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Our Lesson

Our Lesson. Simplify and Equivalent Fractions. Warm up. 1) Is 8 a factor of 2832? Yes 2) List all factors of 49 1, 7 and 49 3) Solve 4 x – 2 y 3 , where x = 2 and y =-1 10

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Our Lesson

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  1. Our Lesson Simplify and Equivalent Fractions

  2. Warm up 1) Is 8 a factor of 2832? Yes 2) List all factors of 49 1, 7 and 49 3) Solve 4x – 2y 3, where x = 2 and y =-1 10 4) Write the prime factorization of 45 5 x 32 5) Write the GCF of 24 and 14 2 Confidential

  3. Lets Review Factors A whole number that divides exactly into another whole number is called a factor of that number. For example 100 / 25 = 4 So, 25 is a factor of 100 as it divides exactly into 20. 20 / 4 = 5 So, 4 is a factor of 20 as it divides exactly into 20. Confidential

  4. Powers and Exponents Exponent 46 Base The exponent can also be referred to as the power 46 means to multiply the base 4 by itself 6 times 46 = 4 x 4 x 4 x 4 x 4 x 4 Confidential

  5. Prime Numbers • A Prime number is a positive integer >1 • A number that has exactly two factors, 1 and itself • A number that cannot be factored . Example: 7 is a Prime number as it has only two factors 1 and 7 Confidential

  6. Composite Numbers When a whole number greater than one has more than 2 factors it is called a Composite Number. 10 is a composite number as it has 1, 2, 5 and 10 as its factors Confidential

  7. Prime Factorization Expressing a composite number as a product of prime numbers is called Prime Factorization The number 60 is a composite number. It can be written as the product 2 x 2 x 3 x 5. Note that 2, 3 and 5 are factors of 60 and all these factors are prime numbers. We call them prime factors. When we express a number as a product of prime factors, we have actually factored it completely. We refer to this process as prime factorization Confidential

  8. Greatest Common Factor Greatest Common Factor of two or more numbers can be defined as the greatest number that is a factor of each number Method 1 List the factors of each number. Then identify the common factors. The greatest of these common factors is theGCF. Method 2 Write the prime factorization of each number. Then identify all common prime factors and find their product. Confidential

  9. Least Common Multiple The least common multiple of the numbers a and b is the smallest number that is divisible by both a and b We denote the least common multiple of a and b by lcm (a, b) Confidential

  10. Lets get started Simplest form of Fraction A fraction is in its simplest form when the GCF of the numerator and the denominator is 1 There is no other common factor except 1 Example 2 17 5 3 31 19 , , Confidential

  11. Steps to expressing a fraction in its simplest form • Find the GCF of the numerator and denominator • Divide the numerator and the denominator by the GCF, and write the resulting fraction Confidential

  12. Lets take an Example Write the 4 in its simplest form 16 Factors of 4: 1, 2, 4 Factors of 16: 1, 2, 4, 8, 16 The GCF of 4/16 is 4 4 16 4 16÷ 4 1 4 ÷ 4 = = Confidential

  13. Equivalent Fractions Method 1 If a and c are two fractions where c m x a b d d m x b = Then, a c b d = Confidential

  14. Method2 If the cross products of two fractions are equal then they are equivalent fractions a c b d If ad = bc then a/b = c/d Confidential

  15. Equivalent fractions In this picture we have ½ of a cake because the whole cake is divided into two congruent parts and we have only one of those parts But if we cut the cake into smaller congruent pieces, we can see that 1 2 2 4 = Confidential

  16. Or we can cut the original cake into 6 congruent pieces, Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same Therefore, 1 2 3 2 4 6 = = Confidential

  17. If you don’t like this, we can cut the original cake into 8 congruent pieces, then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same Therefore, 1 2 3 2 4 6 4 8 = = = We can generalize this to 1 x n 2 x n whenever n is not 0 1 2 = Confidential

  18. reduce reduce reduce Another example: 24 40 30 42 Are and equal? Method 1 3 5 24 40 12 20 12 ÷ 4 20 ÷ 4 24 ÷ 2 40 ÷ 2 = = 5 7 30 42 30 ÷ 6 42 ÷ 6 = 3 5 5 7 = Method 2 24 x 42 = 1008 40 x 30 = 1200 24 x 42 = 40 x30 This shows that these two fractions are not the same! Confidential

  19. Questions • Write the following in the simplest form • 18/20 9/10 • 4/16 ¼ • 36/44 9/11 • 45/105 3/7 • 848/1240 101/155 Confidential

  20. Questions Which of these are equivalent fractions 6) 5/9 and 4/5 no 7) 4/5 and 16/20 yes 8) 9/16 and 5/9 no Fill >,< or = 9) ½ __4/8 = 10) 4/50__5/75 > Confidential

  21. Break Time Confidential

  22. Lets play a Game Click here to play a Game Confidential

  23. 1) Explain how can you find a fraction in which the numerator and denominator are greater than 100 and they have a common factor of 13. Multiply the numerator and denominator of a fraction by 13. (Both numbers must be greater than 7) Example 8 x 13 104 9 x 13 117 = Confidential

  24. 2) Emily had 20 pencils, Sheena had 50 pencils and Ben had 80 pencils. After 4 months, Emily used up 10 pencils, Sheena used up 25 pencils and Ben used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of their pencils? Emily = 10/20 = ½ Sheena = 50/25 = ½ Ben = 40/80 = ½ Yes! Each has used up equal fraction of their pencils Confidential

  25. 3) A sitar is a South Asian instrument that has two sets of strings. One type of sitar has 6 top strings and 16 bottom strings. Express the number of top strings as a fraction of total number of strings. 6 6 3 (16 +6) 22 11 = = Total number of strings Confidential

  26. Lets review what we have learned in this lesson Simplest form of Fraction A fraction is in its simplest form when the GCF of the numerator and the denominator is 1 There is no other common factor except 1 Example 2 17 5 3 31 19 , , Confidential

  27. Steps to expressing a fraction in its simplest form • Find the GCF of the numerator and denominator • Divide the numerator and the denominator by the GCF, and write the resulting fraction Confidential

  28. Equivalent Fractions Method 1 If a and c are two fractions where c m x a b d d m x b = Then, a c b d = Confidential

  29. Method2 If the cross products of two fractions are equal then they are equivalent fractions a c b d If ad = bc then a/b = c/d Confidential

  30. You had a Great lesson Today! Be sure to practice what you have learned Confidential

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