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Numbers O-­β€Level E. Math Reference Notes Rational Numbers Rational numbers are numbers that can be expressed as a fraction. !
Includes integers 𝑒𝑔. 5 π‘π‘Žπ‘› 𝑏𝑒 𝑒π‘₯π‘π‘Ÿπ‘’π‘ π‘ π‘’π‘‘ π‘Žπ‘  ! !
!!
Examples: 0, ! , 0.3, !" ; 4; βˆ’8 Irrational Numbers Irrational numbers are numbers that cannot be expressed as a fraction. Examples: 2, 3, 5, πœ‹, 𝑒 Recurring Decimals Recurring decimals are decimals that have a non-­β€ending string of numbers behind the decimal point that follows a periodic pattern !
Example: !! = 0.8181818181 … = 0. 81 Prime Numbers Prime numbers are positive integers that can be only divided by 1 and itself. Examples: 2, 3, 5, 7, 11, 13 *The number 1 is not a prime number Composite Numbers Numbers (positive integers) that are not prime numbers are composite numbers Prime Factorization A positive integer can be expressed as prime numbers multiplied together Example 140 = 2! × 5 × 7 360 = 2! × 3! × 5 Perfect Squares Perfect squares are squares of an integer Examples: 4, 9, 16, 25, 36, 49, 64 ,... Perfect Cubes Perfect cubes are cube of an integer Examples: 8, 27, 64, 125, 216, 343, … Square Roots Example 2! × 5! = 2 × 5 2! × 3! × 7! = 2! × 3 × 7! Cube Roots Example !
2! × 3! = 2 × 3 !
2! × 3! = 2! × 3 KiX Education Singapore www.kix.sg Numbers O-­β€Level E. Math Reference Notes Highest Common Factor (HCF) The highest common factor of a group of numbers is the greatest common factor among the numbers Lowest Common Multiple (LCM) The LCM of a group of numbers is the smallest common multiple among the numbers Example: LCM of 20 and 25 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, … Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, … LCM = 30 Finding HCF and LCM using prime factorization (Method 1) 84 = 2! × 3 × 7 150 = 2 × 3 × 5! 360 = 2! × 3! × 5 𝐻𝐢𝐹 = 2 × 3 𝐿𝐢𝑀 = 2! × 3! × 5 × 7 Finding HCF and LCM using prime factorization (Method 2) Finding HCF Finding LCM 2 3 84 150 360 42 75 180 14 25 60 2 2 2 3 3 5 5 7 HCF = 2 × 3 84 150 360 42 75 180 21 75 90 21 75 45 7 25 15 7 25 5 7 5 1 7 1 1 1 1 1 LCM = 2! × 3! × 5 × 7 KiX Education Singapore www.kix.sg
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