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Comprehensive Guide to Basic Mathematical Calculations and Conversions

This guide covers essential mathematical calculations, including division in ratios, interest calculations, VAT computations, and train journey time conversions. It provides step-by-step processes to divide numbers in specific ratios, calculate interest on amounts over given periods, and determine VAT on purchases. Additionally, the guide includes conversions between different units of measurement, such as kilometers to meters and liters to milliliters. Perfect for students and anyone needing a refresher on fundamental math concepts.

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Comprehensive Guide to Basic Mathematical Calculations and Conversions

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  1. D S T 25 = 2x2x2x2x2 = 32 5.1 x 104 = 5.1 x 10000 = 51 000 Divide 25 in ratio 2:3 Divide 32 in ratio 3:1 10 15 24 8 80 km 4 min 15 m/s 25 km/hr

  2. Calculate interest on £400 at 3%pa for (i) 2 years (ii) 3 months 3% of £400 for 1 year Interest = = £12 = 12 ÷ 4 So for 2 years 2 x 12 = for 3months = £24 £3.00 Calculate the VAT on £80 item. The VAT rate is 17.5% VAT = 17.5% of £80 8 10% of £80 = 5% 2.5% 4 = £14.00 2 How long did the train journeys take: 1050 to1100 to1600 to 1630 1520 to 1720 to 1755 5 hrs 40 min 2 hrs 35 min Convert to hours and minutes (i) 6.5hrs (ii) 4.3hrs (iii) 2.6hrs 0.5 x 60 = 30 0.3 x 60 = 18 0.6 x 60 = 36 (i) 6 hrs 30min (ii) 4 hrs 18 mins (iii) 2 hrs 36 mins

  3. Scales 1:1000 1kg = g 1000 1 cm : 1000 cm 1 litre = ml 1000 = 10 m 1 tonne = kg 1000 1cm “represents” 10 m 1 km = m 1000 Drawing Real 1 m = mm 1000 1 m = cm 100 3 cm 1cm = mm 10 80 m 1 ml = cm3 1 0.1 cm

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