Add and subtract mixed customary units

Learning Objectives Convert between related customary units of length (inches, feet, yards). Add two or more mixed customary unit measurements, regrouping where necessary. Subtract mixed customary unit measurements, borrowing where necessary. Apply the Pythagorean theorem to right triangles with side lengths given in mixed customary units. Calculate the perimeter of a right triangle by adding side lengths expressed in mixed customary units. Solve multi-step word problems involving right triangles and the addition or subtraction of mixed customary units. Ever planned a construction project, like building a ramp or a frame, and needed to calculate exact lengths? 🛠️ This lesson connects the geometry of right triangles to the real-world measurements you'd use on a job site....

TermDefinitionExample Mixed Customary UnitsA measurement that uses a combination of two or more related customary units, such as feet and inches or yards and feet.A board that is 7 feet and 5 inches long is expressed as 7 ft 5 in. Unit ConversionThe process of changing a measurement from one unit to another equivalent unit.Converting 24 inches to feet: 24 in ÷ 12 in/ft = 2 ft. Regrouping (Carrying)In addition, this is the process of converting a smaller unit into a larger unit when the smaller unit's sum exceeds the conversion factor.When adding 5 ft 8 in and 2 ft 6 in, the inches sum to 14 in. We regroup this as 1 ft 2 in, carrying the 1 ft over to the feet column. Regrouping (Borrowing)In subtraction, this is the process of converting one larger unit into its equivalent smaller uni...

Customary Length Conversions 1 \text{ foot (ft)} = 12 \text{ inches (in)} \newline 1 \text{ yard (yd)} = 3 \text{ feet (ft)} These conversion factors are essential for regrouping (carrying and borrowing) when adding or subtracting mixed units. They are also used to convert all measurements to a single, smaller unit before performing multiplication or division, such as in the Pythagorean theorem. Pythagorean Theorem Formula a^2 + b^2 = c^2 Use this formula to find the length of a missing side in a right triangle, where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse. For calculations, it's best to convert all mixed units to a single unit (like inches) first.