Multiplication and Division of Units of Measurement

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 m

Multiplication - Measurement

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

Multiplication of Measurements

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.

    7 km 346 m

= 7000 m + 346 m

= 7346 m

Now we multiply by 6

= 7346 × 6

= 44076 m

Multiplication Length

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


Multiplication of Units of Mass:

4. Multiply 15 g 16 mg by 25

Solution:

16 mg = \(\frac{16}{1000}\) g

15 g 16 mg = 15.016 g

Multiplication - Measurements

Hence, 15 g 16 mg × 25 = 375.4 g


Multiplication of Units of Capacity:

We can multiply the units of capacity measures l and ml by a number like ordinary numbers.

5. Multiply 9 dℓ 72 mℓ by 6

Solution:

72 mℓ = \(\frac{72}{100}\) dℓ = 0.72 dℓ

9 dℓ 72 mℓ = 9.72 dℓ

Multiplying Measurements

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

Multiplication of Capacity

Hence, 72 l 250 ml × 6 = 433 l 500 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:




Let us convert 2 km 560 m into m.

2 km 560 m

= 2000 m + 560 m

= 2560 m

Now, divide 2560 by 8

Division of Units of Length

Hence, 2 km 560 m ÷ 8 = 320 m


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

Division of Units of Measurements

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

Division of Capacity

Hence, 60 l 750 ml ÷ 5 = 12 l 150 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. 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:

2. (i) 40 km

(ii) 1 km 215 m

(iii) 2 m

(iv) 7 cm 2 mm

(v) 9 m

(vi) 15 m 52 cm


3. 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:

3. (i) 1792 km

(ii) 128 km 496 m 

(iii) 2 m 5 cm

(iv) 23 cm 8 mm

(v) 4044 dm 3 cm


4. 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:

4. (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



4. 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.

Division of Capacity Worksheet

Answers:

(i) 2 times

(ii) 5 times

(iii) 10 times

(iv) 20 times

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