A Fraction Times a Fraction

Using Materials

Problem: “Maurice decides to plant ¾ of a rectangular field in carrots. Draw two copies of a 4 by 5 rectangle. Put one aside for later and cut out ¾ of the other one.

Next day Maurice realises he does not need all this ¾ area for carrots, so he decides to plant 4/5 of this area in carrots. Draw vertical lines to create fifths and cut out 4/5.

Compare the final cut-out shape with the spare copy of the original field. What fraction is in carrots?” (Answer: 9 small squares are in carrots of the original 20  small squares. So the fraction is 9/20.)

Examples:
Draw two 4 by 4 squares to work out ¾ of ¾.
Draw two 3 by 5 rectangles to work out 4/5 of 2/3.
Draw two 3 by 5 rectangles to work out 2/3 of 4/5.

Understanding Number Properties:

Choose a size of rectangle suitable to work out 5/6 of 4/7 and then find the answer. (Answer: 20/42 or 10/21.)

Using Number Properties

Problem: “Look at the answers to the examples above. What pattern do you notice?”

Examples: Work out:
7/10 x 9/10
3/5 x 4/5
8/11 x 3/10
6/7 x 3/100

Understanding Number Properties:

What letters replace the question marks? h/i x j/k = (? x ?) / (? x ?)
(Answer: (h x j)/(i x k).)