1st Semester Final

A unit rate is a comparison of two different quantities when they are combined together. It is expressed as a quantity per one unit of another quantity.

To find the unit rate, divide the total quantity by the number of units. For example, if Johnny read 300 words in 6 minutes, the unit rate is 300 ÷ 6 = 50 words per minute.

Two ratios are proportional if they can be expressed as equivalent fractions. For example, $$\frac{4}{7}$$ and $$\frac{2}{4}$$ are not proportional because they do not simplify to the same value.

To find the cost of one item, divide the total cost by the number of items. For example, if Sally bought 3 candy bars for $18, the cost per candy bar is 18 ÷ 3 = $6.

An inequality is a mathematical statement that compares two expressions and shows that one is less than, greater than, less than or equal to, or greater than or equal to the other.

An inequality can be represented on a number line or a coordinate plane, showing the range of values that satisfy the inequality. For example, the inequality $$k < 3$$ would be represented with an open circle at 3 and a line extending to the left.

A ratio is a comparison of two quantities, while a rate is a specific type of ratio that compares two quantities with different units, such as speed (miles per hour) or price (cost per item).

To determine if a graph represents an inequality, check if the shaded region corresponds to the values that satisfy the inequality. For example, if the inequality is $$k < 3$$ , the graph should shade all values less than 3.

The formula for calculating unit rate is: Unit Rate = Total Quantity ÷ Number of Units.

Two ratios are equivalent if they represent the same relationship between quantities, meaning they can be simplified to the same fraction.