Calculate Total Area from a Fraction Model
Students learn to find the total area represented in a fraction model by multiplying the whole number by the numerator and keeping the same denominator: W x (a/b) = (W x a)/b, as covered in Illustrative Mathematics Grade 5, Chapter 2: Fractions as Quotients and Fraction Multiplication. For example, an area model for 3 x 2/5 shows 3 x 2 = 6 shaded pieces out of 5 per whole, giving a total area of 6/5 square units.
Key Concepts
To find the total area from a model representing a whole number $W$ times a fraction $\frac{a}{b}$, multiply the whole number by the numerator and keep the denominator. $$W \times \frac{a}{b} = \frac{W \times a}{b}$$.
Common Questions
How do you calculate total area from a fraction model?
Count the total shaded pieces (whole number x numerator) and keep the same denominator: W x (a/b) = (W x a)/b; for example, 3 x 2/5 = 6/5.
What does each piece in the fraction area model represent?
Each piece in the fraction area model represents 1/b of a whole unit square, where b is the denominator of the fraction being multiplied.
How do you find the total number of shaded pieces in an area model?
Multiply the whole number by the numerator of the fraction; for 5 x 3/4, the total shaded pieces = 5 x 3 = 15 pieces, each worth 1/4, giving 15/4 total.
Why does multiplying whole number by numerator and keeping denominator work?
Each whole contributes numerator pieces of size 1/b; with W wholes, you have W x numerator total pieces, each of size 1/b, giving (W x numerator)/b.
How does this connect to the general rule for multiplying fractions?
This establishes that W x a/b = (W x a)/b, the general algorithm for multiplying a whole number by any fraction: multiply the whole number by the numerator, keep the denominator.