Unit Rate and Ratio Problems

A unit rate is a comparison of two different quantities when they are combined together. It is expressed as a quantity of one. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, to divide 2/3 by 1/4, you multiply 2/3 by 4/1, which equals 8/3.

A ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, the ratio of 2 to 3 can be written as 2:3.

To find the total number of items per group, divide the total number of items by the number of groups. For example, if there are 720 students and 30 buses, each bus has 720 ÷ 30 = 24 students.

The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3.

To solve a division problem with decimals, you can multiply both the dividend and the divisor by 10, 100, etc., to eliminate the decimal, then divide as usual. For example, 19.84 ÷ 4.6 can be converted to 198.4 ÷ 46.

To simplify a fraction means to reduce it to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). For example, 8/12 simplifies to 2/3.

Ratios can be used in real-world situations such as cooking, where a recipe may require a specific ratio of ingredients. For example, a recipe might call for a ratio of 2 cups of flour to 1 cup of sugar.

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1/4 = 0.25.

A ratio compares two quantities, while a rate compares two quantities with different units. For example, speed is a rate (miles per hour), while a ratio could compare the number of boys to girls.