Addition and Subtraction of Units of Measurement

We will learn Addition and Subtraction of Units of Measurement. 

Addition and subtraction of metric measures can be done as we add and subtract ordinary numbers taking into account the place value of each metric measurement.

We can add the units of measurement like decimal numbers. 


I. Addition of Units of Measurement:

Addition of measurements is just like any other addition.

Observe the following examples:


(i) Addition of  Length:

1. Add 5 m 9 dm and 11 m and 5 dm

Solution:

5 m 9 dm = 5.9 m

11 m 5 dm = 11.5 m

Addition of Length

Hence, 5 m 9 dm + 11 m 5 dm

        = 17 m 4 dm or 17.4 m

2. Add 15 cm 5 mm and 21 cm 9 mm

Solution:

15 cm 5 mm = 15.5 cm

21 cm 9 mm = 21.9 cm

Addition Length

Hence, 15 cm 5 mm + 21 cm 9 mm

        = 37 cm 4 mm or 37.4 cm


3. Add 67 km 250 m and 84 km 720 m

Solution:

67 km 250 m = 67.250 km

84 km 720 m = 84.720 km

Length Addition

Hence, 67 km 250 m + 84 km 720 m

       = 151 km 970 m or 151.97 km


We can add lengths like ordinary numbers.

4. Add 24 km 250 m and 140 km 18 m

Solution:

24 km 250 m = 24.250 km

140 km 18 m = 140.018 km

Addition of Lengths

Hence, 24 km 250 m + 140 km 18 m

       = 164 km 268 m or 164.268 km


More problems on Addition of Units of Length

5. Add 65 km 146 m and 29 km 950 m.

Solution:

Write in column form and add

Add the meters

146 + 950 = 1096 m

1096 m = 1 km + 96 m

Write 96 under the meter column and carry over 1 km to km column.

Add kilometres 65 + 29 + 1 (carry over) = 95 km

Addition of Units of Length

Hence, 65 km 146 m + 29 km 950 m = 95 km 96 m


Addition of Metric Measurements:

6. Add 17 km 540 m; 12 km 800 m; 154 km 325 m

Solution:

Step I: Add metres

540 + 800 + 325 = 1665 m

= 1 km + 665 m

Step II: Write 665 under metres and carry 1 to km

Step III: Add kilometres

1 + 17 + 12 + 15 = 45 km

Step IV: Write 45 under kilometres.

Metric Addition

Therefore, the sum is 45 km 665 m.


7. Add 13 metre 42 centimetre and 5 metre 26 centimetre.

Step I: Add centimetres

42 + 26 = 68 cm

Step II: Write 68 under centimetres

Step III: Add metres

13 + 5 = 18 m

Step IV: Write 18 under metres.

Addition of Length

Therefore, the sum is 18 metre 68 centimetre or, 18 m 68 cm.


(ii) Addition of Mass:

1. Add 21 kilogram 150 gram and 9 kilogram 325 gram.

Step I: Add grams

150 + 325 = 475 g

Step II: Write 475 under grams

Step III: Add kilograms

21 + 9 = 30 kg

Step IV: Write 30 under kilograms.

Addition of Mass

Therefore, the sum is 30 kilogram 475 gram or, 30 kg 475 g


(iii) Addition of Capacity:

1. Add 8 litre 420 millilitre and 34 litre 175 millilitre.

Step I: Add millilitres

420 + 175 = 595 mℓ

Step II: Write 595 under millilitres

Step III: Add litres

8 + 34 = 42 ℓ

Step IV: Write 42 under litres.

Addition of Capacity

Therefore, the sum is 42 litres 595 millilitre or, 42 ℓ 475 mℓ.


II. Subtraction of Units of measurement:

We can subtract the units of measurement like decimal numbers.

Observe the following examples:


(i) Subtraction of  Length:

1. Subtract 25 km 340 m from 61 km 180 m

Solution:

Write in column form and subtract.

As we cannot subtract 340 m from 180 m, we borrow 1 km from 61 km. So 61 km becomes 60 km and 180 m becomes 1 km = 1000 m + 180 m = 1180 m.

Now, subtract 340 km from 1180 m.

1180 – 340 = 840

Subtraction of Units of Length

Subtract km 60 – 25 = 35

Hence, 61 km 180 m - 25 km 340 m 

       = 35 km 840 m


Subtraction of measurements is just like any other subtraction.

2. Subtract 3 metre 12 centimetre from 16 metre 27 centimetre.

Step I: Subtract centimetres

27 - 12 = 15 cm

Step II: Write 15 under centimetre

Step III: Subtract metres

16 - 3 = 13 m

Step IV: Write 13 under metre.

Subtraction of  Length

Therefore, the difference is 13 metre 15 centimetre or, 13 m 15 cm.


(ii) Subtraction of  Mass:

Subtraction of Metric Measurements:

1. Subtract 27 kg 100 g – 15 kg 400 g

Solution:

Step I: 400 g cannot be subtracted from 100 g.

Step II: Borrow 1 kg from 27 kg

1 kg = 1000 g. 1000 g + 100 g = 1100 g

Step III: Subtract grams

1100 – 400 = 700 g

Step IV: Write 700 under grams.

Step V: Now 27 – 1 = 26 remains under kg.

Step VI: Subtract kilograms.

26 – 15 = 11 kg

Step VII: Write 11 under kilograms.

Metric Add

Therefore, the difference is 11 kg 700 g.


2. Subtract 14 kilogram 325 gram from 32 kilogram 758 gram.

Step I: Subtract grams

758 - 325 = 433 gram

Step II: Write 433 under grams.

Step III: Subtract kilograms

32 - 14 = 18 kilograms

Step IV: Write 18 under kilograms.

Subtraction of Mass

Therefore, the difference is 18 kilogram 433 gram or 18 kg 433 g.


3. Subtract 28 dg 7 mg from 90 dg

Solution:

28 dg 7 mg = 28.07 dg

90 dg = 90.00 dg

Subtraction Mass

Hence, 90.00 dg - 28.07 dg

       = 61 dg 93 mg or 61.93 dg


(i) Subtraction of  Capacity:

1. Subtract 185 ℓ 560 mℓ and 200 ℓ 120 mℓ

Solution:

185 ℓ 560 mℓ = 185.560 ℓ

200 ℓ 120 mℓ = 200.120 ℓ

Subtraction of Volumes

Hence, 200 ℓ 120 mℓ - 185 ℓ 560 mℓ

       = 14 ℓ 660 mℓ or 14.660 ℓ


2. Subtract 9 litre 320 millilitre from 17 litre 540 millilitre.

Step I: Subtract millilitres

540 - 320 = 220 gram

Step II: Write 220 under millilitres.

Step III: Subtract litre

17 - 9 = 8 litre

Step IV: Write 8 under litres.

Subtraction of Capacity

Hence, 17 litre 540 millilitre - 9 litre 320 millilitre

       = 8 litres 220 millilitres or 8 ℓ 220 mℓ


Word Problems on Addition and Subtraction of Units of Measurement:

1. The height of building X is 6314 cm and that of building Y is 229 cm less. What is the height of building Y?

Solution:

The height of building X = 6314 cm = 63.14 m

The height of building Y is 229 cm less than building X.

Therefore, the height of building Y = 63.14 m - 2.29 m

Hence, the height of building Y = 60.85 m


Questions and Answers on Addition of Units of Length:

1. Add the given measurements:

(i) 46 m 23 cm + 8 m 95 cm

(ii) 13 km 547 m + 16 km 485 m

(iii) 24 dm 03 cm + 15 dm 01 cm

(iv) 6 km 920 m + 34 km 285 m

(v) 13 km 765 m + 24 km 880 m

(vi) 56 m 09 cm + 16 m 25 cm

(vii) 43 m 04 cm + 27 m 03 cm

(viii) 23 cm 02 mm + 16 cm 03 mm

(ix) 36 cm 00 mm + 8 cm 09 mm

 

Answers:

I. (i) 55 m 18 cm

(ii) 30 km 32 m

(iii) 39 dm 04 cm

(iv) 41 km 205 m

(v) 38 km 645 m

(vi) 72 m 34 cm

(vii) 70 m 07 cm

(viii) 39 cm 05 mm

(ix) 44 cm 09 mm


II. Add the following:

(i) 16 km 528 m + 1 km 325 m + 13 km 502 m

(ii) 25 km 252 m + 10 km 384 m + 31 km 420 m

(iii) 1 km 012 m + 3 km 264 m + 5 km 346 m

(vi) 2 kg 340 g + 3 kg 054 g + 8 kg 714 g

(v) 2 kl 190 l + 3 kl 705 l + 1 kl 784 l

(vi) 1 l 123 ml + 2 l 234 ml +  3 l 545 ml


Answer:

II. (i) 31 km 355 m

(ii) 67 km 56 m

(iii) 9 km 622 m

(vi) 14 kg 108 g

(v) 7 kl 679 l 

(vi) 6 l 902 ml


Questions and Answers on Subtraction of Units of Length:

III. Subtract the given measurements:

(i) 34 m 15 cm – 12 m 10 cm

(ii) 26 km 803 m – 19 km 450 m

(iii) 57 dm 08 cm – 15 dm 09 cm

(iv) 61 km 250 m – 45 km 300 m

(v) 9 m 46 cm – 7 m 96 cm

(vi) 8560 m 00 cm – 7789 m 00 cm

(vii) 63 cm 03 mm – 12 cm 02 mm

(viii) 72 m 06 cm – 35 m 21 cm

(ix) 50 km 000 m – 44 km 390 m

 

Answers:

III. (i) 22 m 05 cm

(ii) 7 km 353 m

(iii) 41 dm 99 cm

(iv) 15 km 950 m 

(v) 1 m 50 cm

(vi) 771 m 00 cm

(vii) 51 cm 01 mm

(viii) 36 m 85 cm

(ix) 5 km 610 m


IV. Subtract the following:

(i) 305 km 296 m – 198 km 485 m

(ii) 74 m 19 cm – 69 m 28 cm

(iii) 25 l 640 ml – 13 l 099 ml

(iv) 15 kg 240 gm – 8 kg 956 gm

(v) 130 km 500 m 75 cm – 65 km 436 m 89 cm

(vi) 12 l 5 dl 6 cl – 9 l 8 dl 9 cl


Answer:

IV. (i) 106 km 811 m

(ii) 4 m 91 cm

(iii) 12 l 541 ml 

(iv) 6 kg 284 gm

(v) 65 km 63 m 86 cm

(vi) 2 l 6 dl 7 cl

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