Ratio, Rate, and Proportion PDF

RATIO, RATE AND PROPORTION LESSON OBJECTIVES 01 Define ratio, and proportion; and Solve word problems involving 02 ratio and proportion. INTRODUCTION  01 RATIOS RATIO is a comparison between two or more numbers it indicates the...

RATIO, RATE AND PROPORTION LESSON OBJECTIVES 01 Define ratio, and proportion; and Solve word problems involving 02 ratio and proportion. INTRODUCTION  01 RATIOS RATIO is a comparison between two or more numbers it indicates the relationship of each quantity to each other. RATIOS example of ratios: ANTECEDENT 3:5 CONSEQUENT RATIOS Ratios can be shown in different ways: using the ":" or “is to” in order to separate the values PART TO PART It compares the number of one It is a comparison of quantity against the two quantities based total quantity of a on the total quantity whole. of a whole. PART TO WHOLE RATIOS AS FRACTION A ratio can also be written as fraction If the ratio is a part-to-whole ratio we simply consider the antecedent as the numerator and the consequent as the denominator 2 2:3 3 RATIOS AS FRACTION A ratio can also be written as fraction A part-to-part ratio is actually converted to two fractions, each equivalent to a part-to-whole ratio for each of the subsets. For example, let’s convert the ratio of 1 peach to 3 oranges in a fruit basket, or 1:3, to fractions. S1: First, find the denominator. By adding the numerals of the ratio S2: Then, put each part of the ratio over the denominator to find the fractions. Therefore, ¼ of the fruit in the basket are peaches and ¾ of the fruit in the basket are oranges. RATIO IN SIMPLEST FORM TAKE NOTE!!! Ratios must always be reduced in its simplest form but make sure both terms are in the same unit. SIMPLIFY THE FOLLOWING RATIOS: 8kg to 12kg 2:3 3 Days to 2 Weeks 3 Days to 14 Days 16 Inches to 3 Feet 16 in. to 36 in. (1 foot = 12 Inches) 4:9 RATE is a special ratio which refers to a comparison of two quantities having different units. It is usually presented as a fraction or the word “per”. THE UNIT RATE The Unit Rate is the rate in which the denominator of the fraction is 1. To find the unit rate, simply divide the numerator by the denominator and copy the unit of both values and present it with a bar or “per” LET’S PRACTICE Php 285 for 4 Kg 285 (𝑝𝑟𝑖𝑐𝑒) = Php71.25/kg 4 𝑘𝑔 125 km for 13L of gas 125𝑘𝑚 = 9.62km/L 13 𝐿 21.5kg of beef for Php8,236.80 8,236.80 (𝑝𝑟𝑖𝑐𝑒) = Php 383.11/kg 21.5 𝑘𝑔 PROPORTION is two ratios which have been set equal to each other. COMPONENTS OF A PROPORTION A:B=C:D The symbol A, B, C, D are the terms of the proportion. The inner terms are called as the Means and the outer terms are called as the Extremes THE LAW OF PROPORTION The law states that the product of the means is always equal to the product of the extremes, therefore in the proportion, a : b = c : d; axd=bxc TYPES OF PROPORTIONS Direct Proportion - In a direct proportion, if the value of one term increases the other would also increase and vice versa. SOLVING MISSING TERM Steps in Solving the Missing Term 1. Identify which term is missing 2. Place the terms in an equation form 3. Follow the formula: (a : b = c : d) ad = bc LET’S PRACTICE Solve the missing term 5 : x = 31 : 155 31𝑥 = 5 × 155 31𝑥 = 775 775 𝑥= 31 𝒙 = 𝟐𝟓 LET’S PRACTICE Solve the missing term 7 21 = 7 ∶ 4 = 21 ∶ 𝑥 4 𝑥 7𝑥 = 4 × 21 7𝑥 = 84 84 𝑥= 7 𝒙 = 𝟏𝟐 LET’S PRACTICE Solve the missing term How many cups of x ∶ 120 = 2 ∶ 15 orange juice powder are 15𝑥 = 2 × 120 needed to prepare an orange drink of 120 cups 15𝑥 = 240 if the ratio of juice 240 powder to water is 2 to 𝑥= 15 cups? 15 𝒙 = 𝟏𝟔 𝒄𝒖𝒑𝒔 TYPES OF PROPORTIONS Inverse Proportion - a number is inversely proportionate to another if its value increases the other would decrease and vice versa. SOLVING INVERSE PROPORTION Steps in Missing term in a Inverse Proportion 1. Represent each term as “x” and “y” 2. Follow the set of formula given to identify each component. 𝑐 𝑐 C – Constant 𝑐 = 𝑥𝑦 ; 𝑥 = ; 𝑦 = X – First Term 𝑦 𝑥 Y- Second Term LET’S PRACTICE 𝑥1 − 24 𝑑𝑎𝑦𝑠, 𝑥2 − ? Solve the missing term 𝑦1 − 6 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 If it takes 24 days 𝑦1 − 12 𝑤𝑜𝑟𝑘𝑒𝑟𝑠 C − 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 for 6 workers to finish a job, how S1: get the S2: solve for the 𝑥2 many days will it value of 𝑐 constant 𝑥2 = take for 12 workers 𝑦 C = xy on the same job? C = 24(6) 144 C = 144 = 12 = 12 𝑑𝑎𝑦𝑠 TYPES OF PROPORTIONS Partitive Proportion - is a proportion of a quantity being distributed or divided unequally into two or more parts. SOLVING PARTITIIVE PROPORTION Steps in Solving Partitive Proportion 1. Add all the terms of the proportion 2. Use the sum as the denominator and the term as the numerator. 3. Multiply the fraction of each term of the ratio to the whole 4. Validate the amount of each proportion must be the same as the amount of the whole LET’S PRACTICE If 5,000 shirts are manufactured in 3 different sizes: Small, Medium and Large in the ratio of 3 : 5 : 2 respectively. What is the number of each shirt for each size? S1: add up all the terms of the ratio: 3 + 5 + 2 = 10 S2: Use the sum as the denominator of each ratio and the term as the numerator 3 5 2 𝑆𝑀𝐴𝐿𝐿 , 𝑀𝐸𝐷𝐼𝑈𝑀. 𝐿𝐴𝑅𝐺𝐸 10 10 10 LET’S PRACTICE If 5,000 shirts are manufactured in 3 different sizes: Small, Medium and Large in the ratio of 3:5:2 respectively. What is the number of each shirt for each size? S3: Multiply the fraction of each term of the ratio to the whole 3 S4: Validate! small = × 5000 = 1500 𝑠ℎ𝑖𝑟𝑡𝑠 1,500 + 2,500 +1,000 = 10 5,000 5 medium = × 5000 = 2500 𝑠ℎ𝑖𝑟𝑡𝑠 10 2 large = × 5000 = 1000 𝑠ℎ𝑖𝑟𝑡𝑠 10 PRACTICE EXERCISE If it takes 20 days and 8 workers to finish a job, how many days will it take 10 workers to finish the same job? PRACTICE EXERCISE A vehicle is moving at an average speed and travelled 245 kilometers in 4 hours. How long will it take the vehicle to travel 567 kilometers? PRACTICE EXERCISE Maria is baking bread based on a recipe using 8 cups of flour. If she used white and wheat flour in the ratio 5 : 9, how many cups of white and wheat flour did she use?