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Variables and Expressions Chapter 1-1 Prentice Hall Pre Algebra 8th Grade Math Check Skills You’ll Need How many days in a week? 7 days in a week How many inches in a foot? 12 inches in a foot How many cents is a nickel? a nickel is 5 cents How many quarts is a gallon? 4 quarts is a gallon How many feet is a yard? 3 feet is a yard Definitions ◦ a mathematical phrase that uses numerals and operation symbols. ◦ Is a letter that stands for a number ◦ a mathematical phrase that uses variables, numerals, and operation symbols. Examples Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable. 7–5 ◦ Numerical expression a+4 ◦ Variable expression ◦ a is the variable Quick Check 1) Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable. 8÷x 2) 100 × 6 3) Numerical expression, no variables d + 43 – 9 4) Variable expression, x is the variable Variable expression, d is the variable 4a Variable expression, a is the variable Real-World Problem Solving The fastest dinosaur may have been Ornithomimus, which could run about 60 ft. in a second. Write a variable expression for the distance Ornithomimus could run in a given time. 1. We know that the dino runs 60 ft in one second. 2. We can label the time in seconds with letter s. 3. We multiply 60ft with by seconds s to find out the distance the dino runs in s seconds. • 60 ∙ s or 60s 4. Can you find out how far the dino runs in one minute? • 360 ft. in one minute Quick Check Bagels cost $.50 each. Write a variable expression for the cost of b bagels. 0.50b Write a variable expression for the number of hours in m minutes. 60h Exercises 1. Write a variable expression for each word phrase: a) 10 less than p p – 10 b) 4 fewer than j j-4 c) 3 divided by n 3÷n d) The sum of 18 and c 18 + c or c + 18 Write an expression 1. The number of days in 4 weeks 2. The number of days in w weeks 3. 7w Number of feet in 100 inches 4. 7 ∙ 4 or 4 ∙ 7 100 ÷ 12 Number of feet in i inches 12i The Order of Operations Chapter 1-2 Prentice Hall Pre Algebra 8th Grade Math Order of Operation Rule: 1. Parenthesis 2. Exponents 3. Multiplication or Division 4. Addition or Subtraction When there are two operation with the same rank, you need to solve them from Left to Right. Example Using order of operation 6 + 15 ÷ 3 (divide) 6+ 5 (then add) 11 CORRECT Not using the order of operation 6 + 15 ÷ 3 (add) 21 ÷ 3 (then divide) 7 WRONG Example 18 ÷ 3 ∙ 2 Same rank operation therefore solve from left to write (division first) 6∙2 12 CORRECT 18 ÷ 3 ∙ 2 Not using order of operation and doing the multiplication first. 18 ÷ 6 3 WRONG Order of Operation Rule: 1. Parenthesis 2. Exponents 3. Multiplication or Division 4. Addition or Subtraction When there are two operation with the same rank, you need to solve them from Left to Right. Quick Check 4 −1∙2+6÷3 4−2+6÷3 4−2+2 2+2=4 5 + 6 ∙ 4 ÷ 2 5 + 24 ÷ 2 − 3 5 + 12 − 3 17 − 3 = 14 −3 P.E.M.D.A.S. Insert grouping symbols () to make the number sentence true: 1. 3 + 5 ∙ 8 = 64 (3 + 5) ∙ 8 = 64 2. 4 ∙ 8 + 3 = 44 4 ∙ (8 + 3) = 44 3. 4 ∙ 8 + 6 ÷ 6 − 3 = 34 4 ∙ 8 + 6 ÷ (6 − 3) = 34 Problem A customer buys orange juice for $.95 and two apples for $.55 each. She gives the cashier a five dollar bill. How much change should the cashier give the customer? (write the numerical expression and than solve the problem) 5 − (0.95 + 2 × 0.55) $2.95 Solving Problems What you need to know to solve this problem: ◦ Area of a rectangle is length times width ◦ A = L xW Urban Planning Some urban planners specialize in planning entire new towns. These towns are designed for livability, with plenty of open space. The sketch shows the dimensions for a new town called Panorama. Find Panorama’s area. Write the numerical expression prior to calculations. Find more than one way to solve the problem.