Lesson 4.2: Ratios And Unit Rates

A ratio is a comparison between two quantities or numbers. It represents the relationship or proportion between the two quantities. In a ratio, the quantities are compared using a colon or a fraction. For example, a ratio of 2:3 represents that the first quantity is two-thirds of the second quantity. Ratios are used to compare and analyze data in various fields such as mathematics, finance, and statistics.

The correct answer is "simplify" because when a fraction or ratio is in its lowest terms, it means that it has been simplified or reduced as much as possible. This involves dividing both the numerator and denominator by their greatest common divisor to make the fraction or ratio smaller and easier to work with. Therefore, "simplify" is the best explanation for the given correct answer.

The word "equal" means that two or more things are the same in quantity, size, value, or importance. It suggests that there is no difference or distinction between the things being compared. In the context of the given options, "equal" is the most appropriate choice as it best conveys the idea of things being identical or having the same value.

Percent means "out of 100". It is a way of expressing a fraction or a portion of a whole in terms of 100 equal parts. For example, 50 percent means 50 out of 100, or half of the whole. Therefore, the correct answer is 100 because percent is based on dividing a value by 100.

The term "unit rate" refers to the rate at which one quantity is compared to one unit of another quantity. It is used to find out how much one quantity would be in terms of a specific unit, such as per gallon, per ounce, or per person. It is a ratio that helps in comparing different quantities on a common scale and is often used in calculations and conversions.

The term "rate" refers to the comparison between two different variables, such as miles to gallons or sandwiches to people. It represents how one quantity changes in relation to another. A rate is often expressed as a ratio, but it specifically emphasizes the comparison between different units or measurements. Therefore, "rate" is the most appropriate term to describe the given scenario.

The phrase "one fourth" is not the correct way to express a ratio. Ratios are typically expressed using numbers separated by a colon (1:4), the word "to" (1 to 4), or the phrase "out of" (1 out of 4). However, "one fourth" is a fraction, not a ratio.

A proportion is a statement that two ratios are equivalent. It compares two ratios and states that they are equal to each other. In other words, a proportion shows that the relationship between the two ratios remains the same. Therefore, the answer "proportion" is correct because it accurately describes the concept of two ratios being equivalent.

The ratio 9:12 is equivalent to 3:4 because both ratios can be simplified to the same fraction. When we divide both 9 and 12 by their greatest common divisor, which is 3, we get 3:4. Therefore, 9:12 is equivalent to 3:4.

The ratio 24:105 can be simplified by dividing both numbers by their greatest common divisor, which is 3. After simplification, the ratio becomes 8:35.