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7th grade Math Chapter 7 Notes Translating in the “math language” Addition plus the sum of more than Subtraction minus difference of decreased by Multiplication Times The product of Multiplied by increased by total added to fewer than less than subtracted Of twice Division Divided by The quotient of Separate into equal parts “a number increased by 7” is written “x + 7” “4 increased by a number is 12” is written “4 + x = 12” Terms are parts of an expression that are added together. If terms have identical variable parts, they are like terms. If a term has a number part and a variable part, the number part is called the coefficient. A term that does not have a variable part is called a constant. An inverse operation is an operation that “undoes” another operation. Adding and subtracting are inverse operations. The Addition Property of Equality- adding the same number to each side of an equation produces an equivalent equation. x– a = b …… x – a + a = b + a Multiplication Property of Equality- multiplying each side of an equation by the same nonzero number produces an equivalent equation. x/a = b……x/a(a) = b(a) Division Property of Equality- dividing each side of an equation by the same nonzero number produces an equivalent equation. ax = b…….ax/a = b/a Solving two-step equations: Our goal is to isolate the variable. When the variable has friends, we have to see how they are connected, and complete an inverse operation to get them away from their friends (isolate them). When there are two friends, disconnect the add/subtract friend first then disconnect the multiply/divide friend. 2x + 1 = 7 2x + 1 - 1= 7 – 1 2x = 6 2x /2 = 6 /2 x=3 Solving inequalities: An inequality uses the signs: <, >, ≥, ≤ The solution to an inequality is often an entire group of numbers (sometimes an infinite amount) We can graph an inequality to model the numbers. < and > use open circles ≥, and ≤ used filled in circles A function is a pairing of each number in one set with a number in another set. Start with an input, and the number that it connects to is called the output. All input values are the domain of a function, all output values are the range of a function. We usually call the input values “x”, and the output values “y”. We can graph functions by using the input (x) values and the output (y) values as ordered pairs describing points on a coordinate plane. Start by making an xy chart, filling in values for y when the x values are set at -2,-1,0,1, 2. Next, graph the 5 points that were just created. If it is a linear function these points will all lie in a line. Connect the dots and place arrows on each end. Graph y = x + 2 x -2 -1 0 1 2 y 0 1 2 3 4 We have created the points: (-2,0), (-1,1), (0,2), (1,3) and (2,4). Plot these on a coordinate plane and connect them to form a line.