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Understanding Equivalent Fractions and Simplifying to Lowest Terms

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mayda
13 diapositives · 306 Views · Aug 10, 2014

This lesson covers the concept of equivalent fractions, guiding students to identify and create fractions that represent the same value. Students will learn to write fractions in simplest form using the greatest common factor (GCF) and the least common denominator (LCD). This knowledge is essential for effectively solving addition and subtraction problems involving unlike denominators, in alignment with California State Standards. Through practice, students will enhance their fraction-solving skills, ensuring a solid foundation in mathematical reasoning.

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Understanding Equivalent Fractions and Simplifying to Lowest Terms
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  1. 4-76th grade math Equivalent Fractions

  2. Objective • To 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 number • ½ = 2/4 • Simplest 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 fractions • 12 is the least common denominator of ¼ and 1/6 • Greatest 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 1/3 • Identity Property of Multiplication • The product of any number and one is that number • 1 x 5 = 5

  5. How to Make Equivalent Fractions 1 4 3 12 1) 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 work 1 4 • 12 LCM of 3 and 12 = 12 1 · 4 = 4 4 3 · 4 = 12 12 4 , 4 12 12

  6. How to Find if Fractions are Equivalent 1 4 3 12 1) 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 12 3 = 3 · 1; 12 = 3 · 4 GCF of 3 and 12 = 4 1 4 ÷ 4 = 1 • 12 ÷ 4 3 The fractions are equivalent or the same.

  7. Simplifying Fractions Simplify 12 24 • Find the GCF of both the numerator and the denominator • Divide the numerator and denominator by the GCF • Check to be sure all numbers are prime. If not, continue to simplify 12 24 GCF of 12 and 24 = 12 12 ÷ 12 = 1 24 ÷ 12 = 2 12 is reduced to 1 24 2

  8. Try It! Simplify • 12 22 • 14 28 3) 24 40 • 12 = 22 12 = ÷ 2 = 6 22 ÷ 2 = 11 • 14 = 28 14 = ÷ 7 = 2 ÷ 2 = 1 • ÷ 7 = 4 ÷ 2 = 2 3) 24 40 24 = ÷ 8 = 3 40 ÷ 8 = 5 

  9. 4) 38 46 5) 24 54 4) 38 = 46 38 = ÷ 2 = 19 46 ÷ 2 = 23 5) 24 = 54 24 = ÷ 6 = 4 54 ÷ 6 = 9

  10. Try Some More! • 8) 7 8 • 6 10 • LCD = 30 • 7 · 5 = 35 8 · 3 = 24 • 6 · 5 = 30 10 · 3 = 30 • 35 , 24 • 30 • 8 4 • 9 12 • LCD = 36 • 8 · 4 = 32 4 · 3= 12 • 9 · 4 = 36 12 · 3= 36 • 32 , 12 • 36 Use the LCD to write each set of fractions as equivalent fractions, or fractions with the same denominator. 6) 5 , 5 6 30 7) 6 , 4 10 30 8) 7 8 6 10 • 8 4 9 12 6) 5 , 5 6 30 LCD = 30 5· 5 = 25 , 5 6 · 5 = 30 30 25 , 5 • 30 7) 6 , 4 10 30 LCD = 30 6 · 3 = 18 , 4 10 · 3 = 30 30 18 , 4 30 30

  11. 4 , 5 , 7 3 8 9 • 4 · 24 5 · 9 7 · 8 3 · 24 8 · 9 9 · 8 LCD = 72 96 45 56 72 72 72

  12. Objective Review • To find equivalent fractions and write fractions in simplest form. Why? You can now solve addition and subtraction problems with unlike denominators.

  13. Independent Practice • Complete problems 12-24 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 25-29 • If still more time, work on Accelerated Math.