, not to the coefficient 2. Squaring before multiplying is a common mistake.
For the fraction: \frac{x + y}{x - y} = \frac{4 + 2}{4 - 2} = \frac{6}{2} = 3. A shortcut saves work with fractions. Cancel common factors before substituting. In \frac{3x^2}{x}, write the numerator as 3 \times x \times x, cancel one x, and get 3x. With x = 4, the result is 12, matching the long way.
When a variable’s value is zero, any term containing it vanishes. If b = 0, then 5ab = 5a \times 0 = 0, and the term disappears. When a variable appears more than once, substitute it everywhere. Missing one occurrence is a common error.
14.3 OPENING OR REMOVING A BRACKET
Two rules govern removing a bracket. They depend on the sign written just before the bracket.
Positive sign before a bracket: remove the bracket and keep every sign inside unchanged. For example, 20 + (9 - 4) = 20 + 9 - 4 = 25.
Negative sign before a bracket: remove the bracket and flip every sign inside. Plus becomes minus, and minus becomes plus. For example, 20 - (9 - 4) = 20 - 9 + 4 = 15.
| Sign before bracket | Signs inside the bracket |
|---|---|
| + | Kept unchanged |
| - | Each sign is flipped |
Common mistake: forgetting to flip a minus to plus when a minus sign sits before the bracket. In 20 - (9 - 4), the 4 must become +4. Writing 20 - 9 - 4 = 7 is wrong. The correct value is 15.
Why does the rule hold? A minus sign before a bracket means the whole bracket is subtracted. Subtracting (9 - 4) is the same as subtracting 9, then adding 4 back. The minus sign distributes over every term inside.
14.4 REMOVAL OF BRACKETS
When an expression contains several brackets, remove them in a fixed order.
- The bar bracket (vinculum) \overline{\phantom{a}}
- The small bracket ( )
- The curly bracket { }
- The square bracket [ ]
A number placed before a bracket multiplies every term inside it. So 5(x + y) = 5x + 5y, and 2(2a - b) = 4a - 2b.
Worked example: simplify 4x - [2x - \{x - (x - 2)\}].
First remove the small bracket. Inside the curly bracket, x - (x - 2) = x - x + 2 = 2. The expression becomes 4x - [2x - 2].
Now remove the square bracket. 4x - [2x - 2] = 4x - 2x + 2 = 2x + 2. That is the simplified form.
Why this order? The bar bracket is removed first because it is the innermost grouping, drawn directly over the terms it covers. Even when it sits inside other brackets, it comes out first. A mnemonic for the order is Very Small Cats Squeak — Vinculum, Small, Curly, Square.
14.5 INSERTING A BRACKET
Inserting a bracket is the reverse of removing one. The same two rules apply, read backwards.
Positive sign before the new bracket: keep every sign inside unchanged. Negative sign before the new bracket: flip every sign inside.
Worked example: rewrite 4x - 2y + 3z with a bracket after the minus sign. The minus sign comes before the bracket, so signs inside flip. Write 4x - (2y - 3z).
Check by removing the bracket: 4x - (2y - 3z) = 4x - 2y + 3z. The operation is reversible. The same expression can also be grouped as 4x + (-2y + 3z), with a positive sign and no sign changes.
This connects directly to section 14.3. Removing and inserting brackets follow the same sign rules, just in opposite directions. Clean bracket work also prepares you for simple linear equations, where grouping terms correctly matters.
What to practise from Substitution Class 6 ICSE
This chapter has three practice blocks.
- EXERCISE 14(B): evaluate and simplify expressions with brackets
- EXERCISE 14(C): 2 questions on inserting brackets
- REVISION EXERCISE (Chapter 14): 8 questions covering substitution and bracket operations
Work through each block in order. The revision exercise at the end mixes substitution values, bracket removal, and multiplication, so it tests everything from this ICSE chapter.
Substitution Class 6 ICSE frequently asked questions
What is substitution in Class 6 ICSE Maths?
Substitution is the process of finding an algebraic expression’s value by replacing each variable with a given number. For example, if x = 4, then 3x + 2 = 14. The expression’s value depends entirely on the values you substitute.
When do signs change while removing a bracket?
Signs change only when a minus sign sits directly before the bracket. Then every sign inside flips: plus becomes minus, and minus becomes plus. With a positive sign before the bracket, signs inside stay unchanged.
In what order should brackets be removed?
Remove the bar bracket (vinculum) first, then the small bracket ( ), then the curly bracket { }, and finally the square bracket [ ]. Follow this order even when a bar bracket sits inside other brackets.
What is a vinculum or bar bracket?
A vinculum is a line drawn over a group of terms, acting as a bracket. In 2x + \overline{3y - 4z}, the line over 3y - 4z is the bar bracket. It is removed first in any combined operation.
How do I evaluate an expression like a^b?
The expression a^b means multiply a by itself b times. If a = 2 and b = 5, then 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32. Substitute the base and the exponent, then multiply out.
Reference: ICSE Class 6 Mathematics textbook material, chapter 14: Substitution — CISCE-aligned.