Write if true or false. A. The cost of 16 pineapples is ₹432. So, the cost of 1 pineapple is ₹26. B. 15 bottles of juice cost ₹225. The cost of 1 bottle of juice is ₹15.

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Asked on March 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-26T01:38:04.462Z

Lesson 1: Introducing Proportion 1. Fill in the blanks. A. The simplest form of the ratio 24:72 is Step 1: Find the greatest common divisor (GCD) of 24 and 72. 24 = 24 × 1 72 = 24 × 3 The GCD is 24. Step 2: Divide both parts of the ratio by the GCD. (24)/(24) : (72)/(24) = 1:3 The simplest form is 1:3. B. 81:153 in its simplest form is Step 1: Find the GCD of 81 and 153. 81 = 9 × 9 153 = 9 × 17 The GCD is 9. Step 2: Divide both parts of the ratio by the GCD. (81)/(9) : (153)/(9) = 9:17 The simplest form is 9:17. C. The simplest form of 132:33 is Step 1: Find the GCD of 132 and 33. 132 = 33 × 4 33 = 33 × 1 The GCD is 33. Step 2: Divide both parts of the ratio by the GCD. (132)/(33) : (33)/(33) = 4:1 The simplest form is 4:1. 2. Write if the ratios are in proportion or not. To check for proportion, we compare the simplified forms of the ratios or cross-multiply. A. 15:45 and 21:63 Step 1: Simplify the first ratio. (15)/(45) = (1)/(3) Step 2: Simplify the second ratio. (21)/(63) = (1)/(3) Since (1)/(3) = (1)/(3), the ratios are in proportion. The ratios are in proportion. B. 14:15 and 56:60 Step 1: Simplify the first ratio. (14)/(15) This ratio is already in simplest form. Step 2: Simplify the second ratio. (56)/(60) = (56 ÷ 4)/(60 ÷ 4) = (14)/(15) Since (14)/(15) = (14)/(15), the ratios are in proportion. The ratios are in proportion. C. 20 L:100 mL and 50 L:250 L Step 1: Convert units for the first ratio to be consistent. 1 L = 1000 mL. 20 L : 100 mL = (20 × 1000) mL : 100 mL = 20000 mL : 100 mL Simplify the first ratio. (20000)/(100) = (200)/(1) Step 2: Simplify the second ratio. 50 L250 L = (50 ÷ 50)/(250 ÷ 50) = (1)/(5) Since (200)/(1) ≠ (1)/(5), the ratios are not in proportion. The ratios are not in proportion. D. 65 people:35 people and ₹600:₹300 Step 1: Simplify the first ratio. (65)/(35) = (65 ÷ 5)/(35 ÷ 5) = (13)/(7) Step 2: Simplify the second ratio. (600)/(300) = (2)/(1) Since (13)/(7) ≠ (2)/(1), the ratios are not in proportion. The ratios are not in proportion. 3. Ryan bought 16 bananas for ₹120 and Kate bought 18 bananas for ₹144. Did they buy the bananas at the same price? Write yes or no. Step 1: Calculate the price per banana for Ryan. Ryan's price per banana = Total costNumber of bananas = (₹120)/(16 bananas) = ₹7.50 per banana Step 2: Calculate the price per banana for Kate. Kate's price per banana = Total costNumber of bananas = (₹144)/(18 bananas) = ₹8.00 per banana Step 3: Compare the prices. Since ₹7.50 ≠ ₹8.00, they did not buy the bananas at the same price. The answer is no. Lesson 2: Proportional Terms 1. Write 3 equivalent ratios for 7:12. To find equivalent ratios, multiply both terms by the same non-zero number. Step 1: Multiply by 2. 7 × 2 : 12 × 2 = 14:24 Step 2: Multiply by 3. 7 × 3 : 12 × 3 = 21:36 Step 3: Multiply by 4. 7 × 4 : 12 × 4 = 28:48 Three equivalent ratios are 14:24, 21:36, 28:48. 2. Find out if the ratios are in proportion by comparing the product of the means and the product of the extremes. If they are, write them in proportion. For a:b::c:d, they are in proportion if ad = bc. A. 7:14 and 6:12 Step 1: Identify extremes and means. Extremes are 7 and 12. Means are 14 and 6. Step 2: Calculate the product of the extremes. 7 × 12 = 84 Step 3: Calculate the product of the means. 14 × 6 = 84 Since 84 = 84, the ratios are in proportion. In proportion: 7:14::6:12. B. 5:8 and 25:40 Step 1: Identify extremes and means. Extremes are 5 and 40. Means are 8 and 25. Step 2: Calculate the product of the extremes. 5 × 40 = 200 Step 3: Calculate the product of the means. 8 × 25 = 200 Since 200 = 200, the ratios are in proportion. In proportion: 5:8::25:40. C. 9:12 and 99:112 Step 1: Identify extremes and means. Extremes are 9 and 112. Means are 12 and 99. Step 2: Calculate the product of the extremes. 9 × 112 = 1008 Step 3: Calculate the product of the means. 12 × 99 = 1188 Since 1008 ≠ 1188, the ratios are not in proportion. The ratios are

Accepted Answer · 2026-03-26T01:38:04.462Z

Lesson 1: Introducing Proportion 1. Fill in the blanks. A. The simplest form of the ratio 24:72 is Step 1: Find the greatest common divisor (GCD) of 24 and 72. 24 = 24 × 1 72 = 24 × 3 The GCD is 24. Step 2: Divide both parts of the ratio by the GCD. (24)/(24) : (72)/(24) = 1:3 The simplest form is 1:3. B. 81:153 in its simplest form is Step 1: Find the GCD of 81 and 153. 81 = 9 × 9 153 = 9 × 17 The GCD is 9. Step 2: Divide both parts of the ratio by the GCD. (81)/(9) : (153)/(9) = 9:17 The simplest form is 9:17. C. The simplest form of 132:33 is Step 1: Find the GCD of 132 and 33. 132 = 33 × 4 33 = 33 × 1 The GCD is 33. Step 2: Divide both parts of the ratio by the GCD. (132)/(33) : (33)/(33) = 4:1 The simplest form is 4:1. 2. Write if the ratios are in proportion or not. To check for proportion, we compare the simplified forms of the ratios or cross-multiply. A. 15:45 and 21:63 Step 1: Simplify the first ratio. (15)/(45) = (1)/(3) Step 2: Simplify the second ratio. (21)/(63) = (1)/(3) Since (1)/(3) = (1)/(3), the ratios are in proportion. The ratios are in proportion. B. 14:15 and 56:60 Step 1: Simplify the first ratio. (14)/(15) This ratio is already in simplest form. Step 2: Simplify the second ratio. (56)/(60) = (56 ÷ 4)/(60 ÷ 4) = (14)/(15) Since (14)/(15) = (14)/(15), the ratios are in proportion. The ratios are in proportion. C. 20 L:100 mL and 50 L:250 L Step 1: Convert units for the first ratio to be consistent. 1 L = 1000 mL. 20 L : 100 mL = (20 × 1000) mL : 100 mL = 20000 mL : 100 mL Simplify the first ratio. (20000)/(100) = (200)/(1) Step 2: Simplify the second ratio. 50 L250 L = (50 ÷ 50)/(250 ÷ 50) = (1)/(5) Since (200)/(1) ≠ (1)/(5), the ratios are not in proportion. The ratios are not in proportion. D. 65 people:35 people and ₹600:₹300 Step 1: Simplify the first ratio. (65)/(35) = (65 ÷ 5)/(35 ÷ 5) = (13)/(7) Step 2: Simplify the second ratio. (600)/(300) = (2)/(1) Since (13)/(7) ≠ (2)/(1), the ratios are not in proportion. The ratios are not in proportion. 3. Ryan bought 16 bananas for ₹120 and Kate bought 18 bananas for ₹144. Did they buy the bananas at the same price? Write yes or no. Step 1: Calculate the price per banana for Ryan. Ryan's price per banana = Total costNumber of bananas = (₹120)/(16 bananas) = ₹7.50 per banana Step 2: Calculate the price per banana for Kate. Kate's price per banana = Total costNumber of bananas = (₹144)/(18 bananas) = ₹8.00 per banana Step 3: Compare the prices. Since ₹7.50 ≠ ₹8.00, they did not buy the bananas at the same price. The answer is no. Lesson 2: Proportional Terms 1. Write 3 equivalent ratios for 7:12. To find equivalent ratios, multiply both terms by the same non-zero number. Step 1: Multiply by 2. 7 × 2 : 12 × 2 = 14:24 Step 2: Multiply by 3. 7 × 3 : 12 × 3 = 21:36 Step 3: Multiply by 4. 7 × 4 : 12 × 4 = 28:48 Three equivalent ratios are 14:24, 21:36, 28:48. 2. Find out if the ratios are in proportion by comparing the product of the means and the product of the extremes. If they are, write them in proportion. For a:b::c:d, they are in proportion if ad = bc. A. 7:14 and 6:12 Step 1: Identify extremes and means. Extremes are 7 and 12. Means are 14 and 6. Step 2: Calculate the product of the extremes. 7 × 12 = 84 Step 3: Calculate the product of the means. 14 × 6 = 84 Since 84 = 84, the ratios are in proportion. In proportion: 7:14::6:12. B. 5:8 and 25:40 Step 1: Identify extremes and means. Extremes are 5 and 40. Means are 8 and 25. Step 2: Calculate the product of the extremes. 5 × 40 = 200 Step 3: Calculate the product of the means. 8 × 25 = 200 Since 200 = 200, the ratios are in proportion. In proportion: 5:8::25:40. C. 9:12 and 99:112 Step 1: Identify extremes and means. Extremes are 9 and 112. Means are 12 and 99. Step 2: Calculate the product of the extremes. 9 × 112 = 1008 Step 3: Calculate the product of the means. 12 × 99 = 1188 Since 1008 ≠ 1188, the ratios are not in proportion. The ratios are

Write if true or false. A. The cost of 16 pineapples is ₹432. So, the cost of 1 pineapple is ₹26. B. 15 bottles of juice cost ₹225. The cost of 1 bottle of juice is ₹15.

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Write if true or false. A. The cost of 16 pineapples is ₹432. So, the cost of 1 pineapple is ₹26. B. 15 bottles of juice cost ₹225. The cost of 1 bottle of juice is ₹15.

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