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Equivalent Fractions

Equivalent Fractions. Lesson 4-7. Bell Work. Name the greatest common factor for each pair. 1. 5 and 10 2. 9 and 12 3. 20 and 24 4. 10 and 14 5. 6 and 8 6. 8 and 15. 5. 3. 4. 2. 2. 1. Today’s Math Standards. Number Sense 1.0 (this is what we are working toward)

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Equivalent Fractions

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  1. Equivalent Fractions Lesson 4-7

  2. Bell Work Name the greatest common factor for each pair. 1.5 and 10 2. 9 and 12 3. 20 and 24 4. 10 and 14 5. 6 and 8 6. 8 and 15 5 3 4 2 2 1

  3. Today’s Math Standards • Number Sense 1.0 (this is what we are working toward) • Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages: • Number Sense 2.4 • Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

  4. Equivalent Fractions • We use the GCF and the LCM to make equivalent fractions • GCF to make smaller equivalent fractions • Reduce • Simplify • Put in lowest terms • LCM to make equivalent fractions • Make common denominators • Addition • Subtraction • Comparing (with and without number lines)

  5. Key Vocabulary • equivalent fractions • Fractions that name the same number • improper fraction • A fraction whose numerator is larger than the denominator • mixed number • A whole number and a fraction

  6. 6 10 3 5 x 2 columns 2 columns = 15 25 3 5 x 5 columns 5 columns x = x Notice how all three of the rectangles still have these same 5 rows. The only thing that has changed is the number of columns. Equivalent Fractions Different fractions can name the same number. 3 5 6 10 15 25 = =

  7. 3 5 6 10 15 25 In the diagram = . These are called equivalent fractions because they are different expressions for the same nonzero number. = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same nonzero number.

  8. Remember! A fraction with the same numerator and denominator, such as is equal to 1. 2 2 Find two fractions equivalent to . 1 5 2 10 14 Multiply the numerator and denominator by 2. = 7 2 1 Multiply the numerator and denominator by 3. 5 3 15 21 = 7 3

  9. 15 21 5 7 10 14 The fractions , , and are equivalent, but only is in simplest form. A fraction is in simplest form when the greatest common divisor of its numerator and denominator is 1. 5 7

  10. 6 12 Find two fractions equivalent to . 1 6 2 12 24 Multiply the numerator and denominator by 2. = 12  2 1 6 ÷ 2 12 ÷ 2 Divide the numerator and denominator by 2. 3 6 =

  11. 18 ÷6 24 ÷ 6 18 ÷6 24 ÷ 6 18 ÷6 24 ÷ 6 18 ÷6 24 ÷ 6 18 24 Write the fraction in simplest form. Find the GCD of 18 and 24. 18 = 2 • 3 • 3 The GCD is 6 = 2 • 3. 24 = 2 • 2 • 2 • 3 1 18 24 3 4 Divide the numerator and denominator by 6. = =

  12. 15 ÷15 45 ÷ 15 15 45 Write the fraction in simplest form. Find the GCD of 15 and 45. 15 = 3 • 5 The GCD is 15 = 3 • 5. 45 = 3 • 3 • 5 1 1 3 15 45 Divide the numerator and denominator by 15. = =

  13. To determine if two fractions are equivalent, simplify the fractions.

  14. 4 6 28 42 2 3 and are equivalent because both are equal to . Determine whether the fractions in each pair are equivalent. 4 6 28 42 and Simplify both fractions and compare. 1 4 6 4 ÷ 2 6 ÷ 2 2 3 = = 1 2 3 28 42 28 ÷ 14 42 ÷ 14 = =

  15. 3 5 4 5 = 20 25 are not equivalent because their simplest and 6 10 forms are not equal. Determine whether the fractions in each pair are equivalent. 6 10 20 25 and Simplify both fractions and compare. 1 6 ÷ 2 10 ÷ 2 6 10 3 5 = = 1 4 5 20 ÷ 5 25 ÷ 5 20 25 = =

  16. 3 9 6 18 and 1 3 1 3 = 6 18 3 9 6 18 1 3 and are equivalent because both are equal to . Determine whether the fractions in each pair are equivalent. Simplify both fractions and compare. 1 3 9 3 ÷ 3 9 ÷ 3 1 3 = = 1 6 ÷ 6 18 ÷ 6 1 3 = =

  17. 1 3 3 16 = 9 48 are not equivalent because their simplest and 4 12 forms are not equal. Determine whether the fractions in each pair are equivalent. 4 12 9 48 and Simplify both fractions and compare. 1 4 ÷ 4 12 ÷ 4 1 3 4 12 = = 1 9 ÷3 48 ÷ 3 9 48 3 16 = =

  18. 3 5 8 5 is an improper 1 is a mixed fraction. Its numerator is greater than its denominator. number. It contains both a whole number and a fraction. 3 5 8 5 = 1

  19. Converting Between Improper Fractions and Mixed Numbers as a mixed number. A. Write 13 5 First divide the numerator by the denominator. Use the quotient and remainder to write the mixed number. 3 5 13 5 = 2 2 3 B. Write 7 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + Use the result to write the improper fraction. 3  7 + 2 2 3 23 3 = = 7 3 

  20. 1 2 = 2 15 6 as a mixed number. A. Write First divide the numerator by the denominator. Use the quotient and remainder to write the mixed number. 3 6 15 6 = 2 1 3 B. Write 8 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. + Use the result to write the improper fraction. 3  8 + 1 1 3 25 3 = 8 = 3 

  21. To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator. In this case, the fractions need to be made equivalent.

  22. Helpful Hint The LCM of two denominators is the least common denominator (LCD) of the fractions.

  23. 24 30 2 2 5 2 3 Find the Lowest Common Denominator for and . 24 = 2 x 2 x 2 x 3 30 = 2 x 3 x 5 LCM = 2 x 2 x 2 x 3 x 5 = 120 x 4 x 4 x 5 x 5

  24. Lesson Quiz 1 2 1 2 3 6 3 6 , , 512 410 1 8 1 8 2 2 20 48 20 48 9 48 9 48 & & 1. Write two fractions equivalent to . 2. Determine if and are equivalent. 3. Write the fraction in simplest form. 4. Write as a mixed number. 5. Write 4 as an improper fraction. 6. Find the LCD, and write equivalent fractions for and . 1. Write two fractions equivalent to . 2. Determine if and are equivalent. 3. Write the fraction in simplest form. 4. Write as a mixed number. 5. Write 4 as an improper fraction. 6. Find the LCD, and write equivalent fractions for and . 12 24 no no 1 3 1 3 16 48 16 48 17 8 31 7 31 7 3 7 5 12 5 12 3 16 LCD = 48

  25. Guided Practice • Holt – Online video tutorial and practice • Holt Online Practice • Holt-common denominators

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