Fundamental Concepts (Including Fundamental Operations)
ICSE Class 7 · Mathematics · Chapter 11
What this chapter covers
- Letters for numbers: constants and variables
- Terms, factors and coefficients
- Like and unlike terms
- Generating algebraic expressions
- Adding algebraic expressions
- Subtracting algebraic expressions
- Using addition and subtraction in problems
- Common errors to avoid
Key points
- A constant has a fixed value; a variable, usually a letter, can take different values.
- An algebraic expression combines constants and variables with operation signs and has no equals sign.
- Terms are the parts of an expression separated by + or - signs, and each term carries the sign in front of it.
- The numerical coefficient is the number part of a term with its sign; in x it is 1 and in -x it is -1.
- Expressions with one, two and three terms are called monomials, binomials and trinomials.
- Like terms have exactly the same letters with the same powers; only like terms can be added or subtracted.
- To add, collect like terms and add their coefficients, keeping the letter part unchanged.
- To subtract, change the sign of every term of the expression being subtracted and then add.
- "Subtract A from B" means B - A; check a subtraction by adding the answer to A.
- A quick check with easy values of the letters catches many mistakes.
Questions answered
In the expression 6x - 7, which part is a variable and which part is a constant?
x is the variable; 6 is its coefficient, and -7 is the constant term.
Write the terms of 4a2 - ab + 9 and give the coefficient of ab.
The terms are 4a2, -ab and 9. The coefficient of ab is -1.
Are 5xy and -3yx like terms? Are 2m and 2m2 like terms? Explain briefly.
5xy and -3yx are like terms, because xy and yx are the same product. 2m and 2m2 are unlike, because the powers of m are different.
Classify 3p + q, -8k and a2 - a + 1 as monomial, binomial or trinomial.
3p + q is a binomial, -8k is a monomial and a2 - a + 1 is a trinomial.
Write an expression for "9 less than three times a number n".
3n - 9.
A packet of biscuits costs b rupees and a carton of milk costs ₹ 28. Write an expression for the cost of 4 packets of biscuits and 2 cartons of milk.
4b + 56 rupees, since 2 × 28 = 56.
Add 6x - 4y + 3 and -2x + 9y - 8.
4x + 5y - 5.
Subtract 5a - 2b from 3a + 4b.
(3a + 4b) - (5a - 2b) = 3a + 4b - 5a + 2b = -2a + 6b.