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By the end of this topic, students will be able to:
A ratio is a way of comparing two or more numbers. It is often written as a fraction or a colon, and can be represented as a part-to-part comparison (e.g. 3:4) or a part-to-whole comparison (e.g. 3/4). A proportion is a statement that two ratios are equal.
For example, if a recipe requires 3 parts of sugar to 4 parts of flour, the ratio of sugar to flour is 3:4. If we want to make a larger batch of the recipe, we can multiply both parts of the ratio by the same number, for example 6:8. This is an example of scaling.
Another example of ratio and proportion is in design. Imagine a picture of a house that is 3 cm wide and 4 cm tall. If we want to make the picture 6 cm wide, we need to find the corresponding height. We can use the ratio of width to height to find the new height: 6:4 = 3:2. Therefore, the new height is 3 cm x 2 = 6 cm.
A recipe for making a cake requires 2 cups of flour and 3 cups of sugar. What is the ratio of flour to sugar in simplest form?
To find the ratio in simplest form, we need to find the greatest common divisor (GCD) of 2 and 3, which is 1. Therefore, the ratio of flour to sugar is 2:3.
Which ratio is greater, 3:4 or 2:3?
To compare the ratios, we can convert them to equivalent fractions. 3:4 is equal to 3/4, and 2:3 is equal to 2/3. Since 3/4 is greater than 2/3, the ratio 3:4 is greater than 2:3.
A bookshelf is 3 meters long and 2 meters high. If we want to make the bookshelf 6 meters long, how tall will it be?
We can use the ratio of length to height to find the new height: 6:2 = 3:1. Therefore, the new height is 3 meters x 1 = 3 meters.
What is the ratio of flour to sugar in the recipe? A) 2:3 B) 3:2 C) 1:1 D) 4:5
Answer: A) 2:3 Why the distractors fail: B) 3:2 is the inverse of the correct answer, C) 1:1 is a ratio where the two parts are equal, and D) 4:5 is a different ratio altogether.
Which ratio is greater, 5:6 or 4:5? A) 5:6 B) 4:5 C) 2:3 D) 3:4
Answer: A) 5:6 Why the distractors fail: B) 4:5 is the inverse of the correct answer, C) 2:3 is a different ratio altogether, and D) 3:4 is a ratio where 3 is greater than 4, but 5 is not greater than 4.
What is the ratio of width to height in the picture of the house? A) 3:4 B) 4:3 C) 2:3 D) 1:1
Answer: A) 3:4 Why the distractors fail: B) 4:3 is the inverse of the correct answer, C) 2:3 is a different ratio altogether, and D) 1:1 is a ratio where the two parts are equal.
A recipe for making a cake requires 2 cups of flour and 3 cups of sugar. If we want to make a larger batch of the recipe, what is the new ratio of flour to sugar? A) 4:6 B) 6:8 C) 3:4 D) 2:3
Answer: B) 6:8 Why the distractors fail: A) 4:6 is a different ratio altogether, C) 3:4 is the original ratio, and D) 2:3 is the original ratio.
A bookshelf is 3 meters long and 2 meters high. If we want to make the bookshelf 6 meters long, how tall will it be? A) 2 meters B) 3 meters C) 6 meters D) 1 meter
Answer: B) 3 meters Why the distractors fail: A) 2 meters is the original height, C) 6 meters is the new length, and D) 1 meter is not related to the problem.
Write the ratio of 6:8 in simplest form.
Answer: 3:4
Compare the ratios 3:4 and 2:3. Which ratio is greater?
Answer: 3:4 is greater than 2:3.
A recipe for making a cake requires 2 cups of flour and 3 cups of sugar. If we want to make a larger batch of the recipe, what is the new ratio of flour to sugar?
Answer: 4:6
Answer: 3 meters
Write the ratio of width to height in the picture of the house.
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