A NOTE ON CALCULATOR USE Many of the problems in this series demand the use of a number of consecutive calculations, often adding, subtracting, multiplying or dividing the same amount in order to complete entries in a table or see a pattern. This demands (or will build) a certain amount of sophisticated use of the memory and constant functions of a simple calculator. 1. To add a number such as 9 repeatedly, it is sufficient on most calculators to enter an initial number (e.g. 30) then press + 9 = = = = to add 9 over and over. • 30, 39, 48, 57, 66, … • To add 9 to a range of numbers, enter the first number (e.g. 30) then press + 9 = 30 + 9 = 39, 7 = gives 16, 3 = gives 12, 21 = gives 30, … • These are the answers when 9 is added to each number. 2. To subtract a number such as 5 repeatedly, it is sufficient on most calculators to enter an initial number (e.g. 92) then press – 5 = = = = to subtract 5 over and over. • 92, 87, 82, 77, 62, … • To subtract 5 from a range of numbers, enter the first number (e.g. 92) then press – 5 = 95 – 5 = 37, 68 = gives 63, 43 = gives 38, 72 = gives 67, … • These are the answers when 5 is subtracted from each number. 3. To multiply a number such as 10 repeatedly, most calculators now reverse the order in which the numbers are entered. Enter 10 x, then press an initial number (e.g. 15) = = = = to multiply by 10 over and over. • 10, 150, 1500, 15 000, 150 000, … • These are the answers when the given number is divided by 8. • This also allows squaring of numbers: 4 x = gives 16 or 42. • Continuing to press = gives more powers: • 4 x = = gives 43 or 64, 4 x = = = gives 44; 4 x = = = = gives 45 and so on. • To multiply a range of numbers by 10, enter 10 x then the first number (e.g. 90) and = • 10 x 90 = 900, 45 = gives 450, 21 = gives 210, 162 = gives 1620, … • These are the answers when each number is multiplied by 10. CALCULATOR BSCX56 AC % 900 ON OFF MRC M– M+ CE 7 8 9 ÷ 4 5 6 x 1 2 3 – 0 . = + 4. To divide by a number such as 8 repeatedly, enter a number (e.g. 128). • Then press ÷ 4 = = = = to divide each result by 4. • 32, 16, 8 , 2, 0.5, … • These are the answers when the given number is divided by 8. • To divide a range of numbers by 8, enter the first number (e.g. 90) and ÷ 4 = 128 ÷ 4 = 32, 64 = gives 4, 32 = gives 8, 12 = gives 1.5, … • These are the answers when each number is divided by 8. 5. Using the memory keys M+, M– and MR will also simplify calculations. A result can be calculated and added to memory (M+). Then a second result can be calculated and added to (M+) or subtracted from (M–) the result in the memory. Pressing MR will display the result. Often this will need to be performed for several examples as they are entered onto a table or patterns are explored directly. Clearing the memory after each completed calculation is essential! A number of calculations may also need to be made before addition, subtraction, multiplication or division with a given number. That number can be placed in memory and used each time without needing to be re-keyed. 6. The % key can be used to find percentage increases and decreases directly. • To increase or decrease a number by a certain per cent (e.g. 20%), simply key the number press = 20% or – 20% to get the answer: • 80 + 20% gives 96 (not 100) – 20% of 80 is 16, 80 + 16 is 96. • 90 – 20% gives 72 (not 70) – 20% of 90 is 18, 90 – 18 is 72. 7. While the square root key can be used directly, finding other roots is best done by a ‘try and adjust’ approach using the multiplication constant described above (in point 3). xx <strong>Problem</strong>-<strong>solving</strong> in mathematics www.ricpublications.com.au R.I.C. Publications ®
ISOMETRIC RESOURCE PAGE 72 <strong>Problem</strong>-<strong>solving</strong> in mathematics www.ricpublications.com.au R.I.C. Publications ®
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