# Mathematics (Primary Classes) ## WEIGHT

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   EXAMPLE 2 Change 5kg to grams Solution To change from kg to grams, multiply by 1000 5kg = 5 x 1000 = 5000 grams   EXERCISE Change the following to kilograms: 2000g 5000g 3500g 1205g 750g   Change to grams 5 kg 5kg 298kg 765kg 020kg 07kg   See also VOLUME OF CYLINDER AREA OF RIGHT ANGLED TRIANGLE PROFIT AND LOSS PERCENT SIMPLE INTERREST MONEY: PROFIT AND LOSS ## VOLUME OF CYLINDER

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 x 7 x 3                     1 x 1 x 1                 = 462cm3   Exercise (take π= 22/7) Find the volume of cylinders whose radii and heights are given as: Radius 3.5cm, height = 10cm Radius 10.5, height 10m Radius 4.2cm, height15cm Diameter = 1o½cm, height 16cm Diameter = 14cm, height 15cm   See also AREA OF RIGHT ANGLED TRIANGLE PROFIT AND LOSS PERCENT SIMPLE INTERREST MONEY: PROFIT AND LOSS SIMPLE PROBLEMS ON PERCENTAGES ## AREA OF RIGHT ANGLED TRIANGLE

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 triangles with the following dimensions Base = 14cm, height = 16cm Base = 10cm, height = 8cm Base = 25cm, height = 22cm Base = 30cm, height = 15cm Base = 24cm, height = 18cm Base = 14cm, height = 16cm Base = 34cm, height = 15cm Base = 52cm, height = 48cm   See also PROFIT AND LOSS PERCENT SIMPLE INTERREST MONEY: PROFIT AND LOSS SIMPLE PROBLEMS ON PERCENTAGES RATIO AND PERCENTAGE ## PROFIT AND LOSS PERCENT

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                  = 300     x   100 3000          1 = 300 x 1 = 300 = 10% 30 x 1       30   EXAMPLE 2 A book bought for \$25,000 was sold for \$22,000. What is the loss percent? Solution Cost price =\$25,000 Selling price= \$22,000 Loss = \$25,000 – \$22,000 = \$3,000   Loss % =loss           x 100 Cost price      1 =3000   x  100  = 12%   25000       1   EXERCISE Cost price Selling price Profit % Loss% 1. \$1,300 \$1,365 1. \$33,555 \$32,446 2. \$56,000 \$59,540 3. \$100,680 \$99,960   See also SIMPLE INTERREST MONEY: PROFIT… Read More »PROFIT AND LOSS PERCENT ## SIMPLE INTERREST

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 is borrowed before it is paid back in full) Rate = 3% (extra money paid)   Simple interest = P  x R x T 100   = 1,000 x 3 x 5                                   100 = 10 x 3 x 5 = \$150     EXAMPLE 2   Seun deposit \$14,500 in a savings Bank account at UBA which pays an interest rate of 15% per annum for 2 ½ years. What is the simple interest?   Solution Principal = \$14,500 Rate= 15% Time= 2 ½ or 2.5 years SI = P x  R x T… Read More »SIMPLE INTERREST ## MONEY: PROFIT AND LOSS

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   EXAMPLE 1 If a clock is bought for \$1,145 and sold for \$1,170, what is the gain or losss Solution Cost price of clock = \$1,145 Selling price = \$1, 170 Since the selling price is more than the cost price, we have a profit Profit = \$1,170 – \$1,145 = \$25   EXAMPLE 2 By selling a tin of oil for \$1,320, a man made a profit of \$150. How much did he pay for it? Solution Selling price = \$1,320 Profit =  \$150 Cost price = \$1,320 – \$150 = \$1,170.  … Read More »MONEY: PROFIT AND LOSS ## SIMPLE PROBLEMS ON PERCENTAGES

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 their lowest terms Solution 7 ½ % = 7 ½ out of 100 = 15/2 × 1/100 = (15 × 1) ÷ 200 = 15 ÷ 200 = 3/40 EXERCISE Change the following fraction to percentage 2/5 2/4 3/30 Change to fractions in their lowest terms 66 ½ % 12 ¼ % 16 2/3 %   See also RATIO AND PERCENTAGE PROFIT AND LOSS PROBLEM ON MULTIPLICATION OF MONEY Money ESTIMATION ## RATIO AND PERCENTAGE

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 weights of bags of sugar = 4kg/ 6kg = 2/3 = 2:3 EXAMPLE 2 A pole of length 165cm is divided into two parts such that lengths are in the ration 7:8. Find the length of each part of the pole? Total ratio = 7 + 8 = 15 First part = 7/15 , second part = 8/15 Length of first part = 7/15 of 165cm =  7/15 × 165 = 7 x 11  = 77cm 1 x 1 Light of second part = 165cm – 77cm = 88cm   DIRECT PROPORTION Examples A marker… Read More »RATIO AND PERCENTAGE ## PROFIT AND LOSS

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 lady bought a wrist watch for N800 and sold it for N600. Will he have money or less money with her?   Solution The selling is price is less than. Therefore, she will have less money with her. That is, she sold at a loss.   Cost price of wrist watch             = N800.00 Selling price                                     = N600.00 Loss                                                   N200.00   EXERCISE The cost price of an article is is N450.30 and the selling price is N510. Find the profit or loss. Mallam jimoh bought a meter of cloth for N155.50 and sold it N147.75,… Read More »PROFIT AND LOSS ## PROBLEM ON MULTIPLICATION OF MONEY

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 while poplin at N212. 85 per meter? Find the cost of 7 chairs if one chair costs N423.50   DIVISION OF MONEY Example Four children were given n624.40 to share equally. how much will each of them. Get? Solution Note that N624.00 = 62400k = N624.00 x 4 = N156.10 EXERCISES Divide N1.68 by 4 Divide N2.25 by 9 Divide N44.80 by 8 Divide N11.76 by 7 610k by 5 Five boys are to share N615.55 equally. How much will each receive? See also Money ESTIMATION HIGHEST COMMON FACTOR (HCF) LEAST COMMON MULTIPLES (LCM) SQUARES… Read More »PROBLEM ON MULTIPLICATION OF MONEY

## Money

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 Find the sum of N128.10, N78.30 and N8.05 I have N1000 in my pocket and my father gave me N174.20 more. How much do I have altogether?   Subtraction of Money Example 1 What is the difference between N167.50 and N345.00?   N    K 345.00 –167. 50 177.50 EXERCISE 2 Find the difference between N406.60 and N322.20 Find the different between N270 and N162.30 Subtract N236.44 from N475.00 I have N150.00 and I bought a spoon for N85. How much is my change? How much more is N147.50 greater than N112.80 How much more is… Read More »Money ## ESTIMATION

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 add 1 to the digit in the units place If this digit is less than 5, replace the digits after the decimal point by zero.   Note: ‘≈’ means ‘is approximately equal to’   Example: round off the following decimal numbers to the nearest whole numbers.   6.7 ≈ 7 to the nearest whole number 6.3 ≈ 6 to the nearest whole number 17 ≈20 to the nearest ten   EXERCISE1. Write to the nearest whole number 7 1 9 6 9 2   Exercise 2 Write to the nearest ten 7 7 9 6… Read More »ESTIMATION

## HIGHEST COMMON FACTOR (HCF)

The product of 2 and 3 is; 2 x 3 = 6 2 and 3 are factors of 6 The factors of a number are numbers that divide the number without a remainder   EXAMPLE Find the common factors of 24 and 36 24 =    1 x 24                                             36 =   1 x 36 =    2 x 12                                                     =   2 x 18 =     3 x 8                                                        =   3 x 12 =     4 x 6                                                        =   4 x 9 =    6 x 6 Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36 Common factors of 24 and 36 are: 1, 2, 3, 4, 6, 12 The highest common factor  is 12.   EXERCISE Find the HCF of: 6 and 9 6 and 27 21 and 14 12 and 18 6 and 21… Read More »HIGHEST COMMON FACTOR (HCF) ## LEAST COMMON MULTIPLES (LCM)

Example 1: Find the least common multiples of 2 and 3 The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24 The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, and 36 Thus the common multiples of 2 and three are 6, 12, 18 and 24   The smallest of these multiple s(i.e. the least) is 6 We say that the least common multiple of 2 and 3 is 6. That is L.C.M of 2 and 3 is 6   EXERCISE   Find the by listing the multiples of: 2 and 5 3 and 4 3 and 5 4, 2 and 6 2 and 7 2 and 12 3 and 7 3 and 12 2, 3 and 5 2 and 10 2, 4 and 6 3 and 15 4 and 7 4 and 7  … Read More »LEAST COMMON MULTIPLES (LCM) ## SQUARES AND SQUARE ROOTS OF NUMBERS

SQUARES AND SQUARE ROOTS OF NUMBERS (1- digit and 2 – digit numbers)   Example: 1: find 22 = 4 2 =( 2 x 2) + ( 4 x 4) = 4 + 16 = 20 Example 2: find 42 – 22 = (4×4) – (2 x 2) = 16 – 4 = 12 Example 3: find 32 + 32 = (3 x 3) + (3 x 3) = 9  +  9 = 18 Example 4: 102 – 42                   = (10 x 10) – (4 x 4) = 100 – 16 = 84   Exercise 1 Find the value of: 42 + 62 52 – 22 5­­­­­2 + 72      102 – 52 82 + 102 82 – 62 22 x 52 32 x 42 42 x 32 52 x 22 62 x22 22 x 32 x 52 22 x 32 x 52 32 x 22 x 52   See… Read More »SQUARES AND SQUARE ROOTS OF NUMBERS ## MULTIPLICATION OF NUMBERS

MULTIPLICATION OF NUMBERS BY 2-DIGIT NUMBERS Example 1 multiply 25 by 12 Method 1: column form                                                  method 2: Expanded form 2    5                                                                25 x 12 = 25 x (10 = 2) x  1    2                                                                              = (25 x 10) = (25 x 2) 2   5   0                  (25 x 10)                                          = 250 + 50 +   5   0                  (25 x 2)                                           = 300 3   0   0   EXERCIES 1: Multiply the following 53 x  50                                                     84  x  10 97 x  10                                                     96  x 40 67 x  50                                                     67  x  50 87 x  20                                                    64  x  30 57 x  40                                                    64  x  40 56 x  10                                                    95  x  20 86 x  20                                                    84  x  50 99 x  50                                                 75  x  10 89 x  30 75 x  40   EXERCISE 2: multiply the following 89  x… Read More »MULTIPLICATION OF NUMBERS

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