1. FRACTIONS Fraction: a numerical quantity that is not a whole number Numerator: the number above the line in a common fraction showing how many of the parts indicated by the denominator are taken Denominator: the number below the line in a common fraction; a divisor. Proper Fractions: The numerator is less than the denominator Examples: 1/3, 3/4, 2/7 Improper Fractions: The numerator is greater than (or equal to) the denominatorExamples: 4/3, 11/4, 7/7 Mixed Fractions: A whole number and proper fraction togetherExamples: 1 1/3, 2 1/4, 16 2/5 Converting Improper Fractions to Mixed Fractions To convert an improper fraction to a mixed fraction, follow these steps: Divide the numerator by the denominator. Write down the whole number answer Then write down any remainder above the denominator. Converting Mixed Fractions to Improper Fractions To convert a mixed fraction to an improper fraction, follow these steps: Multiply, Add, Keep the Same Denominator DIVISIBILITY Factor: a number that divides into a whole number with a remainder of zero. Divisible: a number is divisible by another if upon division, the remainder is zero.

2. PRIME FACTORIZATION Prime Numbers: A whole number greater than ONE that has EXACTLY two factors: 1 and itself Composite Numbers: A whole number greater than ONE that has MORE than two factors. Prime Factorization: Every composite number can be written as the product of prime numbers in exactly one way if you ignore the order of the factors. ** Use Factor Trees ** GREATEST COMMON FACTOR Greatest Common Factor of two or more numbers is the GREATEST number that is a factor of EACH number. find the prime factorization of each number -identify ALL common factors and find their product = GCF LEAST COMMON MULTIPLE / LEAST COMMON DENOMINATOR (LCM / LCD) When you multiply a number by a whole number, you get MULTIPLES. The LCM of two or more numbers is the least of their common multiples, other than 0. Use prime factorization. Identify all common prime factors and solve for GCF. Once you have the GCF, multiply the GCF by the remaining prime factors. Common Denominator: common multiple of the denominators of two or more fractions. LCD: the least common denominator is the LCM of the denominators of two or more fractions.

3. ADDING AND SUBTRACTING FRACTIONS: To add or subtract fractions: 1.) Rename the fractions with a common denominator as necessary 2.) Add or subtract the numerators 3.) Simplify The LCD can be used to rename fractions for addition and subtraction... Remember: the LCD is the LCM of the denominators 7/8 - 1/3 21/24 - 8/24 = 13/24 ADDING AND SUBTRACTING MIXED NUMBERS To add or subtract mixed numbers: 1.) Add or subtract the fractions (find common denominator) Find the LCD if necessary 2.) Add or subtract the whole numbers 3.) Simplify