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Mathematics (All Classes)

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ESTIMATION

ESTIMATION Estimation may be explained as a rough or sensible guess fo a value or calculation. Although, the estimated value is not correct, it gives us an idea of what the correct answer should be. The common units of length are kilometer (km), meters (m), centimeters (cm), millimeters (mm).Mass = (Tonne, kilogram (kg) gramme (g). Capacity = (litre (l), centiliter (cl), militre(ml) It is important to be able to choose the most appropriate metric units of measurement to use. Example: To measure distance less than a metre, smaller units such as milimetre (mm), and centimeter are used to measure large distance, metre and kilometer (km) are used.   State the metric units of the length you would use to measure the following: (a). Length of your class room = metre (m0 (b). Length of your fingers nail = milimetre (mm) (c). your height = centimeter (cm) (d) Distance between Lagos… Read More »ESTIMATION

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ALGERAIC FRACTIONS

ALGERAIC FRACTIONS To add or subtract fractions with different denominators, first change them to equivalent fractions. This is done by finding the L C M of the denominators Example1: Simplify 2a/5 + 4a/3 Solution: The L C M is 15 6a + 20a/ 15 = 26a/15 Example 2: Simplify 3/5x + 1/2x – 1/4x Solution: Find the L C M of the expression = 20X 12 + 10 – 5 = 17/20X   SIMPLIFYING FRACTION Example 1: Reduce 25X4Y3/35X3y3 solution Divide through by 5X3Y3(the common factor ) = 5x/7 Example 2: Reduce 8X3Y2/6X3Z Solution: Divide through by 2X 3(the common factor) 4Y2/3Z   MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTION Example 1: Simplfy (X-2)/7 * 4/(X-2) Solution : X – 2/7 * 4/ X -2 (X-2) divides themselves = 4/7 Example 2: Simplify 6X2/11y ÷ 18X/33Y2 Solution 6X2/11y * 33Y2/18X (division sign change to multiplication) = XY FRACTIONS WITH BRACKETS Example1:… Read More »ALGERAIC FRACTIONS

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MULTIPLICATION AND DIVISION OF DIRECTED NUMBERS

MULTIPLICATION AND DIVISION OF DIRECTED NUMBERS Revision on addition and subtraction of directed numbers Note that:  (a). + + = + OR – – = + (Replacing the same signs that apprear together by a positive sign (b). +  –  = – OR – + = – (Replacing two different signs that appear together by a negative sign   Example 1: Find the values of the following: (a). + 7  + (+8) (b) +13 – (+6) Solution: (a).  + 7 + (+8) = 7 + 8 = 15 (b). + 13 – (+6) = 13 – 6 = 7 Example 2 : Calculate the following (a) 25 – (+3) (b) 12 – (-9) Solution (a). 25  – (+3) = 25 – 3 = 22 (b). 12 –  (-9) = 12 + 9 = 21   MULTIPLICATION OF DIRECTED NUMBERS RULES: +  *  – = –  OR – * + =… Read More »MULTIPLICATION AND DIVISION OF DIRECTED NUMBERS

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APPROXIMATION AND ESTIMATION

APPROXIMATION AND ESTIMATION (SIGNIFCANT AND DECIMAL PLACES) SIGNIFICANT: TO ROUNDOFF A NUMBER CHANGE 0,1,2,3,4 TO 0 WHILE 5,6,7,8,9 TO 1 AND ADD IT TO THE NEXT NUMBER Example 1: round off 492.763 to (a) 3 s.f (b) 3 s.f (c) 2 d.p (d) 4 d.p Solution: (a). 492.763 = 49 (since the third number is 2 it has change to zero) (b). 492.763 = 493 (the 2 as change to 3 because 7 as change to 1 and been added to 2 to become 3) (c).492.763 = 492.76 (in decimal point we count after the point). (d). 492.763 = 492.7630(since the number is not upto 4d.p we add zero to it.) Example 2: calculate the following and round your answer to the given degree of a accuracy (a). 576.175 + 20.82 (2 d.p) (b). 8.52 x 0.0651 (3 s.f) Solution: (a). 576.173 + 20.82 = 596.99 596.99 = 596.99 (2… Read More »APPROXIMATION AND ESTIMATION

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ARITHMETIC | SIMPLE INTEREST, PROFIT AND LOSS, DISCOUNT AND COMMISSION

HOUSEHOLD ARITHMETIC (SIMPLE INTEREST, PROFIT AND LOSS, DISCOUNT AND COMMISSION) PROFIT AND LOSS When a trader buys or sells goods, the price at which he /she sells is called selling price while the price at which he/she buys is called cost price. When the good is sold at a price greater than the cost price, then the trader has made a gain or profit. On the other hand, when the good is sold at a price less than the cost price, then the trader has made a loss. S.P means selling price, C.P means cost price. Profit = SP – CP                      %P = P/CP * 100                    LOSS = CP –SP             %L = L/CP *100 Example 1: a man buys a pair of shoe for Ħ3000 and sold it for Ħ3300. Find the percentage profit. Solution: SP = Ħ3300, CP = Ħ3000, P = SP – CP = Ħ3300 –… Read More »ARITHMETIC | SIMPLE INTEREST, PROFIT AND LOSS, DISCOUNT AND COMMISSION

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ALGEBRAIC PROCESSES

ALGEBRAIC PROCESSES Objective:  Use letter to generalize statements Interpret mathematical symbols Solve simple and problems Generating statement The following symbols are generally used in mathematics “=” means is equal to” Example: 13 – 6 = 7 means thirteen minus six is equal to seven “>” means is greater than” Example: 18 > 10 means eighteen is greater than ten” “<” means is less than” Example:  -10 < 2 mean negative ten is less than two “ ” means is approximately equal to” Example:   is approximately equal to 3.142 that is  3.14 “ ” means not equal to” Example:  2  3 means two is not equal to three. Exercise Write the following using symbols M is equal to 8 (ii) y lies between 8 and 12 (iii)          Twice y equals fourteen, therefore y equals seven.   OPERATION IN ALGEBRA EXAMPLE Write down the meaning of the following and find the values… Read More »ALGEBRAIC PROCESSES

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