15.5 Algebraic proof — Practise with help
Work each problem before revealing support.
Warm-up: remember
Answer these from memory. Do not look back at the section.
- Write an expression for an even number.
- Simplify .
Check the warm-up
- , where is a whole number.
- .
If an answer differs, revisit Section 8.1 for algebraic notation and Section 8.2 for collecting like terms.
Practise with help
1. Prove that the sum of two consecutive integers is odd.
Hint
Represent the integers as and .
First step
Their sum is . Collect the terms.
Full working
. This is odd because it is twice an integer plus one.