Finding Area with Fractional Side Lengths
Students learn to find the area of a rectangle with fractional side lengths by multiplying the fractions together using A = length x width, as covered in Illustrative Mathematics Grade 5, Chapter 2: Fractions as Quotients and Fraction Multiplication. For example, a rectangle 3/4 foot by 2/3 foot has an area of 3/4 x 2/3 = 6/12 = 1/2 square feet, which can be visualized using a unit square divided into smaller rectangles.
Key Concepts
The area of a rectangle is found by multiplying its length and width. This principle applies when the side lengths are fractions. $$A = \text{length} \times \text{width}$$.
Common Questions
How do you find area when sides are fractions?
To find area with fractional side lengths, multiply the fractions together: A = length x width; for example, 1/2 x 1/3 = 1/6 square units.
How do you multiply fractions to find area?
Multiply the numerators together and the denominators together; for example, 3/4 x 2/3 = (3x2)/(4x3) = 6/12 = 1/2 square feet.
How can you visualize area with fractional sides?
Divide a unit square into smaller equal rectangles based on the denominators of the side lengths; the number of shaded parts over the total parts represents the fractional area.
What does the denominator represent in an area model with fractions?
In a fraction area model, the denominator tells you the total number of equal parts in the whole unit square, while the numerator tells you how many of those parts are shaded or covered.
Why does multiplying fractions give us area?
Area is always length times width; this rule applies equally to whole numbers and fractions, because multiplying fractions finds what fraction of the whole unit area is covered by the rectangle.