Adding and Subtracting Lengths

A length tells you how long, tall, or far something is, measured in units such as inches, feet, centimeters, or meters. Once you know how to measure lengths, the next skill is combining or comparing them using addition and subtraction. Adding lengths tells you a total distance or a total measurement when two or more pieces are put together. Subtracting lengths tells you how much is left over, or how much longer one length is than another.

For example, if one rope is 12 centimeters long and another rope is 5 centimeters long, joining them end to end gives a total length of \(12 + 5 = 17\) centimeters. If a ribbon starts at 25 centimeters and you cut off 8 centimeters, the piece that remains is \(25 - 8 = 17\) centimeters.

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.

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.

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.

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 \(30 - 12 = 18\).

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 \(42 = 3 \times 12 + 6\).

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.

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.

Related lessons

• Math 2