ALGEBRAIC EXPRESSION Definition with examples Expansion of algebraic expression Factorization of simple algebraic expressions Definition with examples In algebra, letters stand for numbers. The numbers can be whole or fractional, positive or negative. Example Simplify the following -5 x 2y -3a x -6b -14a/7 -1/3 of 36×2 Solution 1) -5 x 2y = […]
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ADDITION AND SUBTRACTION OF DIRECTED NUMBERS Directed numbers are the positive and negative numbers in any given number line e.g -4 -3 -2 -1 0 1 2 3 4 The (+) and (-) signs show the direction from the origin (o). To add a positive number move to the
APPROXIMATION OF NUMBERS ROUNDING OFF TO DECIMAL PLACES Digits 1,2,34 are rounded down to Zero, while digits 5, 6, 7, 8, and 9 are rounded up to 1 e.g. 126=130 to 2 digits A significant figure begins from the first non-zero digit at the left of a number. Digit should be written with their correct
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Interest is the money paid for saving a particular amount of money. Simple interest can be calculated using the formula Simple interest I = PRT/100 Where P= principal, R=rate & T= time Also total amount =principal +interest Example 1 Find the simple interest on N60, 000 for 5 years at 9% per annum
Fractions and Percentages A fraction can be converted to decimal by dividing the numerator by its denominator. It can be changed to percentage by simply multiplying by 100. Example 5.1 Change 3/8 into a decimal and percentage Convert 0.145 to percentage Solution 1) 3/8 = 0.375 in decimal 3/8 x 100% = 37.5% 2) 0.145×100=14.5%
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Highest Common Factors Highest common factor is the greatest number which will divide exactly into two or more numbers. For example 4 is the highest common factor (HCF) of 20 & 24. i.e. 20 = 1, 2, (4), 5, 10, 20 24= 1, 2, 3, (4), 6, 8, 12, 24 Example 1: Find the
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Difference between Whole Numbers and Decimal Numbers Whole number is a number without fraction. For example 1, 2, 3, 41000, 38888 are examples of whole numbers.71/2 is not a whole number. A decimal number is a fractional number less than 1. It is smaller to a whole number. Examples – 0.1,0.01,0.001etc Whole Numbers in
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Definition of Integer An integer is any positive or negative whole number Example: Simplify the following (+8) + (+3) (ii) (+9) – (+4) Solution (+8) + (+3) = +11 (ii) (+9) – (+4) = 9-4 = +5 or 5 Evaluation Simplify the following (+12) (+7) (ii) 7-(-3)-(-2) Indices The plural of index
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The units used for measuring weight are kilogram (kg) and gram (g). 1000 gram = 1kg 1000kg = 1 ton EXAMPLE1 Change to kilogram 2000g to kilogram 1000g = 1kg 2000g = m Cross multiply 1000 × m = 2000 x 1 1000m = 2000 m = 2000 = 2kg 1000
Volume of cylinder = πr2h = π x r x r x h EXAMPLE Find the volume of a cylinder of radius 3 ½ cm and height 12cm Solution Volume = π x r x r x h =22 x 7 x 7 x 12cm 7 x 2 x 2 x 1 = 22
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A right-angled triangle has 3 – sides Example 1 Calculate the area of a triangle of height 12cm and base 13cm Solution Area of triangle = ½ x base x height = ½ x 12cm x 13cm 1 1 = 1 x 6cm x 13cm = 78cm2 EXERCISE Calculate the area of the
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Profit or loss percent is expressed as a percentage of the cost price EXAMPLE 1 An article bought for $3,000 was sold for $3,300. Find the profit percent Solution Cost price = $3,000 Selling price = $3,300 Profit = $3300 – $3,000 = $300 Profit % = Profit x 100 Cost price 1
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Meaning of interest: interest means the extra money that you [ay back when ypu borrow money that you receive when you invest money. EXAMPLE 1 find the simple interest on $1,000 for 5 years at 3% per annum. SOLUTION Principal = $1,000 (the amount borrowed Time = 5 years (the period for which the money
MEANING OF PROFIT When the selling price of an article is higher or greater than the cost price, we have a profit or gain. Profit = selling price – cost price MEANING OF LOSS When the selling price is less than cost price we have a loss. Loss = cost price – selling price
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Percentages are fractions with 100 as denominator EXAMPLE 1 Change the following fractions to percentages 2/5 = 2/5 of 100 = 2/5 × 100 = 200 = 40% 5 EXAMPLE 2 Change these percentage to fractions 75% = 75 = 15 = 3 100 20 4 EXAMPLE 3 Change 7 ½% to fractions in
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Meaning of Ratio The relation between two quantities (both of the same units) obtained by dividing one quantity with another is called ratio. Ratio can be denoted by using the symbol ( : ). EXAMPLE 1 What is the ratio between the weight two bags of sugar of 4kg and 6kg respectively? Solution Ratio of
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Example 1 A man bought a leather bag for N350.00 and sold it for N360.00 will he have more money or less money with him? Solution Selling price = N460.oo Cost price = – N350.00 Profit (gain) = N110.00 Note: profit or gain = selling price – cost price Example 2 If a
EXAMPLE Find the cost of 3 books at N91.55 each. Solution N91. 55 × 3 N274.65 EXERCISE 52 x 4 75 x 6 75 x 6 91 x 8 37 x 6 A bag of salt costs N585.40. how much will I pay for 5 bags? What is the cost of 6 meters of
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Addition of Money Example: find the sum of N4.36, N3.79 and N4.82 N K 4 36 + 3. 7 9 + 4. 8 2 12. 9 7 EXERCISES Add up 00, N24.70 and N32.55 20, N174.30 and N132.30 00, N152.10 and N184.20 80, N378.35 and N29.46 Fin the sum, of N168.00 and N276.00
Rounding off decimals to the nearest whole number Rules for rounding off decimals to the nearest whole number When the rounding off decimals to the nearest whole number, look at the digit in the tenths place. If this digit is 5 or greater than 5, replace the digits after the decimal point by zero and