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
             1 5 1 8 cm

          + 1 6 2 2 cm

             3 1 4 0 cm

= 31 m 40 cm

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

Case 2:

        m      cm
        1          1
        1 5    1 8

     + 1 6    2 2

        3 1    4 0

(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  
             1 6 1 7 cm        

         + 2 0 2 3 cm

            3 6 4 0 cm    

= 36 m 40 cm

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

Case 2:

            m    cm
                   1 
           1 6   1 7

        + 2 0   2 3

           3 6   4 0

(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.

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  
             4 5 3 7 cm          

          + 3 1 9 2 cm

             7 7 2 9 cm

= 77 m 29 cm

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

Case 2:

          m    cm
                1
         4 5   3 7    

      + 3 1   9 2

         7 7   2 9

(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
             3 8   2 6

                7   0 5

        +  4 5    7 3

            9 1    0 4

(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             

              4 4 7 6 m

         +  5 0 5 4 m

             9 5 3 0 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   4 7 6

         + 5   0 5 4

            9   5 3 0

(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
             3 7     9 6 3

             2 8     0 5 4

        +      8     1 8 1

             7 4     1 9 8

(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
                   2 6    7    8

               +  5 2    5    6

                   7 9    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

To add lengths, write the numbers of km, m and cm in separate columns then add like ordinary numbers starting from the right.

9. Add 46 km 143 m and 53 km 200 m.

                km        m

                46       143

             + 53       200

             _  99       343

Therefore, 46 km 143 m and 53 km 200 m = 99 km 343 m

10. Add 28 km 76 m, 12 km 44 m & 21 km 38 m

                km        m

                28        76

                12        44

             + 21        38

             _ 62         58

11. Find the sum of the following.

(i) 20 m 75 cm + 12 m 42 cm

(ii) 20 km 4 m + 78 km 9 m

Solution: (i) 20 m 75 cm + 12 m 42 cm Fist add the cm together = 75 cm + 42 cm                                      = 117 cm                                     = 1 m 17 cm Now, add meters = 20 m + 12 m + 1 m (carry)                          = 33 m Required sum = 33 m 17 cm

(ii) 20 km 4 m + 78 km 9 m First add meters = 4 m + 9 m                          = 13 m Now add kilometers = 20 km + 78 km                               = 98 km Required result = 98 km 13 m

Word Problems on Addition of Length:

1. Ashley has a red ribbon of length 3 metres 35 centimetres. Stephanie has a blue ribbon of length 2 metres 42 centimetres. They join both the ribbons. What is the length of the two ribbons together?

Solution:

Write m and cm in columns as shown.

Step I: Add cm first. 35 + 42 = 77 Write 77 in the cm column. Step II: Add m now. 3 + 2 = 5 Write 5 in the m column.

Therefore, the length of the two ribbons is 5 m 77 cm.

Worksheet 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

3. Add the following:

Answer:

3. (i) 41 m 00 cm

(ii) 77 m 50 cm 

(iii) 77 m 08 cm 

(iv) 104 m 95 cm 

(v) 70 m 96 cm 

(vi) 123 m 00 cm

(vii) 133 m 20 cm 

(viii) 54 m 42 cm 

(ix) 311 m 30 cm 
 
(x) 204 m 00 cm 

(xi) 855 m 28 cm

(xii) 137 m 85 cm

(xiii) 72 m 44 cm 

(xiv) 181 m 80 cm 

(xv) 103 m 12 cm 

(xvi) 71 m 40 cm 

● 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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