Name: Date: Unit 6: Similar Triangles Homework 1: Ratio & Proportion Bell: 2.30 treadmills to 36 elliptical machines Directions. Write the ratio in simplest form. 1. 28 elementary schools to 16 middle schools EX 10341 To 4 4 3. 18 buses to 66 cars 4. 180 red marbles to 145 blue marbles 6. In the word FLASHLIGHT what
The correct answer and explanation is:
Sure, let’s solve each ratio and provide an explanation:
1. 28 elementary schools to 16 middle schools
- Simplified Ratio: The ratio is 28:1628:16. To simplify, find the greatest common divisor (GCD) of 28 and 16, which is 4. So, divide both sides of the ratio by 4: 284:164=7:4\frac{28}{4} : \frac{16}{4} = 7:4 Answer: 7:4
2. 18 buses to 66 cars
- Simplified Ratio: The ratio is 18:6618:66. Find the GCD of 18 and 66, which is 6. Divide both sides by 6: 186:666=3:11\frac{18}{6} : \frac{66}{6} = 3:11 Answer: 3:11
3. 180 red marbles to 145 blue marbles
- Simplified Ratio: The ratio is 180:145180:145. Find the GCD of 180 and 145, which is 5. Divide both sides by 5: 1805:1455=36:29\frac{180}{5} : \frac{145}{5} = 36:29 Answer: 36:29
4. In the word “FLASHLIGHT”
- Ratio Explanation: In the word “FLASHLIGHT,” you could be asked to find the ratio of letters of different types (e.g., vowels to consonants). The vowels in “FLASHLIGHT” are A, I, and I, so there are 3 vowels. The consonants are F, L, S, H, L, G, H, T, so there are 7 consonants. The ratio of vowels to consonants is 3:73:7. Answer: 3:7
Explanation of Ratios & Proportions:
Ratios compare two quantities and are written as fractions, colons, or words. In each of these problems, we are simplifying the given ratios. Simplification is the process of reducing the numbers to their smallest equivalent form by dividing both terms by their greatest common divisor (GCD). For example, in the ratio 28:1628:16, both numbers can be divided by 4 to simplify the ratio to 7:47:4.
Proportions are equations that show two ratios are equal. For instance, if we have 3:73:7 and 6:146:14, these ratios are in proportion because both can be simplified to 3:73:7.
In everyday situations, ratios can be used to compare things like amounts of ingredients in a recipe, students in a classroom, or even the number of machines in a gym, as seen in this example with treadmills and elliptical machines. Understanding ratios helps us see relationships and make comparisons between different quantities.
By simplifying ratios, we can better understand and analyze situations, especially when the numbers involved are large or not easy to compare directly.