Activities

1. Solve ½ x ½  
   
   
2. List the steps for multiplying fractions.
   
   
3. 12/2 x 2/12
   
   
4. 2/3 * 1/3 = 2 /3   true or false
   
   
5. When multiplying fractions you add the numerators together.  True or False

6. Solve 2/3 x 5/8.
   
   
7. Solve 13/6 x ½ and write the solution as a mixed number.
   
   
8. What is the solution to 5/3 x 9/12?
   1. 9/12
   2. 5/12
   3. 1   1/12
   4. 5/4
      
      
9. 18/4 x 1/2 = ?
   
   
10. Write the solution to 24/9 x 3/5   as an improper fraction.
    
    
11. What is the solution to (ax/b)(b/2x)? What fraction is the solution divisible by?
    
    
12. Is the solution to the following expression a whole number or a fraction?     7  7/8  x 4/21
    
    
13. Write the solution to the expression 1  2/3 x 2/3 as a mixed number and an improper fraction.
    
    
14. How many ways are there to write the solution?    1 ½ x 4/3
    
    
15. Is the solution a whole number or a fraction?  (4ab/c)(2c/8ab)

16. Explain why it is not possible to get an improper fraction when multiplying two fractions that are both less than 1.
    
    
17. Explain under what condition the solution to an improper fraction multiplied by ½ can be written as an improper fraction.
    
    
18. Without solving the expressions below, explain how you know the solution to one of the expressions is much larger than the solution to the other expression.    17/3 x ½       ½ x  3/18
    
    
19. Draw a model to show 2/3 x 3/4.  Explain the connection of the model to the calculations for the solution to the expression.
    
    
20. What expression is represented by the model below if the solution is the blue shaded boxes with the X’s?  Explain your reasoning.

21. Write a problem that will model the expression below.  Explain what the solution means in terms of the problem.  12/ 5 x 2/3
    
    
22. Write an expression for the following situation, solve it, and explain your reasoning.  Two thirds of ½ of the red cupcakes have decorations.   The other half of the red cupcakes have no frosting.  How many cupcakes have decorations if there are 24 red cupcakes?
    
    
23. Compare the work of two students when solving the expression below.  Who is correct?  Explain why.    9/12 x ½

         Student #1                                                                    Student #2

                                                       
                                            
                                                                    Answer is star boxes/lined boxes, so 4/6=2/3

24. Expression #1:  2/3 x 1/b             Expression #2:  1/c x 9/5
    Is it possible for the solution to expression one to be larger than expression two?  Explain.
    
    
25. Janelle works for the Cupcake factory preparing the frosting for 1,100 cupcakes a day.  The recipe she uses makes enough frosting for 80 cupcakes.  It calls for 3 ¾ cups of butter, 1 1/8 cup of water, ¼ cup almond extract, and 9  ¾ cups of powdered sugar.  How much will she need of each ingredient to frost 48 cupcakes?  Explain your thinking.

Answer Key/Rubric

1. 1/4
   
   
2. Students can list steps in a variety of order and use different words.  However, they must somehow indicate that numerators must be multiplied together and denominators must be multiplied together and reside in their respective locations of the solution fraction.
   
   
3. 1
   
   
4. False
   
   
5. False

6. 10/24 or 5/12
   
   
7. 1  1/12
   
   
8. d
   
   
9. 2  ¼ or 9/4
   
   
10. 8/5
    
    
11. a/2   It is divisible by ½
    
    
12. Fraction
    
    
13. 10/9  and 1  1/9
    
    
14. Infinite; the answer is 2 which can be written as 2, 2/1, 4/2 and so on.
    
    
15. Whole number; the answer is 1

16. Answers will vary.  Example:  When two fractions are being multiplied, you are essentially taking a fractional part of a fraction.  Since both fractions are less than one, a fractional part of a fraction is a fraction that is less than one.
    
    
17. Answers will vary.  An improper fraction is greater than 1, which means the numerator is greater than the denominator.  The numerator of the improper fraction must be more than twice the denominator.  The reasoning is because this improper fraction is being multiplied by ½.  So the denominator will be multiplied by 2 and the numerator by 1.  The numerator in the improper fraction must be greater than twice the denominator in order for the product to be improper.
    
    
18. Answers will vary.  When an improper fraction is multiplied by ½ it will always be larger than a fraction less than one multiplied by ½.  Multiplying by ½ is equivalent to dividing by 2.  Dividing a number greater than 1 by 2 is larger than dividing a number less than 1 by 2.
    
    
19. 2/3 x ¾ = 6/12  or ½ . 2/3 of the boxes have a blue line in them.  ¾ of the boxes have a red star in

them.  The boxes with both represent the solution 6 out of 12 or ½ .  The left side of the array is 2/3 of the rows are blue slashed and the top of the array is ¾ of the columns are red starred.

20. Answers will vary.  The expression is ½ x 2/5 and it equals 2/10 or 1/5.  The large rectangle is the whole with the blue shaded boxes representing ½ of the rows and the boxes with X’s representing 2/5 of the columns.  The boxes with blue shading and X’s represent the solution.
    
    
21. Problems and explanations will vary.  Students must calculate the solution correctly and connect it to the word problem.  Answer should be 8/5 or 1 3/5.
    
    
22. Solution method and explanations will vary.    2/3 x ½ = 1/3  1/3 x 24 = 8  First I find 2/3 of ½ which is 1/3, so 1/3 of the 24 cupcakes have decorations, so 8 have decorations.  Or ½ x 24 = 12   1/3 x 12 = 8    I need half of the total cupcakes, which is 24 times ½ = 12.  Finally I need 1/3 of 12 or 1/3 x 12 = 8, so 8 cupcakes have decorations.
    
    
23. Neither student is correct.  Student 1 completed the work correctly until the very end and then added numerators (3+1) instead of multiplying them (3x1).  Student 2 draws the model correctly but does not interpret is correctly.  It should be the number of boxes with both stars and lines divided by the total boxes or 3/8.
    
    
24. No it is not possible (excluding negative numbers of course).  Answers will vary. When an improper fraction is multiplied by a fraction less than one (1/b) it will always be larger than a fraction less than one (2/3) multiplied by another fraction less than one (1 /c).  When you take a fraction (less than 1) of a fraction (less than 1) the solution is a fraction less than one.  The improper fraction is greater than one, and when multiplied by any fraction, the solution will be greater than one.
    
    
25. Butter =2 ¼ cups (3/5 x  3 ¾); water = 27/40 cup (3/5 x 1 1/8); almond = 3/20 cup (¼ x 3/5); sugar = 5 17/20 cups (9  ¾ x 3/5)   Explanations will vary.  A full recipe frosts 80 cupcakes so 48/80 = 3/5 which is the fractional part of the recipe that she is interested in making.  The quantity for each ingredient is then multiplied by 3/5.