What a binary operation is, putting numbers into its rule in the right order, brackets first, two operations in one question, and solving equations that use an operation.
A binary operation takes two numbers and gives one answer by a stated rule. The symbol is usually ∗, ∘, ⊕ or Δ, and the question tells you what it means. For example, if a∗b=2a+b, then to work out 5∗3 you put the first number in place of a and the second in place of b.
a * b = 2a + b
5 * 3 = 2(5) + 3 = 13
Using the ruleThe first number replaces a, the second replaces b
Try it
Working out an operationPick a rule, then change the numbers
a * b = 2a + b
3 * 2 = 2(3) + 2 = 8
2 * 3 = 2(2) + 3 = 7
8a * b7b * anosame?
Put the first number in place of a and the second in place of b. Swapping the numbers changes the answer: the order matters for this rule.
Pick a rule and change a and b. “Swap” works out a∗b and b∗a side by side: for most rules, the order of the two numbers matters. “Brackets” is the next idea.
Brackets first
In (a∗b)∗c, work out the bracket first. Its answer becomes the first number of the next step. In a∗(b∗c), the bracket b∗c comes first, and its answer becomes the second number.
Brackets firstWork out a * b, then combine that answer with c
Some questions use two different operations. Keep each rule for its own symbol, and still start with the bracket.
Solving equations with an operation
When an unknown is inside an operation, write the operation out with the rule first. That turns it into an ordinary equation, often linear, sometimes quadratic.