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15 Cards in this Set
- Front
- Back
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EXPRESSIONS |
an expression is an algebraic sum without an equals sign, for example 4b - 2. an equation is an algebraic sum with an equals sign, for example 4b - 2 = 6. |
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WRITING EXPRESSIONS |
the letters and numbers in expressions are known as terms. in the expression 4b - 2, 4b and -2 are both terms. algebraic expressions must contain at least one letter and can be written based on real life situations. |
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WRITING EXPRESSIONS: example 1 |
pens at a stationary company are packaged in 6s and rulers are packaged in boxes of 10. a teacher orders a pack of pens and a pack of rulers. write an expression for the total number of pens and rulers ordered. firstly, assign letters to the items: p for the pens and r for the rulers. there are 6 pens in each box, so this can be written as 6 x p which is 6p. rulers are boxed in 10s, so the total amount of rulers is 10r. 6p + 10r |
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WRITING EXPRESSIONS: example 2 |
a rectangle has a width of x cm. the height is 3cm less than the width. write an expression for the perimeter of the rectangle. the perimeter is found by adding together the lengths of the sides of a shape. the width (w) of the rectangle is given as x. the height (h) of the rectangle is 3 less than the width: x - 3. perimeter - w + w + h + h perimeter - x + x + x -- 3 + x - 3 perimeter - 4x - 6 |
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QUESTION: john is n years old. kim is three years younger than john. vanessa is half kims age. write an expression for each persons age. |
john - n kim - n - 3 vanessa - |
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SIMPLIFYING ALGEBRA: collecting like terms |
collecting like terms means to simplify terms in expressions which contain the same letters. in the expression 5a + 2b + 3a - 6b, the terms 5a and +3a are like terms, and so are 2b and -6b. |
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COLLECTING LIKE TERMS: example 1 |
simplify b + b + b + b four b's can be written as 4b. |
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COLLECTING LIKE TERMS: example 2
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simplify 5m + 3m - 2m in this expression, all the terms are like terms as they all contain an m. simplify the expression in order: 5m + 3m = 8m 8m - 2m = 6m |
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QUESTION: simplify 9c - 7d + c + 3d + 5 |
9c + c = 10c -7d + 3d = -4d 10c - 4d + 5 |
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QUESTION: simplify 2p2 + 3p + p2 |
2p2 + p2 + 3p = 3p4 + 3p |
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USING LETTERS AND NUMBERS |
algebraic terms can be added and subtracted by collecting like terms, but expressions can also be multiplied and divided. |
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EXPANDING BRACKETS |
expanding brackets means multiplying everything inside the bracket by the letter or number outside the bracket. for example in the expression 3(m + 7) both m and 7 must be multiplied by 3: 3(m + 7) = 3 x m + 3 x 7 = 3m + 21 |
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EXPANDING DOUBLE BRACKETS |
writing two brackets next to each other means the brackets need to be multiplied together. for example (y + 2) x (y + 3). when expanding double brackets, every term in the first bracket has to be multiplied by every term in the second bracket. it is helpful to always multiply the terms in order so none are forgotten. one common method used is FOIL: First, Outside, Inside, Last. |
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EXPANDING DOUBLE BRACKETS: example |
expand the brackets (y + 2)(y + 3) multiply the first items in the brackets: y x y = y2 multiply the terms that are on the outsides of the brackets: y x 3 = 3y multiply the terms on the insides of the brackets: 2 x y = 2y multiply the last terms in the brackets: 2 x 3 = 6 this gives: y2 + 3y + 2y + 6 simplify the like terms (3y + 2y) to give y2 + 5y + 6 |
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QUESTION: expand the bracket (2m - 3)(m + 1) |
2m x m = 2m2 2m x 1 = 2m -3 x m = -3m -3 x 1 = -3 2m2 - m - 3 |
