We will learn how to multiply and divide of units of measurement.
We carry out multiplication and division of measurements as we do for decimal numbers.
Multiplication
of Units of Length:
We can multiply lengths by a number like multiplication of ordinary numbers.
1. Multiply 12 km 56 m by 7.
Solution:
12 km 56 m = 12.056 km
Hence, 12.056 × 7 = 84.392 km
2. Multiply 44 dam 28 cm by 12
Solution:
28 cm = 0.28 m
1 dam = 10 m
28 cm = 0.028 dam
Hence, 44 dam 28 cm × 12 = 528.336
3. Multiply 7 km 346 m by 6
Solution:
We first convert km and m into m and then multiply.
To convert 44076 m to km we separate the last 3 digits from the right and write there as m.
44076 m = 44 km 76 m
Hence, 7 km 346 m by 6 =44 km 76 m
4. Multiply 15 m 326 mm by 6
Step I: 326 × 6 = 1956 mm = 1000 mm + 956 mm = 1 m 956 mm Step II: Write 956 under millimetres and carry 1 to metres. 15 × 6 = 90 90 + 1 = 91 m Step III: Write 91 under metres. |
Therefore, 15 m 326 mm × 6 = 91 m 956 mm
Multiplication of Units of Mass:
1. Multiply 15 g 16 mg by 25
Solution:
16 mg = \(\frac{16}{1000}\) g
15 g 16 mg = 15.016 g
Hence, 15 g 16 mg × 25 = 375.4 g
2. Multiply 7 kg 4 hg 6 dag 7 g by 15.
Step I: Multiply grams. 7 × 15 = 105 g 105 g = 10 dag 5 g Step II: Write 5 under grams and carry 10 to dag. Step III: Multiply decagrams. 6 × 15 = 90 90 + 10 = 100 dag 100 dag = 10 hg 0 dag Step III: Write 0 under dag and carry 10 to hectograms. Step IV: Multiply hectograms 4 × 15 = 60 60 + 10 = 70 hg 70 hg = 7 kg 0 hg Step V: Write 0 under hectogram and carry 7 to kilograms. Step VI: Multiply kilograms. 7 × 15 = 105 kg 105 + 7 = 112 kg |
Multiplication of Units of Capacity:
We can multiply the units of capacity measures l and ml by a number like ordinary numbers.
1. Multiply 9 dℓ 72 mℓ by 6
Solution:
72 mℓ = \(\frac{72}{100}\) dℓ = 0.72 dℓ
9 dℓ 72 mℓ = 9.72 dℓ
Hence, 9.72 dℓ × 6 = 58.32 dℓ
2. Multiply 72 ℓ 250 mℓ by 6
Solution: First convert 72 l 250 ml into ml. 72 l 250 ml = 72 × 1000 ml + 250 ml = 72000 ml + 250 ml = 72250 ml 72250 × 6 = 433500 ml = 433 l 500 ml |
Hence, 72 l 250 ml × 6 = 433 l 500 ml
3. Multiply 7 l 9 cl 2 ml by 16
Step I: Write the units in order. Step II: Since decilitre is missing in the question, put 0 in its place. Step III: Multiply millilitres 2 × 16 = 32 ml 3 cl + 2 ml Carry 3 to the centilitres and write 2 under millilitres. Step IV: Multiply centilitres. 9 × 16 = 144 cl + 3 = 147 cl = 14 dl + 7 cl Step V: Write 7 under centilitres and carry 14 to decilitres Step VI: Multiply decilitres 0 × 16 = 0 0 + 14 = 14 dl = 1 l 4 dl Step VII: Write 4 under decilitres and carry 1 to the litres. Step VIII: Multiply litres 7 × 16 = 112 l 112 + 1 = 113 l Step IX: Write 113 under litres Therefore, 7 l 9 cl 2 ml × 16 = 113 l 4 dl 7 cl 2 ml = 113 l 472 ml |
Division of Units of Length:
We can divide lengths by a number like division of ordinary numbers. If the measurement is given as a combination of two units like km and m or m and cm, we first convert higher unit to lower unit and then divide.
1. Divide 2 km 560 m unit by 8.
Solution:
Hence, 2 km 560 m ÷ 8 = 320 m
Division of Units of Mass:
1. Divide 16 kg 542 g by 6
16 kg 542 g ÷ 6 = 2 kg 757 g
= 2.757 kg
Division of Units of Capacity:
We can divide units of capacity measures l and ml by a number like ordinary numbers.
1. Divide 132 ℓ 64 dℓ by 8
Solution:
64 dℓ = 6.4 ℓ
132 ℓ 64 dℓ = 138.4 ℓ
Hence, 138.4 ℓ ÷ 8 = 17.3 ℓ
2. Divide 60 l 750 ml by 5
Solution: When measurements are given as combination of two units, we first convert the bigger unit to lower unit and then divide. 60 l 750 ml = 60 l + 750 ml
= 60000 ml + 750 ml = 60750 ml Now divide 60750 by 5 60750 ÷ 5 = 12150 ml = 12000 ml + 150 ml = 12 l 150 ml |
Hence, 60 l 750 ml ÷ 5 = 12 l 150 ml
3. Divide 717 l 32 ml by 8
Solution:
717 l 32 ml = 717000 ml + 32 ml
= 717032 ml
Therefore, 717 l 32 ml ÷ 8 =
89629 ml
= 89 l 629 ml
Questions and Answers on Multiplication and Division of Units of Measurement:
1. Multiply the following metric measures of length.
(i) 16 m by 7
(ii) 70 dm 4 cm by 24
(iii) 22 km by 10
(iv) 84 km 560 m by 51
(v) 34 cm by 25
(vi) 48 cm 9 mm by 62
(vii) 26 m 24 cm by 30
(viii) 80 m 5 cm by 10
Answers:
1. (i) 112 m
(ii) 1689 dm 6 cm
(iii) 220 km
(iv) 4312 km 560 m
(v) 850 cm
(vi) 3031 cm 8 mm
(vii) 78 m 720 cm
(viii) 800 m 50 cm
2. Multiply the following:
(i) 8 kg 225 g × 12
(ii) 12 km 450 m × 17
(iii) 7 kl 3 hl 4 dal × 6
(iv) 5 m 4 dm 8 cm 9 mm × 11
(v) 45 m 28 cm × 8
(vi) 115 kg 25 g × 14
Answer:
2. (i) 98.7 kg
(ii) 211.65 km
(iii) 44.04 kl
(iv) 60.379 m
(v) 362.24 m
(vi) 1610.35 kg
3. Divide the following metric measures of length.
(i) 240 km by 6
(ii) 14 km 580 m by 12
(iii) 36 m by 18
(iv) 50 cm 4 mm by 7
(v) 72 m by 8
(vi) 62 m 8 cm by 4
Answers:
3. (i) 40 km
(ii) 1 km 215 m
(iii) 2 m
(iv) 7 cm 2 mm
(v) 9 m
(vi) 15 m 52 cm
4. Divide the following:
(i) 40 km 320 m ÷ 5
(ii) 85 m 67 cm ÷ 13
(iii) 12 kg 264 g ÷ 12
(iv) 13 l 4 dl 8 cl 2 ml ÷ 9
(v) 116 km 280 m ÷ 12
(vi) 2 kg 800 g ÷ 14
Answer:
4. (i) 8.064 km
(ii) 6.59 m
(iii) 1.022 kg
(iv) 1.498 l
(v) 9.69 km
(vi) 0.2 kg
5. Solve the given:
(i) 56 km × 32
(ii) 32 km 124 m × 4
(iii) 30 m 75 cm ÷ 15
(iv) 47 cm 6 mm ÷ 20
(v) 66 dm 3 cm × 61
Answers:
5. (i) 1792 km
(ii) 128 km 496 m
(iii) 2 m 5 cm
(iv) 23 cm 8 mm
(v) 4044 dm 3 cm
6. Multiply the following Metric Measures of Capacity:
(i) 5 l 750 ml × 4
(ii) 12 l 125 ml × 22
(iii) 13 l 124 ml × 10
(iv) 14 l 120 ml × 7
(v) 44 l 85 ml × 15
(vi) 18 l 33 ml × 51
Answers:
6. (i) 23 l
(ii) 266 l 750 ml
(iii) 131 l 240 ml
(iv) 98 l 840 ml
(v) 661 l 275 ml
(vi) 919 l 683 ml
7. Divide the following metric measures of Capacity.
Ron, Sam, Mary and Jack were given different measuring jars. All of them were asked to fill a 1 l Can using their jars. Find out how many times each one of them have to fill their jars and pours them in their Can.
Answers:
7. (i) 2 times
(ii) 5 times
(iii) 10 times
(iv) 20 times
5th Grade Numbers
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