The concept of the addition of lengths is the same as the addition of numbers. The idea of carrying is the same as the addition. For the addition of lengths, we must convert one unit of length to the other unit. Mixed Units of Lengths are arranged one after the other and then added. Refer to Solved Examples on Adding Length and understand the complete concept.

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## How to Add Different Units of Length?

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 added for the addition of length. They are two cases for finding the addition of lengths.

**Case 1:**

Suppose if the addends are in m and cm first convert the addends into cm and then add. After adding then convert the sum into m and cm.

**Case 2:**

If addends are in m and cm, then first cm columns are added, and the sum is placed under the cm column.

Then meter columns are added, and the sum is placed under the meter column.

Let us Consider some examples for adding lengths and get to know the problem-solving approach used.

### Adding Lengths Examples

**Example 1:**

Add 10 m 14cm and 15m 17cm

**Solution:**

**Case 1:**

For adding lengths, meters(m) are converted to centimeters(cm).

Multiply the number with meters by 100 to convert it into centimeters.

10 m14 cm=10*100 cm +14cm=1000 cm +14 cm=1014cm

15m17cm=15*100cm+17cm=1500cm+17cm=1517cm

Now add 1014cm,1517cm

1

1 0 1 4

+ 1 5 1 7

——–——–——–—

2 5 3 1

——–——–——–——

=25m 31cm

Therefore, the addition of lengths of 10 m 14cm and 15m 17cm is 25m31cm.

**Case 2:**

m cm

1

10 14

+ 15 17

——–——–——–—

25 31

——–——–——–——–

First centimeters columns are added and the sum is placed under the centimeters column.

Meters column are added and the sum is placed under the meters column.

Hence, the sum of lengths of 10 m 14cm and 15m 17cm is 25m31cm.

**Example 2:**

Add 23 m 25cm and 13m 19cm

**Solution:**

**Case 1:**

For adding lengths, meters(m) are converted to centimeters(cm).

Multiply the number with meters by 100 to convert it into centimeters.

23 m25 cm=23*100 cm +25cm=2300 cm +25 cm=2325cm

13m19cm=13*100cm+19cm=1300cm+19cm=1319cm

Now add 2325cm,1319cm

1

2 3 2 5

+ 1 3 1 9

——–——–——–—

3 6 4 4

——–——–——–——

=36m44cm

Therefore, the addition of lengths of 23 m 25cm and 13m 19cm is 36m44cm.

**Case 2:**

m cm

1

23 25

+ 13 19

——–——–——–—

36 44

——–——–——–——–

First centimeters columns are added and the sum is placed under the centimeters column.

Meters column are added and the sum is placed under the meters column.

Hence, the sum of lengths of 23 m 25cm and 13m 19cm is 36m 44 cm.

**Example 3:**

Add 19 m 20cm and 12m 13cm

**Solution:**

**Case 1:**

For adding lengths meters(m) are converted to centimeters(cm).

Multiply the number with meters by 100 to convert it into centimeters.

19 m20 cm=19*100 cm +14cm=1900 cm +14 cm=1914cm

12m13cm=12*100cm+13cm=1200cm+13cm=1213cm

Now add 1914cm,1213cm

1

1 9 1 4

+ 1 2 1 3

——–——–——–—

3 1 2 7

——–——–——–——

=31m 27cm

Therefore, the addition of lengths of 19 m 14cm and 12m 13cm is 31m27cm.

**Case 2:**

m cm

1

19 14

+12 13

——–——–——–—

31 27

——–——–——–——–

First centimeters columns are added and the sum is placed under the centimeters column.

Meters column are added and the sum is placed under the meters column.

Hence, the sum of lengths of 19 m 14cm and 12m 13cm is 31m27cm.

**Example 4:**

Add 3 km 234 m and 2 km 23 m.

**Solution:**

Case 1:

Kilometers are changed into meters

3 km 234 m = (3× 1000) m + 234 m = 3000 m + 234 m = 3234 m

2 km 23 m = (2 × 1000) m + 23 m = 2000 m + 23 m = 2023 m

Now Add

3 2 3 4 **m**

+2 0 2 3 **m**

——–———–—

__ 5 2 5 7 m__

= 5 km 257 m

Therefore, 3 km 234 m + 2km 23 m = 5 km 257 m

Case 2:

** km m**

3 234

+__ 2 023__

__ 5 257__

(i) 234 m + 023 m = 257 m, which goes under m.

(ii) 3 km + 2 km = 5 km, which goes under km.

Hence, the sum = 5 km 257 m

**Example 5 :**

Add 25 km 724 m, 19 km 213 m and 15 km 473 m.

**Solution:**

Kilometer and meter are arranged in different columns and then added.

** km m**

2 1 11

25 724

19 213

__15 473__

__ 60 410
__

(i) 724 m + 213 m + 473 m = 1410 m = 1 km 410 m.

410 m is placed under column of meters and 1 km is carried over.

(ii) 1 km + 25km + 19 km + 15 km = 60 km

It is placed under km column.

Hence, the sum = 60 km 410 m

**Example 6:**

Add the following:

**m dm cm**

13 6 5

__+25 8 7__

**Solution:**

**m dm cm**

1 1

13 6 5

__25____ 8____ 7__

__39____ 5____ 2__

(i) 5 cm + 7 cm = 12 cm

2cm is placed under cm column and 1 dm is carried over.

(ii) 6 dm + 8dm + 1 dm = 15dm = 1 m 5 dm

5 dm is placed under dm column and 1 m is carried over.

(iii) 1 m + 25 m + 13 m = 39 m

Hence, the sum = 39 m 5 dm 2cm

**Example 7:**

Add 45 km 782 m, 13 km 66 m and 19 km 423 m.

**Solution:**

Kilometer and meter are arranged in different columns and then added.

**km m**

1 1 1

45 782

13 066

__19 423__

__ 78 271
__

(i) 782 m + 066 m + 123 m = 1271 m = 1 km 271 m.

271 m is placed under column of meters and 1 km is carried over.

(ii) 1 km + 45 km + 13 km + 19 km = 78 km

It is placed under km column.

Hence, the sum = 78 km 271 m

**Example 8**

Add 52 m 4dm 78cm, 18 m 7dm 43cm

**Solution:**

m dm cm

1 1 1 1

52 4 78

+18 7 43

——–——–——–——–

7 1 2 21

——–——–——–——–—

1) 78+43=121=1dm 21cm

21 cm is written under the cm column and 1dm is carried over.

2) 1+4+7=12=1m2dm

2 dm is written under the dm column and 1m is carried over.

3) 52+18+1=71

Hence, the sum=71m 2dm 21cm