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# 7.7 Transforming Formulas

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Chapter 7, Section 7: Transforming Formulas

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### 7.7 Transforming Formulas

1. 1. Chapter 7: Section 7: Transforming Formulas January 14 th , 2009 A Weird Concept Day
2. 2. Warm Up: Evaluate each Formula for the values given. <ul><li>Distance: d = rt, r = 80 km/hr, t = 4 hr. </li></ul><ul><li>Perimeter of a rectangle: P = 2l + 2w, l = 9m, w = 7m. </li></ul>D = 320 km P = 32 km
3. 3. Compound Inequalities <ul><li>Compound inequalities are two inequalities joined by the word AND or the word OR . </li></ul><ul><li>X > 4 and X ≤ 6: A solution of a compound inequality joined by AND is any number that makes both inequalities true . </li></ul><ul><li>X ≤ -2 or X > 3: A solution of a compound inequality joined by OR is any number that makes at least one of the inequalities true . </li></ul>
4. 4. Graphing Compound Inequalities <ul><li>X > -3 AND X ≤ 5 </li></ul><ul><li>X > 20 OR X < 19 </li></ul>Hint: Graph them separately for OR compound inequalities. Hint: Figure out where X overlaps, then fill in the middle for AND compound inequalities.
5. 5. Transforming Formulas <ul><li>Remember: Formulas show the relationship between two or more qualities. </li></ul><ul><li>Qualities are variables that stand for stuff. </li></ul><ul><li>Like, Perimeter = P and A = Area. </li></ul><ul><li>Use (+, -, x, ÷) Properties of Equality to transform a formula to represent one quantity in terms of another. </li></ul><ul><li>Basically, rearrange formulas so that they look different but still do the same thing . </li></ul>
6. 6. Solve the Area Formula for L = Length <ul><li>The area formula is A = LW </li></ul><ul><li>Or, Area = Length times Width. </li></ul><ul><li>Solve for Length . </li></ul><ul><li>How do we get L by itself? </li></ul>Division Property of Equality Divide both sides by W . Simplify. Length now equals Area divided by Width . L = A/W
7. 7. Try These : Solve for the variable indicated in Red. <ul><li>P = S + C </li></ul><ul><li>H = ( K /J) </li></ul><ul><li>I = P RT </li></ul>Hint: Undo all of the quantities on the same side of the RED quantity so that all of the non-red quantities are on the opposite side from the RED quantity you’re solving for. Non-Red = RED
8. 8. Multiple Steps Can Be Needed <ul><li>You may need to use more than one step of equality to solve these problems. </li></ul><ul><li>For Example: Solve the Perimeter formula for L. (P = 2 L + 2W) </li></ul><ul><li>P – 2W = 2 L + 2W – 2W  Sub. 2W </li></ul><ul><li>P – 2W = 2 L  Simplify </li></ul><ul><li>(P – 2W)/2 = 2 L /2  Divide by 2 </li></ul><ul><li>(P – 2W)/2 = L  Simplify/Solution </li></ul>
9. 9. Remember! <ul><li>When you are doing multiple steps, you have to apply each step to both sides COMPLETELY! </li></ul>
10. 10. Try These: Solve for the Red Quantity <ul><li>5 A + 7 = B </li></ul><ul><li>P = 2L + 2 W </li></ul><ul><li>Y = ( X /3) + 8 </li></ul>
11. 11. Real-World Examples <ul><li>You plan a 425-mile trip to Bryce Canyon National Park in Utah. You estimate you will average 500 miles/hour. To find about how long the trip will take, solve the distance formula D = RT for t. Then substitute to find the time. </li></ul>It will take you about 8.5 hours to complete the trip.
12. 12. Temperature <ul><li>An exchange student in your class wants to know the Celsius equivalent of 77 °F. First solve the formula F = (9/5) C + 32 for C . Then substitute to find the temperature. </li></ul>77 °F is 25°C.
13. 13. Whose On First? <ul><li>Solve the batting average formula, A = (H/N) for H. Find the number of hits, H, a batter needs in 40 times at bat, N, to have an average of 0.275. </li></ul>H = AN, 11 hits.
14. 14. Assignment #58 <ul><li>Page 367 : 1-15all, and </li></ul><ul><li>Page 364 : 1-9 all (Graphing). </li></ul><ul><li>Easy problems, lots of graphing. </li></ul><ul><li>Remember to graph with elevated arrows and rays. </li></ul><ul><li>24 Problems. </li></ul>