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Writing Equations: “2 more than twice a number is 5” 2 + 2x = 5 “a number divided by 3 is 8” x 3 = 8 or IS means = sign Sometimes you have to decide what the variable is… It can be any letter. We usually see x and y used as variables.

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“the sum of a number and ten is the same as 15” x + 10 = 15

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“The total pay is the number of hours times 6.50” {Sometimes, two variables are needed}

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Writing an Equation… Track One Media sells all CDs for $12 each. Write an equation for the total cost of a given number of CDs. Define variables and identify key parts of the problem…

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Number of CDs Cost 1$8.50 2$17.00 3$25.50 4$34.00 This table shows the relationship between number of CDs and cost. How much is 1 CD? T = $8.50n

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Number of CDs Cost 1$8.50 2$17.00 3$25.50 4$34.00 Cost = $8.50 times (number of CDs) C = total cost for CDs n = number of CDs bought C = 8.50 n

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We use a table of values to represent a relationship. Number of hours Total pay in dollars 540 1080 15120 20160 From the table, we can come up with an equation. Total pay = (number of hours) times (hourly pay) What is the hourly pay? $8 per hour Total pay = 8 (number of hours) T = 8h

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Write an equation for the data below… # of Hours Total Pay 8$40 12$60 16$80

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Exponents and Order of Operations Math 1 Sept 9

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Check your skills Find each Product 4 x4 7 x 7 5 x 5 9 x 9 Perform the indicated operations 3 + 12 – 8 4 – 2 + 9 5 x 5 + 7 30 ÷ 6 x 2

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To simplify an expression, we write it in the simplest form. Example: Instead of 2 + 3 + 5, we write 10. Instead of 2 · 8 + 2 · 3, we write 22. We use order of operations to help us get the right answer. PEMDAS Parentheses first, then exponents, then multiplication and division, then addition and subtraction. In the above example, we multiply first and then add.

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An exponent tells you how many times to multiply a number (the base) by itself. Means 2 times 2 times 2 times 2 Or 2 · 2 · 2 · 2 This is also read as “2 to the 4 th power” A power has two parts, a base and an exponent, such as is 16 in simplest form.

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Order of Operations Perform any operations inside grouping symbols first. i.e brackets, parenthesis, curly lines. Simplify powers Multiply and Divide left to right Add and Subtract left to right

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Always follow order of operations starting with the inside parentheses. PLEASE EXCUSE MY DEAR AUNT SALLY PParentheses EExponents MMultiplication DDivision AAddition SSubtraction } } Left to right when multiplication and division are the only operations left in the problem Left to right when addition and subtraction are the only operations left in the problem

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Simplifying a Numerical Expression Numerical Expression = a expression with numbers only Simplify: 25 – 8 × 2 + 3 2 25 – 8 × 2 + (3× 3) 25 – 8 × 2 + 9 25 – 16 + 9 18

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6 – 10 ÷ 5 3 * 6 – 4 2 ÷ 2 4 * 7 + 4 ÷ 2 2 5 3 + 90 ÷ 10 4 10 29 134 Remember order of operation

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We evaluate expressions by plugging numbers in for the variables. Example: Evaluate the expression for c = 5 and d = 2. 2c + 3d 2(5) + 3(2) 10 + 6 16

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Simplifying an Expression With Parentheses When you simplify expressions with parentheses, work within the parentheses FIRST. Lets Try! Simplify: 15(13 - 7) ÷ (8 – 5) 15(13-7) ÷ (8 -5) = 15(6) ÷ 3 = 90 ÷ 3 = 30

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Evaluate for x = 11 and y = 8 (11)(8) 2 (11)(8×8) (11)(64) = 704

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Now you Try: (5 + 3) ÷ 2 + (5 2 – 3) 8 ÷ (9 – 7) + (13 ÷ 2)

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Evaluating Expressions with Exponents The base for an exponent is the number, variable, or expression directly to the left of the exponent. For example: B 2 the base would be “B” for exponent “2” 6 3 the base for “3” would be “6”

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Evaluate the expression if m = 3, p = 7, and q = 4

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