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Adding and Subtracting Lengths
This lesson shows how to add and subtract lengths given in the same unit, such as inches, feet, or centimeters. Students line up matching units, use bar models and number lines to picture the total or difference, and apply these skills to word problems involving distances and mixed units.
Step 1: Make Sure the Units Match
Before adding or subtracting, always check that both lengths are measured in the same unit. You cannot add 3 feet and 10 inches directly, because feet and inches are different sized units. This connects closely to comparing lengths, where matching units is just as important before you decide which length is longer or shorter. If the units do not match, convert one length so both lengths use the same unit, then add or subtract as usual.
Adding Lengths: A Worked Example
A pencil is 14 centimeters long. An eraser next to it is 6 centimeters long. What is the total length of the pencil and eraser placed end to end?
Since both lengths are in centimeters, simply add the numbers together: \(14 + 6 = 20\) centimeters. The bar model below shows the two lengths joined into one total bar.
Subtracting Lengths: A Worked Example
A board measures 30 inches long. A carpenter cuts off a piece that is 12 inches long. How long is the piece that is left?
Subtract the length that was cut off from the original length: \(30 - 12 = 18\) inches. The remaining piece is 18 inches long.
Using a Number Line to Add or Subtract Lengths
A number line is another useful way to picture what is happening. To add lengths, start at the first length and move forward by the second length. To subtract lengths, start at the total and move backward by the length being removed. The number line below shows \(30 - 12 = 18\).
Working with Mixed Units
Sometimes a problem mixes units, such as feet and inches, or meters and centimeters. In those cases, convert every length to the smaller unit first, then add or subtract. For example, 2 feet 3 inches is the same as \(2 \times 12 + 3 = 27\) inches. If a second piece is 15 inches long, the total length is \(27 + 15 = 42\) inches, which can be rewritten as 3 feet 6 inches since \(42 = 3 \times 12 + 6\).
Solving Word Problems with Lengths
Many real problems ask you to find a total length, a missing length, or how much longer one object is than another. Read the problem carefully to decide whether you need to add (finding a total or combined length) or subtract (finding a difference or a remaining amount). Estimating first, as in estimating lengths, is a good way to check that your final answer makes sense before you commit to the exact calculation.
Example: A hallway is 9 meters long. A rug covers 4 meters of it. How much of the hallway floor is not covered by the rug? Since you are looking for the leftover distance, subtract: \(9 - 4 = 5\) meters of hallway are not covered.
Quick Tips for Adding and Subtracting Lengths
Always match the units first. Line up the numbers the same way you would for regular addition or subtraction. Use a bar model or number line whenever the problem feels confusing, since drawing the lengths often makes the correct operation obvious. Finally, check your answer by asking whether the total or difference is a reasonable size for the objects described.