1. Chapter 6: Percents Section 4 Solving Percent Problems Using Proportions

2. California Standards  Number Sense 1.0:  Students solve problems involving percentages.  Number Sense 1.3:  Use Proportions to solve problems.

3. Key Vocabulary  Percent:  A RATIO that compares a number to 100.  Example: 35% is EQUAL to 35/100  Proportion:  A mathematical relationship where two ratios are set as equal.  Example: 7/10 = 14/20 OR a/b = c/d  CROSS PRODUCTS PROPERTY (CPP):  A property that states that if there are two ratios that are proportional, the combined products WILL be EQUAL to each other.  a/b = c/d where b and d CANNOT equal ZERO (0).  (a)(d) = (b)(c) -Standard expression  Example: 2/5 = n/25-Proportion where n needs to be found  (2)(25) = (5)(n)-From Bottom to Top crossing diagonally.  50 = 5n-Resulting products. Isolate the variable. Divide out.  n = 10-Resulting answer.

4. The MAGIC FORMULA The Secret to Solving Percent Problems.  The secret to solving Percent Problems relies on the phrasing of the problems and a MAGIC FORMULA.  Within the phrasing itself, you are given a lot of important information.  Read carefully and identify the PERCENT, the PART and the WHOLE. Place these in the correct place within the formula and you can solve using CPP or EF.  The MAGIC FORMULA is used with the elements of the phrasing and will lead to success EVERY time.  The MAGIC FORMULA looks like this:  PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100

5. Finding a Percent  To find a Percent of a Number, it is a straight-forward and easy function to carry out. Here,the basis for solving is based in PROPORTIONS.  To work correctly, you need to ANALYZE the way the question is asked.  Let’s look at the example: What PERCENT of 2000 is 204?  PERCENT tells you that you are solving for an UNKNOWN part (X) of the PERCENTAGE. The word “OF” tells you that the number is the WHOLE. This means “OF” is 2000. The word “IS” tells you that the number is the PART. The “PART” is 204. Place them in the formula and work through.  Using Cross Products Property we solve.  204/2000 = X/100-Note the elements are all placed in the correct places  (204)(100) = (2000)(X)-Use Cross Products Property to begin solving  204,000 = 2000X-Resulting Cross Products  204,000 = 2000X-Dividing each side by 2000 to isolate the variable. 2000 2000  102 = X, or 102%-Resulting answer.

6. Finding A Percent of a Number  Example #1: What percent of 500 is 340?  Magic Formula: PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100  Analyze the problem and identify ALL parts.  500 is the WHOLE. 340 is the PART and the PERCENT is the Unknown (X).  340 = X_-ALL elements placed into formula. 500 100  (340)(100) = (500)(X)-Use Cross Products Property to solve  34,000 = 500X-Divide out the 500 to isolate the variable 500  68 = X, or 68%-Resulting quotient is the answer

7. Finding A Percent of a Number  Example #2: What percent of 80 is 48?  Magic Formula: PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100  Analyze the problem and identify ALL parts.  80 is the WHOLE. 480 is the PART and the PERCENT is the Unknown (X).  48 = X_-ALL elements placed into formula. 80 100  (48)(100) = (80)(X)-Use Cross Products Property to solve  4,800 = 80X-Divide out the 80 to isolate the variable 80 80  60 = X, or 60%-Resulting quotient is the answer

8. Finding a PART  To find a Part of a Number, it is a straight-forward and easy function to carry out. Here,the basis for solving is based in PROPORTIONS.  To work correctly, you need to ANALYZE the way the question is asked.  Let’s look at the example: 30% of 60 is what number?  The PERCENT is stated. Here it is 30%. The word “OF” tells you that the number is the WHOLE. This means “OF” is 60. The word “IS” tells you that the number is the PART. The “PART” is UNKNOWN (X). Place them in the formula and work through.  Using Cross Products Property we solve.  X/60 = 30/100 -Note the elements are all placed in the correct places  (100)(X) = (30)(60) -Use Cross Products Property to begin solving  100X = 1,800 -Resulting Cross Products  100X = 1800 -Dividing each side by 100 to isolate the variable. 100 100  X = 18, or 18% -Resulting answer.

9. Examples of Finding A Part of a Number  Example #1: 70% of 600 is what number?  Magic Formula: PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100  Analyze the problem and identify ALL parts.  600 is the WHOLE, the PERCENT is 70%, the PART is the Unknown (X)  X = 70_-ALL elements placed into formula. 600 100  (100)(X) = (600)(70)-Use Cross Products Property to solve  100X = 42,000-Divide out the 100 to isolate the variable 100 100  X = 420-Resulting quotient is the answer

10. Examples of Finding A Part of a Number  Example #2: 27% of 120 is what number?  Magic Formula: PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100  Analyze the problem and identify ALL parts.  120 is the WHOLE, 27 is the PERCENT, and the PART is the Unknown (X).  48 = X_-ALL elements placed into formula. 80 100  (48)(100) = (80)(X)-Use Cross Products Property to solve  4,800 = 80X-Divide out the 80 to isolate the variable 80 80  60 = X, or 60%-Resulting quotient is the answer

11. Finding the WHOLE  To find a WHOLE of a Number, it is a straight-forward and easy function to carry out. Here,the basis for solving is based in PROPORTIONS.  To work correctly, you need to ANALYZE the way the question is asked.  Let’s look at the example: 30% of what number is 48?  The PERCENT is stated. Here it is 30%. The word “IS” tells you that the number is the PART. The “PART” is 48. The word “OF” tells you that the number is the WHOLE. This means “OF” is the UNKNOWN (X). Place them in the formula and work through.  Using Cross Products Property we solve.  48/X = 30/100 -Note the elements are all placed in the correct places  (48)(100) = (30)(X) -Use Cross Products Property to begin solving  4800 = 30X -Resulting Cross Products  4800= 30X -Dividing each side by 30 to isolate the variable. 30 30  X = 160 -Resulting answer.

12. Examples of Finding A Whole of a Number  Example #1: 40% of what number is 60?  Magic Formula: PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100  Analyze the problem and identify ALL parts.  40 is the PERCENT, 60 is the PART, and the WHOLE is the Unknown (X).  60 = 40-ALL elements placed into formula. X 100  (60)(100) = (40)(X)-Use Cross Products Property to solve  6,000 = 40X-Divide out the 40 to isolate the variable 40 40  1500 = X-Resulting quotient is the answer

13. Examples of Finding A Whole of a Number  Example #2: 56% of what number is 112?  Magic Formula: PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100  Analyze the problem and identify ALL parts.  56 is the PERCENT, 112 is the PART, and the WHOLE is the Unknown (X).  112 = 56-ALL elements placed into formula. X 100  (112)(100) = (56)(X)-Use Cross Products Property to solve  11,200 = 56X-Divide out the 56 to isolate the variable 56 56  200 = X-Resulting quotient is the answer

14. Quick Review  The Basis for solving for Proportions is the MAGIC FORMULA!!!  Goal is to carefully analyze the problem to find the required elements that will be placed within the MAGIC FORMULA.  The MAGIC FORMULA looks like this:  PART = PERCENT OR IS = PERCENT WHOLE 100 OF 100  Magic Formula is pretty failsafe. Work carefully and you will be successful every time.

15. Check for Understanding  Please determine the BEST answer for the following expression.  Carry out ALL work and calculations in your NOTES for later reference  Please write your answer on your wipe boards and wait for the teacher’s signal.  On the count of 3, hold up your wipe boards.

16. C4U Question #1  Question #1:  What percent of 30 is 18?  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

17. C4U Question #2  Question #2:  What is 70% of 500?  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

18. C4U Question #3  Question #3:  30% of what number is 75?.  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

19. C4U Question #3  Question #4:  What percent of 60 is 48?  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

20. C4U Question #3  Question #5:  What is 15% of 300?  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

21. C4U Question #3  Question #6:  30% of what number is 75?.  Please work out the problem within your notes  Write the correct answer on your wipe board.  Wait for Teacher’s Signal.

22. Guided Practice  Students will work on a worksheet/book work, focusing only on the problems assigned by the teacher.  Work carefully, show your problem solving process, and double check all calculations.  Use scratch paper to carry out your work.  Once you have completed the assigned problems, please raise your pencil.  The teacher will then check your work and release you to complete the independent practice.

23. Independent Practice  Once you have been signed off and released to complete Independent Practice, please complete the following assignment: