Addition of Length

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 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.

4. 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

5. 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

6. 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

7. 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

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● Related Concepts

● Standard Unit of Length

● Conversion of Standard Unit of Length

● Subtraction of Length

3rd Grade Math Worksheets

3rd Grade Math Lessons

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