Ratios And Unit Rates

Explanation
A ratio is a comparison of two quantities or numbers. It is a way to express the relationship between two values and is often written as a fraction or with a colon. Ratios are used to compare different quantities and can be used to solve problems involving proportions. Therefore, the correct answer is "ratio".

Explanation
The term "rate" refers to the comparison between two different variables, such as miles to gallons or sandwiches to people. It represents the amount of one variable in relation to another. In this context, rate is the most appropriate term to describe the comparison between these variables.

Explanation
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. This term is commonly used in mathematics and is helpful in solving various real-life problems involving rates and ratios.

Explanation
A proportion is a statement that two ratios are equal. It is a way of comparing two quantities. In a proportion, the ratio of the first two terms is equal to the ratio of the last two terms. This means that if the first ratio is multiplied or divided by a certain number, the same operation must be done to the second ratio in order to maintain their equality. Therefore, a proportion is the correct answer because it represents the concept of two ratios that are equivalent.

Explanation
The word "equal" means that two or more things are the same in quantity, size, value, or importance. In the given options, "equal" is the only word that accurately represents this meaning. "Equivalent" means having the same value or meaning, but it does not necessarily imply that the quantities or sizes are the same. "Various" means different or diverse, which is the opposite of equal. "Total" and "sum" refer to the overall amount or quantity, but they do not necessarily indicate that things are the same. Therefore, "equal" is the correct answer.

Explanation
The correct answer is "simplify" because putting a fraction or ratio in lowest terms means to reduce it to its simplest form by dividing both the numerator and denominator by their greatest common divisor. This process simplifies the fraction or ratio and makes it smaller by removing any common factors between the numerator and denominator.

Explanation
"One fourth" is not the correct way to say a ratio because it represents a fraction rather than a ratio. Ratios compare two quantities using a colon or the word "to," such as "1:4" or "1 to 4." "One out of four" is also an acceptable way to express a ratio. However, "one fourth" is a fraction that represents the division of one quantity by another, not a comparison of two quantities.

Explanation
The ratio 9:12 is equivalent to 3:4 because both ratios can be simplified to the same value. When we divide both numbers in the ratio 9:12 by 3, we get the simplified ratio 3:4. Therefore, 9:12 is equivalent to 3:4.

Explanation
The ratio 24:105 can be simplified to its lowest terms by dividing both numbers by their greatest common divisor, which is 3. When we divide 24 by 3, we get 8, and when we divide 105 by 3, we get 35. Therefore, the ratio 24:105 in lowest terms is 8:35.

Explanation
Percent means out of 100. It is a way to express a fraction or a part of a whole in terms of a hundred. For example, if something is 50 percent, it means it is 50 out of 100. Therefore, the correct answer is 100 because percent is always out of 100.