Visual Models <br />for<br />Fraction Operations<br />
Addition<br />+<br />
Addition of Fractions: For any fractions a/b and c/d, <br />a + c = ad + bc = ad + bc<br />b    d    bdbdbd<br />
Approximating  Method when Adding Fractions<br />_3_<br />4<br />_1_<br />2<br />_1_<br />  3<br />When the two shaded amo...
Finding the sum of two fractions is easy when they have the same denominator.<br /> 4_<br /> 6<br /> 3_<br /> 6<br /> 4_<b...
Addition of fractions can also be illustrated using a number line:<br />
Adding Unlike Denominators<br />¼ + ⅓  <br />= ?<br />
First, find the smallest common denominator of ¼ and ⅓.<br />1 × 3 = _3_ <br /> 3     12<br />1 × 4 = _4_<br />3    4     ...
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 />
Subtraction<br />_<br />
Subtraction of Fractions: For any fractions a/b and c/d, <br />a _ c = ad _ bc =ad – bc<br />b    d    bdbdbd<br />
Using a Number Line:<br />
Using Fraction Bars:<br />_1_        _1_       _2_       _1_<br />  2            6            6           3<br />_<br />=<...
Subtracting Unlike Denominators:<br />This is what’s left over.<br />_5_<br />  6<br />_1_<br />  4<br />_5_      _1_<br /...
…<br />The smallest common denominator of ⅚ and ¼ is 12.<br />•  5 × 2 = 101 × 3 = 3  <br />    6    2    12	     4    3  ...
Multiplication<br />×<br />
Whole Number Times a Fraction: For any whole number k and fraction a/b, <br />k × a = ka<br />   b     b<br />
Multiplication of a fraction and a whole number can be illustrated in a couple of different ways.<br />
Whole Number Times a Fraction<br />1 Whole Bar<br />3 ×  1  =  1  +  1  +  1  = 3 or  1    1_ <br />        2      2      ...
Fraction Times a Whole Number<br />A<br />B<br />C<br /> 1  ×  4 =  1  +   1  +  1  +  1 =    4_<br /> 3              3   ...
Fraction Times a Whole Number<br /> 1<br />⅓<br /> 1 1<br /> 3                 3<br />×  4  =<br />1<br />
Multiplication of Fractions: For any fractions a/b and c/d,<br />a× c = ac<br />	b    d    bd<br />
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_...
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_...
Division<br />÷<br />
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<b...
 5  ÷   1_<br /> 6      12<br />_1_<br />12<br />_5_<br />6<br />goes into          10 times.         <br />= 10<br />…<br />
 5  ÷   1__1_<br /> 6       3             2<br />= 2<br />Remainder<br />Divisor<br />
Inverting the Divisor and Multiplying<br />TRIPLE BOTH AMOUNTS<br />)<br />)<br /> 1  1  1_ 1_ 3_ 3_<br /> 2        3     ...
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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 />
  2. 2. Addition<br />+<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 />

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