1 Math Chapter 1: Number Sense and Operations 1.1 Order Rational Numbers Rational Numbers: all numbers that can be expressed as a ratio of two integers 𝑎 𝑏 where b ≠ 0 Irrational Numbers: cannot be expressed as a ratio of two integers; they have non-terminating decimals that DO NOT repeat Example: Pi - 3.1415926535 8979323846 2643383279 5028841971 6939937510….. 2 Fractions and Decimals Fractions: millionths Hundred thousandths Ten thousandths thousandths Hundredths tenths and ones tens hundreds ten thousands hundred thousands millions . Decimals: Compare Fractions and Decimals Fractions Same denominator? Look at the numerator Different denominators? Rewrite one or both fractions with a common denominator Examples: 1. 2/4 and 6/ 8 2. 1/2 and 4/5 3 Absolute Value Symbol: | | Definition: the distance a number is away from 0 |-2| = 2 |2| = 2 1.2: Apply Number Properties Factors and Multiples Factor: any whole number that can be multiplied by another number Prime Factor: Can only be divided by itself or the number 1; not 0 or 1 o Examples: 2, 3, 5, 7, Prime Factorization: shows a number written as a product of its factors 4 Greatest Common Factor: the greatest factor shared by two composite (not prime) numbers Least Common Multiple: least multiple shared by two numbers 5 Properties of Numbers Order of Operations 1.3: Compute with Exponents Notation 𝑏𝑒 : b = base; e = exponent example: 33 = 3 x 3 x 3 Any number raised to the power of 0 is ______ 6 Reciprocal: Squares and Cubes Squares = raised to the 2nd power; 𝑎2 Cubes = raised to the 3rd power; 𝑎3 Rules of Exponents 1. Product of Powers Property (Multiplication) 𝑎𝑚 X 𝑎𝑛 = 𝑎𝑚+𝑛 2. Quotient of Powers Property (Division) 𝑎𝑚 𝑎𝑛 = 𝑎𝑚−𝑛 3. Power of a Power Property (𝑎𝑚 )𝑛 = 𝑎𝑚𝑛 4. Power of a Product Property 𝑎𝑛 𝑏 𝑛 = (𝑎𝑏)𝑛 5. Power of a Quotient Property 𝑎𝑛 𝑏𝑛 𝑎 𝑛 = (𝑏 ) 7 Scientific Notation: dealing with very large numbers Radicals and Rational Exponents Dividing Radicals: