DIRECT PROPORTION Learning Objectives: After implementing this lesson students will be able to : 1. Comprehend a direct proportion 2. Find a value based on a direct proportion 3. Calculating direct proportion by unit value 4. Calculating direct proportion by proportion The characters building: Discipline, respect, diligence and responsibility. Description: To be easier in comprehending direct proportion, see following description! IIn a grocery shop the price of 1 kg of rice is Rp.7, a. If Mrs. Ani buys 2 kg, how much will Mrs. Ani pay them? b. How many rupiahs must Mrs. Ani pay if she wants to buy 5 kg of rice? Price list and amount of rice can be presented in the following table. 17, , , , , , ,000 The proportion of 2 kg of rice to 3 kg of rice is 2 : 3 The proportion of price 2 kg rice to 3 kg rice is 14,000 : 21,000 = 2 : 3 (simplified by dividing it by 7,000) The proportion of 8 kg of rice to 10 kg of rice is 8 : 10 = 4 : 5 The proportion of price 8 kg of rice to price of 10 kg of rice is 56,000 : 70,000 = 4 : 5 (simplified by dividing it by 14,000) If we observe every two corresponding lines in the table, we will see that the proportion of the amount of rice and the price of rice is the same, that is: 1 : 2=7,000 : 14,000 2 : 3=14,000 : 21,000 3 : 4=21,000 : 28,000 4 : 5=28,000 : 35,000 8 : 10=56,000 : 70,000 and so forth. The more rice bought, the higher its price. Proportion of amount of rice and its price is called Direct proportion. THE GROUPS : 1. Group 1 : Taufik Iqbal, Adyo P, Aezel L R, dan Hadyan N F. 2. Group 2 : Rafiedhia Abel, M Ari A, M Irsyad S, dan Hendra G. 3. Group 3 : Nabila P, Della D, Dian R H, dan Kholifah. 4. Group 4 : Zahrul I S, Fitria P S, Hana N F, dan Naufal Izzul I. 5. Group 5 : Vidya V, Kiki N A, Ratna S P, dan Shella D W. 6. Group 6 : Rosa H N M, Mentari A P, Rosipa, dan Sylviana M Y WORK SHEET Discuss and Solve the Following Problems ! 1. If price for 3 breads is Rp.12,000.00, what is the price for 7 of breads ? 2. Andi runs for 6 km in 30 minutes at constant speed. What is distance he reaches for 3/4 hours ? Calculating the Direct Proportion By Unit Value By Proportion Calculating the Direct Proportion a. By Unit Value To comprehend calculation of direct proportion by unit value, pay attention to following problem example: IIf price for 3 breads is Rp.12,000.00, what is the price for 7 of breads ? AAnswer: oToThe unit price of bread is oToThe price for 7 breads is = 7 x Rp.4, = Rp.28, So, the price for 7 breads is Rp.28, = Rp.4,000.00 PROBLEM EXAMPLES SOLVE BY UNIT VALUE THE PROBLEMS BELOW ! 1. Andi runs for 6 km in 30 minutes at constant speed. What is distance he reaches for hours? Answer: hours = x 60 minutes = 45 minutes. 6 km = 6000 m(1 km = 1000 m) o The unit distance of speed Andi runs: o The distance which Andi reaches for hours is = 200 x 45 = 9000 m = 9 km So, the distance Which Andi reaches for hours is 9 km. = 200 meters/minutes Definition of Direct Proportion The problems above are examples of direct proportion. Proportion of amount of rice and its price is called Direct proportion. Proportion of amount of breads and its price is called Direct proportion. Proportion of times of Andis runs and the distance that Andi reaches is called Direct proportion. Generally, if proportion direct with proportion then =, with a, b, c, and d positive rational number. 2. Complete the table price below ! Calculating the Direct Proportion 2. By Proportion See the table list price of rice below ! From above table, to define the amount of rice if the price that must paid is Rp.28,000.00, We can calculate it by proportion, that is: Let: the amount of rice that will define = x, then 3 21,000 x 28,000 7, , ,000 28,000 = 3 21,000 x 28,000 21,000x = 3.(28,000) 21,000x = 84,000 x = 84,000 21,000 x = 4 Therefore, the amount of rice if the price that must paid is Rp.28,000.00, is 4 kg. = PROBLEM EXAMPLES SOLVE BY PROPORTION THE PROBLEMS BELOW ! 1. The price of 6 kg of grapes is Rp.90, What is the price of 9 kg of grapes? Answer: Let: the price of 9 kg of grapes = x then, ,000 x 6x = 9.(90,000) 6x = 810,000 x = 810,000 6 x = 135,000 Therefore, the price of 9 kg of grapes is Rp.135, = 2. A person walks 60 steps to travel the distance of 24 m. how many steps the person walks if he travelled 320 m? AAnswer: Let: the number of steps the person walks if he travelled 320 m = b then b b = 60 x b = 19,200 b = 19, b = 800 Therefore, the number of steps the person walks if he travelled 320 m is 800 steps. = EXERCISE 1 1. Determine the unit price of: a. 13 liters of oil, which cost Rp.61, b. A dozen eggs, which cost Rp.9, c. 86 apples, which cost Rp.154, Five bananas are Rp.3, a. If you have Rp.1, how many bananas can you buy? b. How much do you pay for 27 bananas? 3. Wage that will be received by a person working for 8 hours is Rp.35, If he receives of Rp.1,094,700.00, how long has he worked? THANK YOU VERY MUCH FOR YOUR ATTENTION MAY GOD BLESS OUR SCIENCE ALWAYS SPIRIT TO STUDY SEE YOU.,., WASSALAMUALAIKUM WR. WB. EXERCISE 2 1.Every week a television channel broadcast two live football matches. How many times will the TV channel broadcast live football matches in a year (1 year = 52 weeks) 2.Fifteen litres of can be used for 120 km. If you have 12 litres of petrol, how many kilometres can you reach? 3.Mrs. Dina needs kg flour for 15 cakes. If Mrs. Dina want to make 75 cakes, how many kilograms of flour does she need? 4.Rent of a hotel room for 5 days is Rp.750, what is rental cost for 11 days? 5.Wage that will be received by a person working for 8 hours is Rp.35, If he receives of Rp.1,094,700.00, how long has he worked?