1. Copyright © Ed2Net Learning, Inc.1 Fractions Grade 6

2. Copyright © Ed2Net Learning, Inc. 2 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: 2/3; 17/31; 5/19 To convert a fraction to simplest form:  Find the GCF of the numerator and denominator  Divide the numerator and the denominator by the GCF, and write the resulting fraction  Example: Write 6/15 in the simplest form. Factors of 6: 1, 2, 3, 6 Factors of 15: 1, 3, 5, 15 6/15 = (6÷3)/(15÷3) = 2/5 GCF is 3

3. Copyright © Ed2Net Learning, Inc. 3 a c b d If ad = bc then a/b = c/d 6 2 15 5 30 = 30 Equivalent Fractions Method 1: If the cross products of two fractions are equal then they are equivalent fractions 6/15 and 2/5 are equivalent fractions

4. Copyright © Ed2Net Learning, Inc. 4 If a and c are two fractions where c m x a b d d m x b Then, a c b d = = Same Example: 6 2 6 3 x 2 15 5 15 3 x 5, With the GCF of 3 = Equivalent Fractions Method 2: 6/15 and 2/5 are equivalent fractions

5. Copyright © Ed2Net Learning, Inc. 5 Your Turn! 1. Are these are equivalent fractions? 64/24 and 8/3 2. Write the following in the simplest form. 180/45

6. Copyright © Ed2Net Learning, Inc. 6 Comparing Fractions To compare fractions  Rewrite each fraction using the same denominator  Now you need only to compare the numerators  The fraction with the bigger numerator is the larger fraction  A common denominator is a common multiple of the denominators of two or more fractions  The Least Common Denominator (LCD) is the Least Common Multiple (LCM) of the denominators of two or more fractions

7. Copyright © Ed2Net Learning, Inc. 7 Example: 1 2 15 15 < 1 < 2 so, 1/15 < 2/15 with the same denominator Example: 1 1 2 3 > Comparing Fractions 1)Fractions with the same denominator are Like fractions 2) If the fractions have the same numerators but different denominators, the fractions with the smaller denominator is greater

8. Copyright © Ed2Net Learning, Inc. 8 Example: 2 3 3 4, Since 3 and 4 are not common factors or multiples of each other we need to take the LCM of 3 and 4 are 12 2 2 x 4 8 3 3 x 4 12 == 3 3 x 3 9 4 4 x 3 12 = = 8 9 12 < Comparing Fractions 3) To compare two fractions with different denominators and numerators, We find their equivalent fractions with the same denominators and then just compare the numerators

9. Copyright © Ed2Net Learning, Inc. 9 Your Turn! Find the LCD for the pair of fractions  8/24, 9/16

10. Copyright © Ed2Net Learning, Inc. 10 Improper Fraction to Mixed Number Divide the numerator by the denominator The remainder you get put it over the denominator (i.e. in the numerator) The quotient in the place of the whole number  The mixed fraction will be Quotient Remainder Divisor Improper Fraction: A fraction in which the numerator is greater than the denominator A mixed number (fraction) is a number that has a part that is a whole number and a part that is a fraction

11. Copyright © Ed2Net Learning, Inc. 11 Mixed Number to Improper Fraction Multiply the whole number with the denominator Add your answer to the numerator Put your new number over the denominator (Whole number x Denominator) + Numerator Denominator

12. Copyright © Ed2Net Learning, Inc. 12 Your Turn! Express 80/6 as mixed fraction.

13. Copyright © Ed2Net Learning, Inc. 13 Example 3 12 + 5 12 The answer is (3+5) 12 Which can be simplified to 2 3 Fractions with equal denominators Addition Subtraction 11 3 12 - 11 3 11 - 3 12 12 12 = -= 8 12 Example:

14. Copyright © Ed2Net Learning, Inc. 14 NOTE BOOK Find the LCD of the fractions. Adding and Subtracting Fractions Rewrite the fractions using the LCD. Add or subtract the fractions. Simplify if possible. Fractions with Different Denominators

15. Copyright © Ed2Net Learning, Inc. 15 Adding Fractions EXAMPLE 1 Kate spent about of her day playing softball and of her day playing soccer. To answer the real-world question above, find the sum +. 1818 1 12 1818 1 12 1818 1 12 = 3 24 5 24 –––––––– + = 2 24 ––––– + Rewrite both fractions using the LCD, 24. Add the fractions. ANSWER Kate spent of her day playing sports. 5 24 Fractions with Different Denominators  3 3 3 3  2 2 2 2

16. Copyright © Ed2Net Learning, Inc. 16 Rewriting Sums of Fractions EXAMPLE 2 Find the sum +. 5858 3434 5858 3434 5858 = 6868 = –––––––– + ––––– + 11 8, or 1 3838 Add the fractions. Rewrite using the LCD, 8. 3434 Fractions with Different Denominators  2 2 2 2

17. Copyright © Ed2Net Learning, Inc. 17 Subtracting Fractions EXAMPLE 3 4545 = 12 15 Rainfall Last week, inch of rain fell on Monday and inch fell on Tuesday. How much more rain fell on Tuesday than on Monday? 2323 4545 2323 = 10 15 SOLUTION ANSWER You need to find the difference –. 4545 2323 –––––––– – ––––– – 2 15 On Tuesday, inch more rain fell than on Monday. 2 15 Rewrite both fractions using the LCD, 15. Subtract the fractions. Fractions with Different Denominators  3 3 3 3  5 5 5 5

18. Copyright © Ed2Net Learning, Inc. 18 Your Turn! 6/7 + 1/7 = 4/13 + 3/8

19. Copyright © Ed2Net Learning, Inc. 19 Adding & Subtracting Mixed Numbers Rewrite the fractions using the LCD Add or subtract the fractions, then the whole numbers Simplify is possible

20. Copyright © Ed2Net Learning, Inc. 20 Subtracting Mixed Numbers by Renaming Rewrite the fractions using the LCD Rename if necessary Subtract. Simplify is possible.

21. Copyright © Ed2Net Learning, Inc. 21 Multiplying Fractions

22. Copyright © Ed2Net Learning, Inc. 22 Multiply. The answer is in simplest form. Use the rule for multiplying fractions. Multiplying with Mixed Numbers EXAMPLE 1 Write 2323 1 as an improper fraction. 5858 2323 1  5353  5858 = = 5  5 8  3 = 25 24 1, or 1 24 Use the rule for multiplying fractions. Multiply. The answer is in simplest form. Write 3434 1 and 3 as improper fractions. = 21 4, or 1414 5 7474 3131  = 3434 1  3 Multiplying Mixed Numbers = 7  3 4  1

23. Copyright © Ed2Net Learning, Inc. 23 Multiplying Mixed Numbers Use the rule for multiplying fractions. Divide out common factors. Multiply. The answer is in simplest form. Rewrite. Simplifying Before Multiplying EXAMPLE 2  2929 2 4545 4 =  24 5 20 9 = 20  24 9  5 3 8 4 1 4  8 3  1 = = 32 3, or 2323 10 2929 2 Writeandas improper fractions. 4 4545

24. Copyright © Ed2Net Learning, Inc. 24 Multiplying Mixed Numbers Use the rule for multiplying fractions. Divide out common factors. Multiply. The answer is in simplest form. Rewrite. Simplifying Before Multiplying EXAMPLE 2  2929 2 4545 4 =  24 5 20 9 = 20  24 9  5 3 8 4 1 4  8 3  1 = = 32 3, or 2323 10 C HECK Round 2929 2 to 2 and to 5. Because 2  5 = 10, the 2323 10 is reasonable.product 4545 4 2929 2 Writeandas improper fractions. 4 4545

25. Copyright © Ed2Net Learning, Inc. 25 = 148  7 21  2 Multiplying Mixed Numbers = Length  Width 1212 3 1 21 7 Substitute for length and width. ANSWER Multiply. The answer is in simplest form. Write formula for area of a rectangle. Write 1 21 7 1212 3 andas improper fractions. SOLUTION Multiplying to Solve Problems EXAMPLE 3 Area = Length  Width = 148 21  7272 Use the rule for multiplying fractions. Divide out common factors. 3 1 74 1 = 3, or 2323 24 The area of the jump zone is square feet. 24 2323 Trampoline Olympic trampoliners get points deducted from their scores if they land outside a rectangle called the jump zone. The jump zone measures feet by feet. What is the area of the jump zone? 1 21 7 1212 3

26. Copyright © Ed2Net Learning, Inc. 26 Break!!

27. Copyright © Ed2Net Learning, Inc. 27

28. Copyright © Ed2Net Learning, Inc. 28 Dividing Fractions

29. Copyright © Ed2Net Learning, Inc. 29 Dividing Mixed Numbers

30. Copyright © Ed2Net Learning, Inc. 30 Review Assessment 1.Write 84/18 in its simplest form 2.Are 21/14 and 63/42 equivalent fractions? Find the LCD for the following pair of fractions 3.19/68, 38/78 4. 8/27, 5/72 Replace the blanks with >,=,< 5. 51/87_____ 74/99

31. Copyright © Ed2Net Learning, Inc. 31 Review Assessment 6. Express 784/24 as a mixed fraction 7.Express 5 4/7 as an improper fraction 8. 5/42 + 5/9 = 9. 5 2/7 - 3 1/9 = 10. 2 5/7 ÷ 4 3/6 =

32. Copyright © Ed2Net Learning, Inc. 32 You had a great session today! Remember to practice all these concepts well