Lesson 2: Solve problems involving mixed units of length.

Property

To add mixed units of length, you can use various strategies.

1. Add and Regroup: Add like units, then convert smaller units to larger ones.

2. Make the Next Whole Unit: Decompose one addend to make a whole unit with the other.

3. Compensation: Add then Subtract

Property

Subtraction of mixed units can be performed using multiple strategies, such as regrouping larger units, subtracting in parts, or counting up to find the difference.

Examples

Problem: $5 \text{ ft } 3 \text{ in} - 2 \text{ ft } 8 \text{ in}$
Regrouping: Decompose 1 foot into 12 inches.

• $5 \text{ ft } 3 \text{ in} \rightarrow 4 \text{ ft } 15 \text{ in}$

Subtracting in Parts: Subtract the feet first, then the inches.

• $5 \text{ ft } 3 \text{ in} - 2 \text{ ft} = 3 \text{ ft } 3 \text{ in}$
• $3 \text{ ft } 3 \text{ in} - 8 \text{ in} = 2 \text{ ft } 15 \text{ in} - 8 \text{ in} = 2 \text{ ft } 7 \text{ in}$

Adjust Both Measurements (Add to Make Subtraction Easier): Add the same amount to both measurements so the inches in the subtrahend "round up" to the next foot.

• Add 4 in to both: 5 ft 3 in → 5 ft 7 in, 2 ft 8 in → 3 ft 0 in.
• Now subtract: 5 ft 7 in − 3 ft 0 in = 2 ft 7 in.

Explanation

Subtracting mixed units of length often requires regrouping, similar to subtraction with whole numbers. One common method is to decompose a larger unit into smaller units before subtracting, ensuring the top number in each unit is greater than the bottom number. Alternatively, you can use a "subtracting in parts" strategy by first subtracting the larger units and then the smaller units. A third approach is to "count up" from the smaller measurement to the larger one to find the total difference between them.

Property

To solve a word problem involving mixed units of length, first determine the operation (addition or subtraction) needed to answer the question. Then, perform the calculation using one of the learned strategies, such as operating on like units or converting to the smallest unit.

Examples