Addition of Length

The process of addition of units of length is exactly similar to addition of ordinary numbers.

Learn how the values of length are arranged in different columns for the addition of length.

1. Add 15 m 18 cm and 16 m 22 cm

Solution:

Case 1:

Lengths to be added are converted into cm.

15 m 18 cm = 1500 cm + 18 cm = 1518 cm

16 m 22 cm = 1600 cm + 22 cm = 1622 cm

Now, sum

             1 1
             1518 cm

          + 1622 cm
             3140 cm

= 31 m 40 cm

Therefore, 15 m 18 cm + 16 m 22 cm = 31 m 40 cm

Case 2:

        m    cm
        1     1
        15    18

+ 16 22
31 40

(i) First cm are added, 18 cm + 22 cm= 40 cm. This sum is placed under cm column

(ii) Now meters are added, 15 m + 16 m = 31 m. This 31 m is placed under m column.

Hence, sum = 31 m 40 cm.

2. Add 16 m 17 cm and 20 m 23 cm

Solution:

Case 1:

Lengths to be added are converted into cm.

16 m 17 cm = 1600 cm + 17 cm = 1617 cm

20 m 23 cm = 2000 cm + 23 cm = 2023 cm

Now, sum

1
1617 cm

+ 2023 cm
3640 cm

= 36 m 40 cm

Therefore, 16 m 17 cm + 20 m 23 cm = 36 m 40 cm

Case 2:

            m   cm
                 1
           16   17
        + 20   23
           36   40

(i) First cm are added, 17 cm + 23 cm= 40 cm. This sum is placed under cm column

(ii) Now meters are added, 16 m + 20 m = 36 m. This 36 m is placed under m column.

Hence, sum = 36 m 40 cm.

3. Add 62 m 34 cm, 27 m 73 cm and 9 m 5 cm.

Solution:

Let us add

Step I: Arrange the numbers vertically.

Step II: Write the lengths to be added in m and cm as shown.

Step III: First, add centimetres from right and then add the metres.

$Addition of Length$

Thus, 62 m 34 cm + 27 m 73 cm + 9 m 5 cm = 99 m 12 cm

4. Add 45 m 37 cm and 31 m 92 cm.

Solution:

Case 1:

45 m 37 cm = (45 × 100) cm + 37 cm = (4500 + 37) cm = 4537 cm

31 m 92 cm = (31 × 100) cm + 92 cm = (3100 + 92) cm = 3192 cm

Now, sum

1
4537 cm

+ 3192 cm
7729 cm

= 77 m 29 cm

Therefore, 45 m 37 cm + 31 m 92 cm = 77 m 29 cm

Case 2:

          m   cm
              1
   45   37

+ 31 92
77 29

(i) 37 cm + 92 cm = 129 cm = 1 m 29 cm. 29 is placed under cm column and 1 m is carried over to m column.

(ii) Now 1 m + 45 m + 31 m = 77 m. It is placed under m column.

Hence, sum = 77 m 29 cm.

5. Add 38 m 26 cm, 7 m 5 cm and 45 m 73 cm.

Solution:

The values of length are arranged in columns of m and cm and then added.

         m cm
            2 1   1
            38   26

             7   05

        + 45   73
            91   04

(i) 26 cm + 05 cm + 73 cm = 104 cm = 1 m 04 cm.

04 is placed under cm column and 1 m is carried over.

(ii) 1 m + 38 m + 7 m + 45 m = 91 m and it is placed under m column.

Hence, the sum = 91 m 04 cm

6. Add 4 km 476 m and 5 km 54 m.

Solution:

Case 1:

Kilometers are changed into meters

4 km 476 m = (4 × 1000) m + 476 m = 4000 m + 476 m = 4476 m

5 km 54 m = (5 × 1000) m + 54 m = 5000 m + 54 m = 5054 m

Now sum

1 1
             4476 m

         + 5054 m
         9530 m

= 9 km 530 m

Therefore, 4 km 476 m + 5 km 54 m = 9 km 530 m

Case 2:

          km    m
                1 1
            4   476

         + 5   054
            9   530

(i) 476 m + 054 m = 530 m, which goes under m.

(ii) 4 km + 5 km = 9 km, which goes under km.

Hence, the sum = 9 km 530 m

7. Add 37 km 963 m, 28 km 54 m and 8 km 181 m.

Solution:

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

               km    m
             2 1   1
   37   963

             28   054

        + 8   181
             74   198

(i) 963 m + 54 m + 181 m = 1198 m = 1 km 198 m.

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

(ii) 1 km + 37 km + 28 km + 8 km = 74 km

It is placed under km column.

Hence, the sum = 74 km 198 m

8. Add the following:

m dm cm

26 7 8

+ 52 5 6

Solution:

   m   dm   cm
                      1     1
                   26    7    8

               + 52    5    6
     79    3    4

(i) 8 cm + 6 cm = 14 cm = 1 dm 4 cm

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

(ii) 7 dm + 5 dm + 1 dm = 13 dm = 1 m 3 dm

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

(iii) 1 m + 26 m + 52 m = 79 m

Hence, the sum = 79 m 3 dm 4cm

Questions and Answers on Addition of Length:

1. Add the following.

(i) 32 m 78 cm + 15 m + 9 cm

(ii) 22 m 98 cm + 63 m + 89 cm + 7 m 7 cm

(iii) 143 m 50 cm + 112 m + 76 cm + 84 m 45 cm

(iv) 78 m 36 cm + 15 m 8 cm

(v) 153 m 28 cm + 49 m 25 cm + 70 m 20 cm

(vi) 69 m 59 cm + 15 m 15 cm + 56 m 9 cm

Answers

1. (i) 47 m 87 cm

(ii) 93 m 94 cm

(iii) 340 m 71 cm

(iv) 93 m 44 cm

(v) 272 m 73 cm

(vi) 140 m 83 cm

2. Add the following.

(i) 139 m 68 cm, 66 m 46 cm and 42 m 7 cm

(ii) 140 m 23 cm, 33 m 48 cm and 32 m 17 cm

(iii) 179 m 16 cm, 69 m 59 cm and 7 m 6 cm

(iv) 35 m 50 cm, 317 m 46 cm and 93 m 47 cm

(v) 64 m 18 cm, 48 m 36 cm and 14 m 82 cm

Answers

2. (i) 248 m 21 cm

(ii) 205 m 88 cm

(iii) 255 m 81 cm

(iv) 446 m 43 cm

(v) 127 m 36 cm

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