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# Visual Models for Fraction Operations

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### Visual Models for Fraction Operations

1. 1. Visual Models <br />for<br />Fraction Operations<br />
3. 3. Addition of Fractions: For any fractions a/b and c/d, <br />a + c = ad + bc = ad + bc<br />b d bdbdbd<br />
4. 4. Approximating Method when Adding Fractions<br />_3_<br />4<br />_1_<br />2<br />_1_<br /> 3<br />When the two shaded amounts are combined, the total is approximately . <br />_3_<br />4<br />
5. 5. Finding the sum of two fractions is easy when they have the same denominator.<br /> 4_<br /> 6<br /> 3_<br /> 6<br /> 4_<br /> 6<br /> 3_<br /> 6<br /> 7_<br /> 6<br /> 1_<br /> 6<br />=<br />1<br />+<br />OR<br />
6. 6. Addition of fractions can also be illustrated using a number line:<br />
7. 7. Adding Unlike Denominators<br />¼ + ⅓ <br />= ?<br />
8. 8. First, find the smallest common denominator of ¼ and ⅓.<br />1 × 3 = _3_ <br /> 3 12<br />1 × 4 = _4_<br />3 4 12<br />1 = _3_<br />4 12<br />1 = _4_<br />3 12<br />So…<br />
9. 9. 1 + 1<br />4 3<br />=<br />_3_ + _4_<br /> 12 12<br />=<br />_7_<br /> 12<br />1 + 1 = _7_<br />4 3 12 <br />
10. 10. Subtraction<br />_<br />
11. 11. Subtraction of Fractions: For any fractions a/b and c/d, <br />a _ c = ad _ bc =ad – bc<br />b d bdbdbd<br />
12. 12. Using a Number Line:<br />
13. 13. Using Fraction Bars:<br />_1_ _1_ _2_ _1_<br /> 2 6 6 3<br />_<br />=<br />OR<br /> 1_<br /> 2<br />_1_<br /> 6<br />_1_<br /> 3<br />
14. 14. Subtracting Unlike Denominators:<br />This is what’s left over.<br />_5_<br /> 6<br />_1_<br /> 4<br />_5_ _1_<br /> 6 4 <br />_<br />= ?<br />…<br />
15. 15. …<br />The smallest common denominator of ⅚ and ¼ is 12.<br />• 5 × 2 = 101 × 3 = 3 <br /> 6 2 12 4 3 12<br /> • 10 - 3 = 7 <br /> 12 12 12<br />10<br />12<br /> 3<br />12<br /> 7<br />12<br />
16. 16. Multiplication<br />×<br />
17. 17. Whole Number Times a Fraction: For any whole number k and fraction a/b, <br />k × a = ka<br /> b b<br />
18. 18. Multiplication of a fraction and a whole number can be illustrated in a couple of different ways.<br />
19. 19. Whole Number Times a Fraction<br />1 Whole Bar<br />3 × 1 = 1 + 1 + 1 = 3 or 1 1_ <br /> 2 2 2 2 2 2<br />
20. 20. Fraction Times a Whole Number<br />A<br />B<br />C<br /> 1 × 4 = 1 + 1 + 1 + 1 = 4_<br /> 3 3 3 3 3 3<br />
21. 21. Fraction Times a Whole Number<br /> 1<br />⅓<br /> 1 1<br /> 3 3<br />× 4 =<br />1<br />
22. 22. Multiplication of Fractions: For any fractions a/b and c/d,<br />a× c = ac<br /> b d bd<br />
23. 23. Fraction Times a Fraction<br />1_<br /> 5<br />×<br />1_<br /> 3<br /> 1_<br />15<br /> 1 × 1 = 1_ OR 1 of 1 = 1_<br /> 3 5 15 3 5 15<br /> 1_<br />15<br />
24. 24. Fraction Times a Fraction<br />4_<br />5<br />×<br />2_<br />3<br /> 8_<br />15<br /> 2 × 4 = 8_ OR 2 of 4 = 8_<br /> 3 5 15 3 5 15<br /> 8_<br />15<br />
25. 25. Division<br />÷<br />
26. 26. Division of Fractions: For any fractions a/b and c/d, with c/d ≠ 0,<br />a ÷ c = a × d = ad<br />b d b c bc<br />
27. 27. 5 ÷ 1_<br /> 6 12<br />_1_<br />12<br />_5_<br />6<br />goes into 10 times. <br />= 10<br />…<br />
28. 28. 5 ÷ 1__1_<br /> 6 3 2<br />= 2<br />Remainder<br />Divisor<br />
29. 29. Inverting the Divisor and Multiplying<br />TRIPLE BOTH AMOUNTS<br />)<br />)<br /> 1 1 1_ 1_ 3_ 3_<br /> 2 3 2 3 2 2<br />(<br />(<br />=<br />=<br />=<br />÷<br />× 3<br />÷<br />× 3<br />÷ 1<br />Simplified Version of Equation Above<br /> 1 1 1 3 3 1_<br /> 2 3 2 1 2 2<br /> =<br />= 1<br />×<br />÷<br />=<br />