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7/27/2019 Mathematics Notesjjjjj

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1) Whole numbers are 0, 1, 2, 3...2) Steps to round off a whole number:

a) Identify the digit in the place value to be rounded off.b) If the digit to the right of the digit in (a) is

i. Less than 5, replace all the digits to the right of the digit in(a)with zeros.

ii. Equal to or greater than 5, add 1 to the digit in(a) and replaceall the digits to the right zeros.

3) For computations involving combined operations, we work out from left toright and follow the following sequence of operations.

a) Calculations within the bracketsb) Multiplications or divisionsc)Additions or subtractions

1)A sequence is a list of numbers that follow a certain rule.2) Odd numbers are 1, 3, 5, 7, 93) Even numbers are 2, 4, 6, 8, 104)A prime number is a whole number that is divisible by itself and 1 only.

Hence, prime numbers are 2, 3, 5, 7, 11 .

5)A factor of a set of whole numbers is the number that can divided exactlyevery number in the given set of numbers.

6)A prime factor of a set of whole numbers is the prime number that becomesthe factor of the set of numbers.


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7)A multiple of a whole number is the product of the whole number and a nonzero number .

8)A common multiple of a set of whole numbers is the number that becomes themultiple of every number in the set of numbers.

9) The lowest common multiple (LCM) of a set of whole numbers is the commonmultiples having the smallest value.

10)A common factor of asset of whole numbers is the number that becomes thefactor of every number in the set.

11)The highest common factor (HCF) of a set of whole numbers is the commonfactor having the largest value.

12)We use the algorithm of repeated divisions to determine the LCM and theHCF of set of given numbers.

1)A fraction is a number representing a part of the whole.2)A fraction is written in the form of a/b where a is called the numerator and

b is called the denominator.

3) Equivalent fractions are fractions having the same value.4) If two fractions have the same denominator, the one having the greater

numerator is the greater fraction. Hence, when comparing two fractions,

change the fractions to their respective equivalent fraction having the same

denominator first.

5)A mixed number is a number consisting of a whole number and a fraction.For example, 3 .

6)A proper fraction is a fraction in which the numerator is smaller than thedenominator

7)An improper fraction is a fraction in which the numerator is equal to orgreater than the denominator.


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8) When performing additions and subtractions of fractions, change thefractions to their respective equivalent fractions having the same

denominator first.

9) When performing multiplications and divisions, change the fractions toimproper fractions first.

1)A decimal is a number representing a fraction with denominator being thepower of 10.

2) The number of decimal places of a decimal is the number of digits to the rightof the decimal point that the decimal has.

3) We use the same rule to round off a decimal to a desired number of decimalsplaces.

4) When performing additions and subtractions of decimals, the decimals mustbe arranged in such a way that the decimal points are aligned on a vertical

line.

5)

In a multiplication of two decimals, the number of decimal places theproduct has is the total number of decimal places which the two decimals to

be multiplied have.

6) When performing a division of decimals, we must first multiply both thedividend and the divisor by a power of 10 so that the divisor becomes a

whole number.

7) We follow the same rule when performing calculations involving combinedoperations.


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1) A percentage is a fraction with 100 as the denominator.2) Percentage is denoted using the % sign. For example, 45/100 is written as

45%.3) (a) An increase = Final valueOriginal value

(b) A decrease = Original valueFinal value

4) Percentage increase/decrease = Increase/Decrase 100 %Original value

5) Final value after an increase= 100 + Percentage increase Original value

100

6) Final value after a decrease= 100 - Percentage decrease Original value

100

7)An increase could be a profit, a simple interest, a commission or dividend.8)A decrease could be a loss or a discount.

1)An integer is a whole number which could be a positive integer, a negativeinteger or zero.

2)A positive integer is a whole number greater than zero. It usually does notcarry any sign but can be denoted using a plus sign (+). For example, +$, 6

and 7 are positive integers.

3)A negative Integer is a whole number smaller than zero. It is denoted usinga minus sign (-). For example, -4, -9 and -13 are negative integers.

4)A positive integer is usually used to represent a gain, an increase, a rise, anaddition and so on.

5)A negative integer is usually used to represent a loss, a decrease, a descent,a subtraction and so on.


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6)Addition of integers is a process of determining the sum of two or moreintegers.

7) Subtraction of two integers is a process of determining the differencebetween the two integers.

8)Addition and subtraction of integers can be simplified as follows.a + (+b) = a + b a+(-b) = a- b

a- (+b)=ab a-(-b) = a + b

1)An unknown is a quantity whose value is yet to be determined.2) Examples of algebraic terms in one unknown : 4y1 5m1 2a3) The coefficient of an unknown is an algebraic term in one unknown is the

number lying before unknown.

4) Like terms are terms having the same unknown.5) Unlike terms are terms having different unknown.6) When numbers and algebraic terms are combined using plus or minus signs,

we shall obtain an algebraic expression.

1) Length is a measurement of distance between two points.2) The units of length are km, m, cm and mm.3) Mass is the measurement of the amount of matter in an object.4) The units of mass are tone, kg, g, and mg.5) Time is the measurement of interval between two events.6) The units of time include year, month, week, day, hour, minute and second.7)A time in a day is indicated using the 12-hour system or the 24-hour system.


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1)Angle is the measurement of a rotationusing the unit of degree ().2)A rotation of a whole turn is 360.3) Types of angles: acute, obtuse, right, reflex.4) The sum of anglesof a straight line is 180.5) The sum of angles at the point is 360.6) Parallel lines are lines that never meet.7) Perpendicular lines are lines that cross at the right angle.8) Vertically opposite angles are equal.9) If the sum of two is a right angle, they are said to be complementary angles.10)If the sum of two angles is 180, they are said to be supplementary angles. 11)The sum of two adjacent angles on a straight line is 180.

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