1. Visual Models for Fraction Operations

2. Addition +

3. Addition of Fractions: For any fractions a/b and c/d, a + c = ad + bc = ad + bc b d bdbdbd

4. Approximating Method when Adding Fractions _3_ 4 _1_ 2 _1_ 3 When the two shaded amounts are combined, the total is approximately . _3_ 4

5. Finding the sum of two fractions is easy when they have the same denominator. 4_ 6 3_ 6 4_ 6 3_ 6 7_ 6 1_ 6 = 1 + OR

6. Addition of fractions can also be illustrated using a number line:

7. Adding Unlike Denominators ¼ + ⅓ = ?

8. First, find the smallest common denominator of ¼ and ⅓. 1 × 3 = _3_ 3 12 1 × 4 = _4_ 3 4 12 1 = _3_ 4 12 1 = _4_ 3 12 So…

9. 1 + 1 4 3 = _3_ + _4_ 12 12 = _7_ 12 1 + 1 = _7_ 4 3 12

10. Subtraction _

11. Subtraction of Fractions: For any fractions a/b and c/d, a _ c = ad _ bc =ad – bc b d bdbdbd

12. Using a Number Line:

13. Using Fraction Bars: _1_ _1_ _2_ _1_ 2 6 6 3 _ = OR 1_ 2 _1_ 6 _1_ 3

14. Subtracting Unlike Denominators: This is what’s left over. _5_ 6 _1_ 4 _5_ _1_ 6 4 _ = ? …

15. … The smallest common denominator of ⅚ and ¼ is 12. • 5 × 2 = 101 × 3 = 3 6 2 12 4 3 12 • 10 - 3 = 7 12 12 12 10 12 3 12 7 12

16. Multiplication ×

17. Whole Number Times a Fraction: For any whole number k and fraction a/b, k × a = ka b b

18. Multiplication of a fraction and a whole number can be illustrated in a couple of different ways.

19. Whole Number Times a Fraction 1 Whole Bar 3 × 1 = 1 + 1 + 1 = 3 or 1 1_ 2 2 2 2 2 2

20. Fraction Times a Whole Number A B C 1 × 4 = 1 + 1 + 1 + 1 = 4_ 3 3 3 3 3 3

21. Fraction Times a Whole Number 1 ⅓ 1 1 3 3 × 4 = 1

22. Multiplication of Fractions: For any fractions a/b and c/d, a× c = ac b d bd

23. Fraction Times a Fraction 1_ 5 × 1_ 3 1_ 15 1 × 1 = 1_ OR 1 of 1 = 1_ 3 5 15 3 5 15 1_ 15

24. Fraction Times a Fraction 4_ 5 × 2_ 3 8_ 15 2 × 4 = 8_ OR 2 of 4 = 8_ 3 5 15 3 5 15 8_ 15

25. Division ÷

26. Division of Fractions: For any fractions a/b and c/d, with c/d ≠ 0, a ÷ c = a × d = ad b d b c bc

27. 5 ÷ 1_ 6 12 _1_ 12 _5_ 6 goes into 10 times. = 10 …

28. 5 ÷ 1__1_ 6 3 2 = 2 Remainder Divisor

29. Inverting the Divisor and Multiplying TRIPLE BOTH AMOUNTS ) ) 1 1 1_ 1_ 3_ 3_ 2 3 2 3 2 2 ( ( = = = ÷ × 3 ÷ × 3 ÷ 1 Simplified Version of Equation Above 1 1 1 3 3 1_ 2 3 2 1 2 2 = = 1 × ÷ =