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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…..
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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
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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
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Greatest Common Factor: the greatest factor shared by two composite (not prime) numbers
Least Common Multiple: least multiple shared by two numbers
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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 ______
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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 )
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Scientific Notation: dealing with very large numbers
Radicals and Rational Exponents
Dividing Radicals: