Expressions using Letter-Numbers
Back to arithmetic expressions
Revise the tools for arithmetic expressions, since algebra uses every one of them.
Algebra uses all the tools from the last chapter, so let's revise them:
- Terms: the parts joined by +
- Swapping: add in any order
- Grouping: add whichever parts are convenient first
- Brackets, including a minus sign in front of a bracket
- Distributive property: the multiple of a sum is the sum of the multiples
23 − 10 × 2 as terms: 23 + (−10 × 2) = 23 + (−20) = 3. (Taking 10 from 23 first and then doubling would wrongly give 26.)
83 + 28 − 13 + 32: swap and group to make it easy: (83 − 13) + (28 + 32) = 70 + 60 = 130.
68 − (18 + 13): bracket first, 68 − 31 = 37. Or remove the bracket, flipping the signs inside: 68 − 18 − 13 = 50 − 13 = 37. Same answer.
Practise: 34 − 14 + 20; 42 + 15 − (8 − 7); 7 × 4 + 9 × 6; 20 + 8 × (16 − 6).
The link to algebra: an algebraic expression becomes a number as soon as you put numbers in place of its letters, just as a + 3 became 26 when a = 23.
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