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Simplifying and Comparing Fractions

This guide provides a thorough overview of simplifying and comparing fractions. A fraction is said to be simplified when its numerator and denominator have a greatest common factor (GCF) of 1. To simplify fractions, divide both the numerator and denominator by their GCF. For comparing fractions, use a number line to graph them, or find a common denominator by calculating the least common multiple (LCM). Additionally, the heart method offers a visual approach for comparing fractions effectively.

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Simplifying and Comparing Fractions

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  1. Simplifying and Comparing Fractions 5.4

  2. Simplifying Fractions • A fraction is “simplified” when its numerator and denominator have a GCF of 1

  3. To Simplify Fractions • Divide the numerator and denominator by the GCF

  4. Example Simplify: • What is the GCF of 12 and 20? • 4

  5. Simplify • What is the GCF between 4 and 10? • 2

  6. Simplifying With Variables • Divide numbers by GCF • List the variables out • Cancel out the variables

  7. Simplify: 1 3

  8. Simplify:

  9. Comparing Fractions Using a Number Line • Graph the fractions on the number line • The number to the left is the smaller number

  10. Graph and Order from Least to Greatest

  11. Comparing Fractions • Get the same denominator (LCD) • Find the LCM of the denominators • Make an Equivalent fraction • Multiply each the fraction (numerator and denominator) by number to make the LCM • Once the denominators are the same compare the numerators

  12. Compare Using <, > or =

  13. Compare Using <, > or =

  14. Heart Method to Compare Fractions • Multiply the diagonals, bring down and compare the products

  15. Use the heart method to compare

  16. Use the heart method to compare

  17. Homework Page 236 (16-42) even

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