Measurements link maths with everyday life. In 11 Plus Maths, pupils explore units, conversions, and formulas that help them solve practical problems with precision and confidence.
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If 1 lb = 454 g, then 7 lb = 7 × 454 = 3,178 g. 1 kg = 1,000 g ? 3,178 g = 3,178 ÷ 1,000 = 3.178 kg. You have to divide by 1,000 because you want to find out how many 'lots' of 1,000 there are in 3,178: each 'lot' equals 1 kg. If you don't like this method, you can keep on adding 'lots' of 1,000 to itself until you get to 3,178. D'oh!
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Obviously the highest number: 9 ft = 9 × 30 = 270 cm = 270 ÷ 100 = 2.7 m would not pass under the bridge BUT the lowest height that would not be able to pass under the bridge is 8.5 ft = 8.5 × 30 = 255 cm = 255 ÷ 100 = 2.55 m. It's 5 cm too high!
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Air is escaping at 80 cm3 each minute ? 5 × 80 = 400 cm3 will have escaped after 5 minutes. The air left in the balloon = 640 - 400 = 240 cm3. How fast or how slow something happens is called a 'rate', e.g. the balloon is losing air at the RATE of 80 cm3 per minute
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Learn this stuff!
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The volume of the rectangular container is = 40 × 40 × 50 = 80,000 cm3. Half the volume = 40,000 cm3. If water from a tap is pouring in at 1,000 cm3 every minute, then it will take 40,000 ÷ 1,000 = 40 min to half fill the tank. You have to divide by 1,000 because you want to find out how many 'lots' of 1,000 there are in 40,000 : each 'lot' equals 1 minute. If you don't like this method, you can keep on adding 'lots' of 1,000 to itself until you get to 40,000. D'oh! How fast or how slow something happens is called a 'rate', e.g. the tank is filling at the RATE of 1,000 cm3 per minute
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120,500 g = 120.5 kg: just divide 120.5 by 1,000. Now add the weights: 120.5 + 35.5 + 58 = 214 kg
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13 st 10 lb = 13 × 14 + 10 = 192 lb. 1 kg = 2.2 lb ?192 lb = 192 ÷ 2.2 = 87.27 kg. You have to divide by 2.2 because you want to find out how many 'lots' of 2.2 there are in 192: each 'lot' equals 1 kg
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If 1.61 km = 1 mile, then 245 miles = 1.61 × 245 = 394.45 km
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If 1.61 km = 1 mile, then 254 km = 254 ÷ 1.61 = 157.76 miles. You have to divide by 1.61 because you want to find out how many 'lots' of 1.61 there are in 254: each 'lot' equals 1 mile
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1 oz (ounces) = 28.34 g ? 6 oz = 28.34 × 6 = 170 g. 1 kg = 1,000 g ? 170 g = 170 ÷ 1,000 = 0.170 kg. By the way, there are 16 oz (ounces) in 1 lb (pound)
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