We learn how to multiply and divide units of measure.

We perform multiplications and divisions of measures as with decimal numbers.

Multiplication of units of length:

We can multiply lengths by a number, like multiplying ordinary numbers.

1. Multiply 12 km 56 m by 7.

Solution:

12 km 56 m = 12.056 m Hence 12.056 × 7 = 84.392 km

2. Multiply 44 perineum 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 to m and then multiply.

 7 km 346 m² = 7000 m + 346 m = 7346 m Now let’s multiply by 6 = 7346 × 6 = 44076 m 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 m²

So 7 km 346 m times 6 = 44 km 76 m

Multiplication of mass units:

4. Multiply 15g 16mg by 25

Solution:

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

15 g 16 mg = 15.016 g Hence 15g 16mg x 25 = 375.4g

Multiplication of the capacity units:

We can multiply the units of measure of capacity 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 Hence 9.72 dℓ × 6 = 58.32 dℓ

2. Multiply 72 ℓ 250 mℓ by 6

 Solution: First convert 72 l 250 ml to ml. 72 l 250 ml = 72 × 1000 ml + 250 ml = 72000 ml + 250 ml = 72250 ml 72250 × 6 = 433500 ml = 433 l 500 ml So 72 l 250 ml × 6 = 433 l 500 ml

Division of the length units:

We can divide lengths by a number, like dividing ordinary numbers. If the measurement is given as a combination of two units such as km and m or m and cm, we first convert the higher unit to a lower one and then divide.

1. Divide 2 km 560 m unit by 8.

Solution:

 Let’s convert 2 km 560 m to m. 2 km 560 m² = 2000 m + 560 m = 2560 m Now divide 2560 by 8 So 2 km 560 m ÷ 8 = 320 m

Division of the capacity units:

We can divide the capacity units l and ml by a number, like normal numbers.

1. Divide 132 ℓ 64 dℓ by 8

Solution:

64 dℓ = 6.4 ℓ

132 ℓ 64 dℓ = 138.4 ℓ So 138.4 ℓ ÷ 8 = 17.3 ℓ

2. Divide 60 l 750 ml by 5

 Solution: When measurements are given as a combination of two units, we first convert the larger unit to a 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 So 60 l 750 ml 5 = 12 l 150 ml

Questions and answers about multiplying and dividing units of measure:

1. Multiply the following metric length measures.

(i) 16 m by 7

(ii) 70 dm 4 cm x 24

(iii) 22 km by 10

(iv) 84 km 560 m by 51

(v) 34 cm by 25

(vi) 48 cm 9 mm x 62 in

(vii) 26 m 24 cm x 30

(viii) 80 m 5 cm x 10

Reply:

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 length measures.

(i) 240 km times 6

(ii) 14 km 580 m by 12

(iii) 36m by 18

(iv) 50 cm 4 mm x 7 in

(v) 72 m by 8

(vi) 62 m 8 cm x 4 in

Reply:

2. (i) 40 km

(ii) 1 km 215 m²

(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 in

Reply:

3rd (i) 1792 km

(ii) 128 km 496 m²

(iii) 2 m 5 cm

(iv) 23 cm 8 mm

(v) 4044 dm 3 cm

4. Multiply the following Metic capacity measures:

(i) 5 L 750 ml x 4

(ii) 12 L 125 ml x 22

(iii) 13 L 124 ml x 10

(iv) 14 L 120 ml x 7

(v) 44 L 85 ml x 15

(vi) 18 L 33 ml x 51

Reply:

4th (i) 23 liters

(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 for capacity.

Ron, Sam, Mary and Jack were given different measuring glasses. Everyone was asked to fill a 1 liter can with their glasses. Find out how often each of them has to fill their glasses and pour them into their can. Reply:

(i) 2 times

(ii) 5 times

(iii) 10 times

(iv) 20 times

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