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BASIC CALCULATION SKILLS What students need to know: Students should be confident with the items in the chapter’s ‘Before you start...’ section. Specifically they should: • know the meanings of the words sum, quotient, product and difference; SUM: the aggregate of two or more numbers, magnitudes, quantities, or particulars as determined by or as if by the mathematical process of addition: The sum of 6 and 8 is 14. A particular aggregate or total, especially with reference to money: The expenses came to an enormous sum. Quotient:a result obtained by dividing one quantity by another Product: A product in math is defined as the answer of an equation in which two or more variables are multiplied. In other terms, a product is the answer to any multiplication problem. The product of 4 and 5 is 20. Difference:A difference is the result of a subtraction problem. The difference of 10 and 7 is 3. • be able to use formal and informal methods and algorithms, both mental and written, for the four operations of arithmetic; An Algorithm is a step-by-step solution. It is like a cooking recipe for mathematics. Example: one algorithm for adding two digit numbers is "add the units, add the tens and combine the answers" Long Division is another example of an algorithm: when you follow the steps you get the answer. • understand the distributive law; The Distributive Law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. a(b + c) = ab + ac • know that multiplication and addition are commutative The "Commutative Laws" say we can swap numbers over and still get the same answer … ... when we add:a +b = b+a Or when we multiply a×b = b×a