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Algebra Readiness

In this lesson, we explore essential algebraic formulas and concepts, starting with variables, which are letters representing one or more numbers. We will discuss formulas for finding the perimeter and area of rectangles and squares, as well as calculating distance, rate, and time. Examples will illustrate how to apply these formulas in real-life scenarios, such as calculating the perimeter of a soccer field or the total cost of items purchased. This foundational knowledge is crucial for success in algebra and its applications.

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Algebra Readiness

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  1. Algebra Readiness Chapter 1 Section 3

  2. Lesson 1.3 Use Formulas Vocabulary and Concepts: A variable is a letter used to represent one or more numbers. A formula gives a relationship between two or more variables. Some common formulas are as follows:

  3. Perimeter and Area of a Rectangle The perimeterp of a rectangle with length l and width w is : P=2l + 2w The areaA of a rectangle with length l and width w is: A = lw

  4. Perimeter and Area of a Square The perimeterp of a square with side length s is: P =4s The areaA of a square with side length s is: A = s²

  5. Distance, Rate, and Time Distance traveled d is equal to the speed (rate of travel) r times the travel timet. d=rt

  6. Total Cost The total costT of n items is the costc of one item (the unit cost) times the number of items. T=cn

  7. Example 1 SOLUTION Write perimeter formula. P 2l + 2w = ( ) ( ) + 2 100 2 64 Substitute 100 for l and 64 for w. = 200 + 128 Multiply. = Add. 328 = Finding Perimeter and Area International soccer is played on a rectangular field that has a length of 100 meters and a width of 64 meters. What are the perimeter and the area of the soccer field?

  8. You Try: A picture frame holds a picture that has a length of 6 inches and a width of 4 inches. What are the perimeter and the area of the picture?

  9. Answer: What is the length? 6 in. What is the width? 4 in. What is the formula for perimeter for this shape? P= 2l + 2w P = 2(6) + 2(4) = 12 + 8 = 20 in. What is the formula for area for this shape? A=lw A=6(4) = 24 in.²

  10. Example 2: Finding distance traveled. A sea turtle travels at an average rate of about 20 kilometers per day. How far can a sea turtle travel in 4 days? d = rt = 20 · 4 = 80 km Write the formula for distance traveled. Substitute 20 for r and 4 for t. Multiply. A sea turtle can travel 80 kilometers in 4 days.

  11. Example 3: Finding total cost. A school is purchasing 35 microscopes that cost $119 each for the science department. What is the total cost? T = cn = 119 · 35 = 4165 Write the formula for total cost. Substitute 119 for c and 35 for n. Multiply. The total cost for 35 microscopes that cost $119 each is $4165.

  12. You Try: Kayla bought 26 jars of poster paint. She paid $3 for each jar. What was the total cost?

  13. Answer: What is the formula for finding total cost? T = cn What is the cost of one item? $3 What is the number of items? 26 T = 3 · 26 = $78

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