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George drew the diagram at right to represent the number . “Look,” said Helena, “This is the same thing as .” What do you think? Explore this idea in parts (a) through (c) below.  

  1. Is Helena correct? If so, explain how she can tell that the diagram represents . If she is not correct, explain why not.

    How much does each piece represent?
    How many pieces are shaded?

    Since each square is divided into equal pieces, each piece is equal to one fifth.
    There are shaded pieces, so this diagram represents

  2. Draw a diagram to represent the mixed number . How can you write this as a single fraction greater than one?

    Use the diagram for part (a) to help you design this diagram.
    How many pieces are in a whole? How many do you shade?

    To represent this mixed number as a single fraction greater than one, equal pieces will need to be shaded.
    How much of a whole will each piece represent?

  3. How can you write as a mixed number? Be sure to include a diagram in your answer.

  • How many whole numbers does this represent?
    How many pieces are left over?
    Remember to draw a diagram.

The diagram is 3 rectangles each divided into 5 equal sections. The first two rectangles are fully shaded. The third rectangle has 2 of the 5 sections shaded.