ADDITION MULTIPLICATION TABLE Example 1 Calculate 79 + 123 + 4 + 897 79 123 4 + 897 1103 REMEMBER: Place values Set sum out in a column Example 2 Calculate 0·23 + 1·06 + 23·6 0·23 1·06 + 23·6 24·89 REMEMBER: Keep decimal points in line SUBTRACTION REMEMBER: Place values ‘Exchange’ if you can’t subtract one number from another Example 1 Calculate 634 – 58 5 12 1 2-5 You can’t do! Exchange 6 for 5 and 1 4-8 You can’t do! Exchange 3 for 2 and 1 634 58 576 Example 2 Calculate 7·62 – 1·073 7·620 - 1·073 6·547 REMEMBER: Fill in blank places with ‘0’s Keep decimal points in line ROUNDING REMEMBER: Always round up for 5 and above Look at the number one to the right of the one you are interested 1835 to the nearest 10in = 1840 1835 to the nearest 100 = 1800 1835 to the nearest 1000 = 2000 627·5 to the nearest whole number = 628 627·5 to the nearest 10 =630 627·5 to the nearest 100 =600 8.65 to 1 decimal place (d.p.)= 8·7 0·0645 to 2 d.p.= 0·06 19·99 to 1 d.p. = 20·0 3·955 to 1 significant figure (sig.fig.) = 4 3·955 to 2 significant figures (sig.fig.) = 4·0 PROPORTION FRACTIONS REMEMBER: If two quantities change by a related amount, they are said to be ‘in proportion’ The top of a fraction is called the numerator The bottom of a fraction is called the denominator Example If 20 files can be copied in 4 minutes, how many files can be copied in 56 minutes? Example 1 1 Find /4 of 36 REMEMBER: Record appropriate headings with the value you have to find on the right Find the value for one item first Multiply by the required number Divide by 4 to find files copied in 1 minute Time (min) Files 4 20 1 20 ÷ 4 = 5 56 5 × 56=280 REMEMBER:  To add or subtract fractions, you must convert the fractions to have a common denominator Example 1 The common denominator is 20 Example 2 The common denominator is 6 Find 3/5 of £120 To find 1/4 divide by 4 5 1 36 ÷ 4 = 9 To find 1/5 divide by 5 1 /5 of £120 = £120 ÷ /4 of 36 = 9 = £24 /5 = 1/5 × 3 3 3 280 files can be copied in 56 minutes ADDING AND SUBTRACTING FRACTIONS Example 2 /5 of £120 = £24 × 3 = £72 SCIENTIFIC NOTATION REMEMBER: Scientific notation is sometimes called standard form It is really useful for writing very big and very small numbers It is a way of writing numbers as a number between 1 and 10 multiplied by 10 to a power Example 1 86 500 000 = 8·65 x 107 107 because the decimal point has been moved 7 places to the left to get 8·65 Example 2 0·000 000 000 034 = 3·4 x 10-11 10-11 because the decimal point has been moved 11 places to the right to get 3·4 USING UNITS 1 USING UNITS 2 Remember to use appropriate units in all situations. UNITS ARE IMPORTANT! WEIGHT mg, g, kg LENGTH mm, cm, m, km kilogram (kg) ×1000 ÷1000 ×1000 ÷1000 AREA mm2, cm2, m2, hectare kilometre (km) 1 cm2 = 10 mm x 10 mm = 100 mm2 1 m2 = 100 cm x 100 cm = 10 000 cm 2 1 hectare = 100 m x 100 m = 10 000 m 2 metre (m) VOLUME l, ml, cm3 ×1000 ÷1000 gram (g) Remember to use appropriate units in all situations. UNITS ARE IMPORTANT! ×100 ÷100 1 litre = 1000 ml litre (l) ×1000 ÷1000 centimetre (cm) ×10 milligram (mg) ÷10 1 ml = 1 cm3 millilitre (ml) millimetre (mm) USING FORMULAE REMEMBER: Write down the formula Rewrite the formula replacing the letters with the appropriate numbers (substitution) Carry out the calculation Interpret the answer and put the appropriate units back in context Example P = 2l + 2b where P = perimeter of rectangle in cm l = length of rectangle in cm b =l breadth of rectangle Find P when = 6cm and b = 7cm in cm 1 Write formula: 2 Replace letters: 3 Carry out calculation: 1 litre = 1000 cm3 P= P= P= = 2l + 2b 2x6 + 2x7 12 + 14 26 4 Interpret answer remembering units: The perimeter of the rectangle is 26 cm EQUATIONS REMEMBER: Always keep the equation balanced by performing the same operation to each side e.g. add, subtract, multiply or divide Example 1 Find the value for 1x which makes the equation true (we write 1x as x) Solve ‘x’ is written in italics, x ,so that it is different from the multiplication sign 2x - 5 = 9 = 14 = 7 Add 5 to both sides 2x Divide both sides by 2 x one ‘=’ sign per line ‘=’ signs placed beneath each other Example 2 Solve 3y + 2 = 7 5 5 /3 Subtract 2 from both sides 3y = Divide both sides by 3 y= PERCENTAGES % PERCENTAGES % WITHOUT A CALCULATOR WITH A CALCULATOR REMEMBER: ‘per cent’ means ‘out of 100’ 12% = 12/100 6% = 6/100 59% = 59/100 25% = 1/4 1% = 1/100 331/3% = 1/3 1 50% =