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May 2012

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The ideas in this fraction lesson are taken from the Math Mammoth Fractions 2 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Multiplication and Area
Free fraction lesson plan from HomeschoolMath.net

The area of a rectangle is found by multiplying side length by side length. For example, in the rectangle on the right, the sides are 4 units and 7 units, and the area is 28 square units.

We can apply that idea to fractions, too. The one side of the rectangle is 1 unit (in terms of length). The other side is 1 unit also. The whole rectangle also is 1 square unit, in terms of area. 1 2 × 2 3 =   2 6 = 1 3     side length side length AREA, compared to total area   Remember: The two fractions to multiply represent the length of the sides, and the answer fraction represents area.

Example. On the top side, 2/5 of the side is colored. On the left side, 1/2 of the side is colored. We multiply those fractions:   1 2  ×  2 5   =  2 10  =  1 5 The answer means that 2/10 or 1/5 of the total area is colored.

Example. On the top side, 2/3 of the side is colored. On the left side, 3/4 of the side is colored. We multiply those fractions:   2 3  ×  3 4   =  6 12  =  1 2 So, 6/12 or 1/2 of the whole area is colored.

1. Write the multiplication sentence that matches each picture. 

a.		b.	[available in the book]
	×    =

2. Write the multiplication sentence that matches each picture. 

a.		×    =		b.
c.	[available in the book]
e.				f.	[available in the book]

3. Multiply the fractions, and shade a picture to illustrate the multiplication. Simplify your answers.

a.   1 4  × 1 2  =
	h.   2 9  ×  2 3  =

4. a. Draw a 1-in by 1-in square. What is its area?

    b. Draw a rectangle with sides 3/4 in and 5/8 in.
        so that its two sides touch the sides of the
        1-in by 1-in square you drew.
        See the illustration below (not to scale).
      

    c. Find the area of your rectangle.

5. a. [available in the book]

6. a. [available in the book]

7. a. [available in the book]

    b. [available in the book]
 

[available in the book]

Continue to the next lesson: Simplifying before multiplying

The ideas in this fraction lesson are taken from the Math Mammoth Fractions 2 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.