Adding and subtracting lengths

A tailor needs 1 m 25 cm cloth for a shirt and 1 m 50 cm for trousers. How much in total? To add lengths, we line up the same units.

What is this?

When lengths are given as just one unit, addition is easy:

$350 \text{ cm} + 220 \text{ cm} = 570 \text{ cm}$

When lengths are given as mixed units, like "1 m 25 cm", we add the larger units together and the smaller units together. If the smaller unit total goes above 100 (for cm) or 10 (for mm to cm), we carry over to the bigger unit.

$1 \text{ m } 25 \text{ cm} + 1 \text{ m } 50 \text{ cm} = 2 \text{ m } 75 \text{ cm}$

If the cm total crosses 100, we exchange 100 cm into 1 m. For example:

$2 \text{ m } 80 \text{ cm} + 1 \text{ m } 40 \text{ cm} = 3 \text{ m } 120 \text{ cm} = 4 \text{ m } 20 \text{ cm}$

Subtraction works the same way, but in reverse , if we don't have enough cm to subtract from, we borrow 1 m and turn it into 100 cm.

$3 \text{ m } 20 \text{ cm} - 1 \text{ m } 50 \text{ cm} = 2 \text{ m } 120 \text{ cm} - 1 \text{ m } 50 \text{ cm} = 1 \text{ m } 70 \text{ cm}$

The same logic applies for m and km. 1 km = 1,000 m, so we carry or borrow with 1,000.

A neat tip: convert everything to the smaller unit first if you find the mixed-unit method confusing. Add or subtract, then convert back.

Worked examples

Example 1. A piece of ribbon is 2 m 35 cm and another is 1 m 80 cm. Total length?

• m: 2 + 1 = 3 m.
• cm: 35 + 80 = 115 cm = 1 m 15 cm.
• Total: 3 m + 1 m 15 cm = 4 m 15 cm.

Example 2. From a 5 m wire, 2 m 70 cm is cut. How much wire is left?

• Convert to cm: 5 m = 500 cm. 2 m 70 cm = 270 cm.
• 500 − 270 = 230 cm = 2 m 30 cm.

Example 3. A road is 12 km 250 m long. A car has covered 7 km 800 m. Distance left?

• Convert to m: 12,250 − 7,800 = 4,450 m = 4 km 450 m.

Try it

1. 3 m 40 cm + 2 m 75 cm.
2. 5 m 20 cm − 2 m 60 cm.
3. 4 km 500 m + 2 km 750 m.
4. 8 km − 3 km 400 m.
5. A roll of cloth has 25 m. After selling 9 m 50 cm, how much is left?

Hands-on

Wall to wall. With a measuring tape, find the lengths of two walls in your room. Add them together. Now subtract the smaller from the bigger.

Tailor's challenge. Choose a piece of cloth at home. Estimate its length first. Then measure it. How close was your estimate?