Chapter 2: Arithmetic Expressions
Expressions like 30 + 5 × 4 or 100 − (15 + 56) describe everyday situations. In this chapter we compare expressions without long calculations, use brackets and terms to evaluate them in one clear way, swap and group terms, remove brackets correctly, and use the multiple of a sum to multiply quickly.
In this chapter you will
- write and compare arithmetic expressions
- find the terms of an expression and evaluate it
- swap, group and remove brackets correctly
- use a × (b + c) = a × b + a × c to multiply quickly
Topics
- Simple Expressions NCERT 2.1
An expression like 5 × 30 has a value; = links an expression to its value.
- Brackets and Terms NCERT 2.2
Brackets first; then work out each term; then add the terms.
- Swapping and Grouping NCERT 2.2
Swapping terms or grouping them differently never changes the sum.
- Removing Brackets NCERT 2.2
Minus before brackets: signs inside change (a − (b + c) = a − b − c; a − (b − c) = a − b + c).
- Multiples of Sums and Differences NCERT 2.2
a × (b + c) = a × b + a × c and a × (b − c) = a × b − a × c.
Key words
- Expression
- a mathematical phrase like 5 × 30 or 13 + 2
- Value
- the number an expression works out to
- Term
- a part of an expression joined to the rest by +
- Inverse
- the same number with the opposite sign (14 and −14)
- Commutative
- swapping terms does not change the sum
- Associative
- grouping terms differently does not change the sum
Summary
- Expressions have values; compare them by their values or by their changes.
- Brackets first, then each term, then add; terms are joined by + (83 − 14 = 83 + (−14)).
- Terms can be added in any order; minus before brackets changes the signs inside.
- a × (b + c) = a × b + a × c; 97 × 25 = 100 × 25 − 3 × 25.