The addition and subtraction of measuring lengths can be done very easily. It is the same as addition and subtraction. Like addition and subtraction here also we will apply the concept of carrying and borrowing. For addition and subtraction of measuring lengths, we have to know the relation between lengths. It also explains the definition of length, the relation between lengths, how to add and subtract the lengths. You can also check the solved examples on adding, subtracting lengths for a better understanding of the concept.

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## Length – Definition

Length is defined as the size of the object from starting point to the endpoint of the object. Length is measured in m,cm,dm,km,etc. For smaller units of length, we use m, dm, mm, cm. For measuring larger units of length we use km.

For example, in day-to-day life, we measure the length of the cloth, the height of the person, the length of the road, etc.

Meter is the standard use of length. If the meter is divided into 100 equal parts then each part is called a centimeter. In short notation, meters and centimeters are represented by m, cm. We can measure meters, centimeters by using the scale or measuring tape, etc.

Relation between meter, centimeter, kilometer are as follows:

1 meter=100cm
100cm=1m 1 km=1000m |

### Adding and Subtracting Lengths Examples

Here we will explain how to add/subtract the measuring lengths with the help of the examples.

**Example 1:**

A room is of length 30m and breadth 15m. Find the sum of length and breadth and find the difference between length and breadth.

**Solution:**

1. Sum of Length and breadth=30+15

3 0

+1 5

——–——–—

4 5

——–——–—

Hence, sum=45

2. Difference in length and breadth

3 0

-1 5

——–——–——–

1 5

——–——–——–

Hence, Difference=15.

**Example 2:**

If the length of a bed is 425 cm and breadth is 210 cm, by how much does the length exceed the breadth? Find the sum of the length and breadth in m and cm.

**Solution:**

Length of the bed=425

The breadth of the bed=210

Length exceeds by the breadth is

4 2 5

-2 1 0

——–——–——–

2 1 5

——–——–——–

The Sum of length and breadth is

4 2 5

+ 2 1 0

——–——–——–

6 3 5

——–——–——–

The sum of length and breadth is 6m 35 cm.

**Example 3:**

Sita has a rope 8m long and Gita has a rope that is 10m long. what is the total length of both ropes? Find the difference between the ropes?

**Solution:**

Sita’s rope length=8

Gita’s rope length=10

The total length of two ropes

1 0

+ 8

——–—

1 8

——–—

Therefore, the total length of ropes=18m.

Difference between ropes

1 0

-8

——–——–——–

2

——–——–——–

Therefore, the difference between the two ropes=2m

**Example 4:**

Sindhu has a material of length 80m and breadth 100m. Find the sum of length and breadth? and find the difference of length and breadth?

**Solution:**

Material length=80

Material breadth=100

Sum of length and breadth=100+80=180.

Difference of length and breadth=100-80=20.

**Example 5:**

Raju has a bat which is of length 40m and breadth 10m. Find the sum of length and breadth of the bat?

**Solution:**

Length of the bat=40m

The breadth of the bat=10m

The Sum of length and breadth of the bat is

4 0

+1 0

——–——–

5 0

——–——–

**Example 6:**

Sita draws two line segments. One is 8 cm long and the other is 5 cm long.

(i) Find the total length of both the line segments.

(ii) Find the difference between the lengths of the segments.

**Solution:**

length of the line segment=8

another length of the line segment=5

The total length of the line segments is 8+5=13

Difference of the line segments=8-5=3.

**Example 7:**

Addition of 7m 20 cm, 9m 30 cm

**Solution:**

m cm

7 20

+9 30

——–——–——–

16 50

——–——–——–

First arrange meters, centimeters columns

First centimeters columns are added i.e. 20+30=50 and the sum 50 is placed under the centimeters column.

Meters column are added i.e. 7+9=16 and the sum 16 is placed under the meters column.

Therefore, the Addition of 7m20cm, 9m30cm is 16m50cm.

**Example 8:**

Find the addition of 42cm,76cm

**Solution:**

4 2

+7 6

——–——–——–

11 8

——–——–——–

Therefore, the addition of 42cm,76cm is 118cm.

**Example 9:**

Find the subtraction of 18m 38cm,12m18cm

**Solution:**

First arrange meters, centimeters in columns.

Then subtract 18cm from 38 cm

38-18=20

Write 20 in cm column

Subtract 12 from 18

18-12=6

write 6 in m column

18 38

-12 18

——–——–——–

6 20

——–——–——–

Therefore, the difference is 6m20cm.

**Example 10:**

(i) Find the subtraction of 6m 89cm,5m 35cm

**Solution:**

First arrange meters, centimeters in columns.

Then subtract 35cm from 89 cm

89-35=54

Write 54 in cm column

Subtract 5 from 6

6-5=1

write 1 in m column

m cm

6 89

-5 35

——–——–——–

1 5 4

——–——–——–

Therefore, the difference is 1m 54cm.

(ii) Find the subtraction of 3m 63cm, 1m 42cm

**Solution:**

First arrange meters, centimeters in columns.

Then subtract 42cm from 63 cm

63-42=21

Write 21 in cm column

Subtract 1 from 3

3-1=2

write 2 in m column

m cm

3 63

1 42

——–——–——–

2 21

——–——–——–

(iii) Sita bought a rope of length 25m long. If the rope is cut off 6m then find the length of the rope?

**Solution:**

Rope length=25m

rope cutoff=6m

Now Length of the rope after cutoff=25-6=19.

Therefore, the length of the rope=19m.