Lesson 1: Solve problems involving mixed units of capacity.

Property

To add mixed units of capacity, you can use two common strategies:

1. Add the like units separately, then regroup the smaller units into larger units.
2. Add on to one of the measurements to make the next whole unit, then add the remaining amount.

Examples

• Strategy 1: Add and Regroup

To solve $3 \text{ gal } 2 \text{ qt} + 2 \text{ gal } 3 \text{ qt}$:
Add gallons: $3 \text{ gal} + 2 \text{ gal} = 5 \text{ gal}$
Add quarts: $2 \text{ qt} + 3 \text{ qt} = 5 \text{ qt}$
Regroup the quarts: $5 \text{ qt} = 1 \text{ gal } 1 \text{ qt}$
Final answer: $5 \text{ gal} + 1 \text{ gal } 1 \text{ qt} = 6 \text{ gal } 1 \text{ qt}$

• Strategy 2: Make the Next Whole Unit

To solve $3 \text{ gal } 2 \text{ qt} + 2 \text{ gal } 3 \text{ qt}$:
Start with $3 \text{ gal } 2 \text{ qt}$. Add $2 \text{ qt}$ to make the next whole gallon: $3 \text{ gal } 2 \text{ qt} + 2 \text{ qt} = 4 \text{ gal}$.
Decompose the second addend: $2 \text{ gal } 3 \text{ qt} = 2 \text{ gal} + 2 \text{ qt} + 1 \text{ qt}$.
Add the remaining parts: $4 \text{ gal} + 2 \text{ gal} + 1 \text{ qt} = 6 \text{ gal } 1 \text{ qt}$.

Explanation

Adding mixed units of capacity is similar to adding mixed numbers. One strategy is to add the larger units and smaller units separately, then convert any excess smaller units into larger ones (regrouping). Another useful strategy is to add on to one number to reach the next whole unit, which simplifies the addition. Both methods will result in the same correct answer, so you can choose the one that makes the most sense for the problem.

Property

To subtract from a whole unit of capacity, decompose the whole unit into an equivalent number of smaller units. This process is similar to rewriting a whole number as a fraction with a common denominator, such as rewriting $1$ as $\frac{4}{4}$ to solve $1 - \frac{3}{4}$.

Examples

Property

To solve word problems with mixed units, first identify the given quantities and the required operation (addition or subtraction). Then, perform the calculation, regrouping or decomposing units as needed to find the solution.

Examples