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

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

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

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

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

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.

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.

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.

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.

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

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.

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.

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.

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

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

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.

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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