 Subtraction of Lengths – Definition, Examples | How Values of Lengths are Arranged in Subtraction?

The concept of the subtraction of lengths is the same as the subtraction of numbers. The concept of borrowing is the same as subtraction. For the subtraction of lengths, we need to convert one unit of length to the other unit. Arrange all the units one after the other and perform the subtraction. Make use of the Examples on Subtracting Lengths as a reference and apply the knowledge while solving related problems.

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How to Subtract Lengths?

We will discuss how the mixed units of lengths i.e.(m, cm, or cm,m, etc)  are arranged one after the other and then subtracted for the subtraction of length. They are two cases for finding the subtraction of lengths.

Case 1:

Suppose if the minuend, subtrahend are in mixed units of lengths i.e. m and cm first convert them into smaller units( cm) and then subtract. After subtracting then convert the difference into m and cm.

Case 2:

If minuend, subtrahend are in m and cm, then first cm columns are subtracted, and the difference is placed under the cm column.

Then meter columns are subtracted, and the difference is placed under the meter column.

Consider some examples for subtracting lengths.

Subtracting Lengths Examples

Example 1:

Subtract 15 m 34 cm from 57 m 98 cm

Solution:

Case 1:

Both the numbers i.e. minuend and subtrahend are converted into smaller units.

15 m 34 cm = (15 × 100) cm + 34 cm = (1500 + 34) cm = 1534 cm

57 m 98 cm = (57 × 100) cm + 98 cm = (5700 + 98) cm = 5798 cm

Now subtract

57 m 98 cm       =          5798 cm

– 15 m 68 cm        =       – 1568 cm
4230 cm

= 4200 cm + 30 cm

= 42 m 30 cm

Therefore, 57 m 98 cm – 15 m 68 cm = 42 m 30 cm

Case 2:

As the minuend is greater than the subtrahend, the minuend is placed above the subtrahend. Then meters and centimeters are arranged in different columns.

Now subtract

m   cm
57   98

15  68
42   30

(i) Subtracting cm, 98 cm – 68 cm = 30 cm.
It is placed under the cm column.

(ii) Subtracting m, 57 m – 15 m = 42 m.
It is placed under the m column.

Hence, difference = 42 m 30 cm

Example 2:

Subtract 26 m 73 cm from 63 m 40 cm.

Solution:

Case 1:

Both the numbers i.e. minuend and subtrahend are converted into smaller units.

26 m 73 cm = (26 × 100) cm + 73 cm = (2600 + 73) cm = 2673 cm

63 m 40 cm = (63 × 100) cm + 40 cm = (6300 + 40) cm = 6340 cm

Now subtract

6340  cm

-2673   cm
——–——–—

3 6    6 7

——–——–——–

= 3600 cm + 67 cm

= 36 m 67 cm

Therefore, 63 m 40 cm – 26 m 73 cm = 36 m 67 cm.

Case 2:

As the minuend is greater than the subtrahend, the minuend is placed above the subtrahend. Then meters and centimeters are arranged in different columns. Minuend 63 m 40 cm is placed above subtrahend 26m 73 cm.

m          cm

63       40

-26        73

——–——–——–

36    67

——–——–——–

(i) 73  cm > 40 cm. So, 73 cm cannot be subtracted from 40 cm.
1 m or 100 cm is borrowed from 63m leaving 62 m in the m column.

(ii) Now 140 cm – 73 cm = 67 cm. It is placed under cm column.

(iii) Now in the m column, 62 m – 26 m = 36 m.
It is placed under the m column.

Hence, the difference is 36 m 67 cm.

Example 3:

Subtract 28m 3cm from 69m

Solution:

Case 1:

We have, 69 m – 28 m 3cm

Both the numbers i.e. minuend and subtrahend are converted into smaller units.

69 m        = (69 × 100) cm            = 6900 cm

28 m 3 cm = (28 × 100) cm + 3 cm = (2800 + 3) cm = 2803 cm

Now subtract

6900   cm

2803   cm
4097   cm

= 4000 cm + 97 cm

= 40 m 97 cm

Therefore, 69 m – 28 m 3cm = 40 m 97 cm.

Case 2:

As the minuend is greater than the subtrahend, the minuend is placed above the subtrahend. Then meters and centimeters are arranged in different columns. Minuend 69 m 00 cm is placed above subtrahend 28 m 03cm.

m     cm
1     100
69     00

-28     03
40     97

(i) 03 cm > 0 cm. So, 3 cm cannot be subtracted from 0 cm.
1 m or 100 cm is borrowed from 69 m leaving 68 m in the m column.

(ii) Now 100 cm – 03 cm = 97 cm. It is placed under cm column.

(iii) Now in the m column, 68 m – 28 m = 40 m.
It is placed under the m column.

Hence, the difference is 40 m 97 cm.

Example 4:

Subtract 35 km 532 m from 73 km 80 m.

Solution:

Case 1:

Boththe numbers i.e. minuend and subtrahend are converted into smaller units (conversion method).

73 km 80 m = (73 × 1000) m + 80 m = (73000 + 80) m = 73080 m

35 km 532 m = (35 × 1000) m + 532 m = (35000 + 532) m = 35532 m

Now subtract

73080 m

35532 m
37548 m

= 37000 m + 548 m

= 37 km 548 m

Therefore, 73 km 80 m – 35 km 532 m = 37 km 548 m.

Case 2:

As the minuend is greater than the subtrahend, the minuend is placed above the subtrahend. Then kilometers and meters are arranged in different columns. Minuend 63 km 70 m is placed above subtrahend 45 km 282 m (without conversion).

km      m
1     1000
73     080

–  35     532
37     548

(i) 532 m > 80 m. So, 532 m cannot be subtracted from 80 m.
1 km or 1000 m is borrowed from 73 km leaving 72 km making 80 m to 1080 m (Since, 1 km = 1000 m and 80 m = 1080 m).
Now 1080 m – 532 m = 548 m. It is placed under the m column.

(ii) Now in the km column, 73 – 1 = 72 km. 72 km – 35 km = 37 km.
It is placed under the km column.

Hence, the difference is 37 km 548 m.

Example 5:

Subtract 6 m 5 dm 3 cm from 45 m 3 dm 9 cm.

Solution:

As the minuend is greater than the subtrahend, the minuend is placed above the subtrahend. Then meters, decimeters, and centimeters are arranged in different columns. Minuend 26 m 4 dm 8 cm is placed above subtrahend 8 m 7 dm 5 cm.

m    dm    cm
1      10
45     3      9

–    6     5   3
38     8      6

(i) 9 cm – 3 cm = 6 cm. It is placed under cm column.

(ii) 5 dm > 3 dm. So, 75dm cannot be subtracted from 3 dm.
1 m or 10 dm is borrowed from 45 m leaving 44 m making 3 dm to 13 dm.
Now 13 dm – 5 dm = 8 dm. It is placed under the dm column.

(iii) Now in the m column, 45 – 1 = 44 m. 44 m – 6 m = 38 m.
It is placed under the m column.

Hence, the difference is 38 m 8 dm 6 cm.

Example 6:

Subtract 10 m 6 dm 4 cm from 14 m 4 dm 9 cm.

Solution:

As the minuend is greater than the subtrahend, the minuend is placed above the subtrahend. Then meters, decimeters and centimeters are arranged in different columns. Minuend 14 m 4 dm 9 cm is placed above subtrahend 10 m 6dm 4 cm.

m    dm    cm
1      10
14     4      9

–  10    6      4
3     8      5

(i) 9 cm – 4 cm = 5 cm. It is placed under cm column.

(ii) 6 dm > 4 dm. So, 6 dm cannot be subtracted from 4 dm.
1 m or 10 dm is borrowed from 14 m leaving 13 m making 4 dm to 14 dm.
Now 14 dm – 6 dm = 8 dm. It is placed under the dm column.

(iii) Now in the m column, 14 – 1 = 13 m. 13 m – 10 m = 3 m.
It is placed under the m column.

Hence, the difference is 3 m 8 dm 5 cm.

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