2 ObjectiveTo find equivalent fractions and write fractions in simplest form.Why? To help you solve addition and subtraction problems with unlike denominators.
3 California State Standards NS 1.0 : Solve problems involving fractions … NS 2.4 : Determine the least common multiple (LCM) and the greatest common divisor (GCD)of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator … to find the reduced form for a fraction)
4 Vocabulary Equivalent Fractions Fractions that name the same number½ = 2/4Simplest Form (Reduced Form) (Lowest Terms)A fraction is in simplest form when the greatest common factor of the numerator and denominator is one.2/4 = ½ (÷2)Least Common Denominator (LCD)The least common multiple of the denominators of two or more fractions12 is the least common denominator of ¼ and 1/6Greatest Common Divisor (GCD)The greatest number that can be divided into both the numerator and denominator to reduce the fraction to lowest terms.The GCD is 3 to reduce 2/6 to 1/3Identity Property of MultiplicationThe product of any number and one is that number1 x 5 = 5
5 How to Make Equivalent Fractions ) Use what you know to find the LCM of the numbers in the denominators 2) Multiply both the numerator and denominator by the same number that changed the denominator to the new LCM 3) Check your work12LCM of 3 and 12 = 121 · 4 =3 · 4 =4 , 4
6 How to Find if Fractions are Equivalent ) Use what you know to find the GCF of the numbers in the denominators 2) Divide both the numerator and denominator by the same number that changed the denominator to the new GCF 3) Check your work. Do NOT simplify.1 4= 3 · 1; 12 = 3 · 4GCF of 3 and 12 = 4÷ 4 = 112 ÷The fractions are equivalent or the same.
7 Simplifying Fractions 24Find the GCF of both the numerator and the denominatorDivide the numerator and denominator by the GCFCheck to be sure all numbers are prime. If not, continue to simplify12 24 GCF of 12 and 24 = ÷ 12 = 1 24 ÷ 12 = 2 12 is reduced to