Fundamental Operations (Related to Algebraic Expressions)
ICSE Class 6 · Mathematics · Chapter 19
What this chapter covers
- Addition of like terms
- Addition and subtraction of algebraic expressions
- Multiplication of algebraic terms
- Division of algebraic terms
Key points
- Like terms are combined by adding or subtracting their numerical coefficients; the literal part stays the same.
- Unlike terms cannot be combined into one term by adding or subtracting.
- To add expressions, group like terms (in a row or in columns) and combine each group.
- To subtract an expression, change the sign of each of its terms and then add.
- "Subtract A from B" means B - A.
- To multiply terms, multiply the numbers and then the letters; for the same letter, add the powers.
- To divide terms, divide the numbers and cancel common letters; for the same letter, subtract the powers.
- Check a subtraction by adding, and check a division by multiplying.
Questions answered
Add: 7k + 2k + k.
10k
Simplify: -6ab + 9ab - 2ab.
ab, since -6 + 9 - 2 = 1.
Can 4x and 4y be added into a single term? Give a reason.
No. They are unlike terms, because their letters are different. The sum stays as 4x + 4y.
Add 3a - 5b + 2 and a + 7b - 6.
4a + 2b - 4
Subtract 4x + y from 9x - 2y.
9x - 2y - 4x - y = 5x - 3y
Multiply 3p × 7q.
21pq
Multiply 2x2 × 4x3.
8x5, because 2 × 4 = 8 and the powers add: 2 + 3 = 5.
Divide 24y3 by 8y.
3y2