Substitution (Including Use of Brackets as Grouping Symbols)
ICSE Class 6 · Mathematics · Chapter 20
What this chapter covers
- Substitution of values in expressions
- Evaluation of algebraic expressions
- Brackets as grouping symbols
- Removal of brackets
Key definitions
Substitution is the replacing of each letter in an expression by a number that is given for it.
Evaluation is the working out of the number that an expression stands for, once the values of its letters are known.
Brackets are signs placed around a group of numbers or terms, which tell you to treat the group as one quantity.
Key points
- Substitution means putting the given number in place of each letter.
- A hidden multiplication sign must be brought back: 5a means 5 × a.
- A power such as x2 means x × x, not 2 × x.
- Evaluation means working out the value of an expression, using the usual order of operations.
- The value of an expression changes when the values of its letters change. It may be positive, zero or negative.
- Brackets are grouping symbols. The four kinds are the bar, round, curly and square brackets.
- Work from the innermost bracket outwards.
- A + before a bracket: drop the bracket and keep the signs.
- A - before a bracket: drop the bracket and change every sign inside.
- A number before a bracket: multiply every term inside by that number.
- Check a simplification by substituting an easy value into both the question and the answer.
Questions answered
What is substitution?
Substitution is replacing each letter in an expression by the number given for it.
If y = 6, find the value of 4y - 5.
4 × 6 - 5 = 24 - 5 = 19.
A student says that when n = 3, 7n = 73. Is the student right?
No. 7n means 7 × n, so 7n = 7 × 3 = 21.
If a = 2 and b = 7, find the value of ab + a2.
2 × 7 + 2 × 2 = 14 + 4 = 18.
If p = 3 and q = 4, find the values of 3(p + q) and 3p + q. Are they equal?
3(p + q) = 3 × 7 = 21, but 3p + q = 9 + 4 = 13. They are not equal.
Name the four grouping symbols and the order in which you work through them.
Bar (vinculum), round brackets, curly brackets and square brackets, in that order, starting from the innermost.
Remove the brackets and simplify: 8x - (3x - 2).
8x - 3x + 2 = 5x + 2.
Simplify 4m + \2m - (m + 6)\ and check your answer with m = 10.
4m + \2m - m - 6\ = 4m + \m - 6\ = 5m - 6. Check: the original gives 40 + \20 - 16\ = 44, and 5 × 10 - 6 = 44.