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


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


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


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 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 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


Questions and Answers on Multiplication and Division of Units of Measurement:

1. Multiply the following metric measures.

(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.

(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

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