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W5, , Learning Area, Quarter, , Mathematics, Third, , I. LESSON TITLE, II. MOST ESSENTIAL LEARNING, COMPETENCIES (MELCs), III. CONTENT/CORE CONTENT, IV. LEARNING, Suggested, Time Frame, PHASES, 30 minutes, A. Introduction, , Grade Level, Date, , Nine, , Proportion and Application of Fundamental Theorems of Proportionality, Lesson 1: Describes a proportion M9GE-IIIf-1, Lesson 2: Applies the fundamental theorems of proportionality to solve problems, involving proportions M9GE-IIIf-2, Describing a proportion and solving problems involving proportion, Learning Activities, Let’s find out what you already know about proportion., Answer the following., A. Which of the following pair of pictures is an example of proportion?, , B. There are different sets of ingredients in preparing buko pie. Given below are, the ingredients for pie filling which is good for eight persons., Pie Filling, 1⁄ cup, cornstarch, 3, 1⁄ cup, coconut, water, 2, 1⁄ cup, all-purpose cream, 2, 3⁄ cup, sugar, 4, 4 cups, young coconut meat, If you are asked to prepare for 24 persons, how much coconut water is needed, in preparing the filling?, C. Is there a possible way to find the height of the, flag of the Philippines raised at San Pablo City, Plaza without directly measuring it?, , B. Development, , 60 minutes, , PROPORTION, When we recall the definition of ratio of two numbers, it is the comparison of, two quantities. For any two numbers, x and y, y ≠ 0 the ratio is the quotient, obtained by dividing x and y. The two numbers are called the terms. The ratio can, be written in the following form: 𝑥⁄𝑦(fraction form), x:y(read as “x is to y”),x to y., 6 30, The following ratios can be reduced to the same value: ,, , 4 : 6. Their, 9 45, 2, simplest form is 2 : 3 or . Ratios that can be reduced to the same value are called, 3, equivalent ratios., Example, Given: x = 6, y = 18, z = 15., Give each ratio in simplest form., 𝑥, a., b. y to z, c. x + z : y, 𝑦, Solution, 𝑥, 6, 1, a., =, =, 𝑦 18 3, b. y to z is 18 to 15 or 6 to 5, c. x + z : y is 21 : 18 or 7 : 6, The equation stating that two ratios are equal is called a proportion. In symbols,, 𝑎 𝑐, = , where b and d ≠ 0, or a : b = c : d (read as “a is to b as c is to d”)., 𝑏 𝑑

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IV. LEARNING, PHASES, , Suggested, Time Frame, , Learning Activities, Example 1, , 2, 5, , 4, , =, , 10, , So 2 out 5 is equal to 4 out 10. They are in proportion., Example 2, When four meters of cable wire costs 90 pesos, then:, , 10 meters of that cable wire costs 225 pesos, , 12 meters of that cable wire costs 270 pesos, 4 10, 12, 2, All these ratios: ,, , and, can be simplified as ., 90 222, 270, 45, Thus, the following are proportions:, 4, 10, 12, =, =, 90 222 270, The ratio and proportion have many uses or relationship in our everyday life, such as dealing with the measures of the ingredients in cooking recipes, the, amount of profit earned per sale, enlarging or reducing the size of a drawing,, measuring the height of an object without directly measuring it, and so many, others., APPLICATION OF FUNDAMENTAL THEOREMS OF PROPORTIONALITY, In geometry, we used proportion to compare lengths of segments. To solve for, unknown length, we often used the properties of proportion., Properties of Proportion, 𝑎 𝑐, If a : b = c : d or = , and a, b, c, and d ≠ 0, then each of the following is true:, 𝑏 𝑑, ,  ad = cb, 𝑎, 𝑏, 𝑎, 𝑏,  𝑐 = 𝑑 or 𝑐 = 𝑑, 𝑏, , , , , =, , 𝑏, 𝑎−𝑏, , , If, , 𝑑, , =, , 𝑎, 𝑐, 𝑎+𝑏, 𝑐+𝑑, , 𝑎, , =, , 𝑏, 𝑐, , =, , 𝑑, 𝑐−𝑑, 𝑒, , 𝑑, , 𝑎, , = , and b, d and f ≠ 0, then =, , 𝑐, , =, , 𝑒, , =, , 𝑎+𝑐+𝑒, , = k., , 𝑏, 𝑑, 𝑓, 𝑏, 𝑑, 𝑓, 𝑏+𝑑+𝑓, Here are some examples on how to apply the fundamental theorems of, proportionality to solve problems involving proportions., Example 1, 𝑚 4, Use the proportion, = to complete each proportion., 𝑛 7, 𝑛, 4, 𝑛, 𝑛+𝑚, a. = ___ b. = ___ c. = ___ d., = ___, 7, 𝑚, 𝑚, 𝑚, , Solution, 𝑚, 4 7, 𝑛 7, 𝑛+𝑚 11, =, b., =, c., =, d., =, 7 4, 𝑚 𝑛, 𝑚 4, 𝑚, 4, Example 2, Find the value of x in the following proportions., 9 15, 𝑥+3 9, 𝑥+2 4𝑥, a. =, b. x :6 = 15 : 18, c., =, d., =, 𝑥 20, 4, 2, 3, 6, Solution, 9 15, 1, 1, a. =, → 15 ∙ x = 9 ∙ 20 → 15x = 180 → ( )15x = ( )180 → x = 12, 𝑥 20, 15, 15, 1, 1, b. x :6 = 15 : 18 → 6 ∙ 15 = 18 ∙ x → 90 = 18x → ( )90 = ( )18x → 5 = x or x = 5, 18, 18, 𝑥+3 9, c., = → 4 ∙ 9 = 2 (x + 3) → 36 = 2x + 6 → 36 – (6) = 2x + 6 – (6) → 30 = 2x, 4, 2, 1, 1, → ( ) 30 = ( )(2x) → 15 = x or x = 15, 2, 2, , a., , 𝑛

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IV. LEARNING, PHASES, , Suggested, Time Frame, , Learning Activities, 𝑦, 𝑦+5 9, 𝑦+4 7𝑦, 2𝑦−3 3𝑦−7, 28, =, b., =, c., =, d., =, 21 49, 12, 4, 6, 18, 3, 2, 3. If m :n = 5 : 3, find 3m+ 4n : 6m- 2n., 4. Find the ratio e : f, if 5e2 – 13ef – 6f2 = 0 where e and f ≠ 0., Directions: Answer the following accordingly., 1. How would you describe proportion?, 2. Cite an example where you can apply proportion in your everyday life., Describe how you can you apply the proportion in that situation., 3. If a : b : c = 5 : 3 : 2 where a, b and c > 0, find the values of a, b and c when a2 – b2 c2 = 108., Directions: Choose the letter of the correct answer., 1. The following describe a proportion EXCEPT letter ___., a. 3 : 7 = 18 : 42, , a., , D. Assimilation, , V. ASSESSMENT, , (Learning Activity Sheets for, Enrichment, Remediation or, Assessment to be given on, Weeks 3 and 6), , 20 minutes, , 20 minutes, , b., c., , d., , 2. If, a., , 𝑚, , 𝑛, , 𝑛, , 𝑚, , =, , =, 𝑘, , ℎ, 𝑘, , , which of the following is not true?, , ℎ, , b. km = hn, 3. Find the value of x in, , VI. REFLECTION, , Prepared by:, , 20 minutes, , Edgar V. Tuico, , c., d., , 𝑚, 𝑛, 𝑚, , =, =, , 𝑘, ℎ, 𝑛, , ℎ 𝑘, 5𝑥+4 3𝑥, = ., 10, 5, , a. 5 b. 4 c. 3 d. 2, 4. Find the ratio x : y if 4x2 – 8xy – 5y2 = 0 where x and y≠ 0., a. -1 : 2 or 5 : 2, c. -1 : 1 or 5 : 4, b. 1 : 2 or -5 : 2, d. 1 : 1 or -5 : 4, 5. The length and width of a rectangle whose perimeter is 60 cm are in the ratio, 3 : 2. What is the area of the rectangle?, a. 108 sq. cm, c. 360 sq. cm, b. 216 sq. cm, d. 600 sq. cm, , The learners communicate the explanation of their personal assessment, as indicated in the Learner’s Assessment Card., , The learners will write their personal insights about the lesson in their, notebook using the prompts below:, I understand that ___________________., I realize that ________________________., I need to learn more about __________., Checked by: MA. FILIPINA M. DRIO