Multiply Unit Fractions Using an Area Model
Multiply Unit Fractions Using an Area Model is a Grade 5 math skill in Eureka Math, Chapter 23: Multiplication of a Fraction by a Fraction, where students draw a rectangle and use overlapping shaded regions to visualize multiplying two unit fractions such as 1/3 times 1/4. The area model makes the product intuitive — one piece of a rectangle partitioned both horizontally and vertically.
Key Concepts
To find the product of two unit fractions, such as finding a fraction 'of' another fraction, you can multiply the denominators. The resulting product is a new unit fraction. $$\frac{1}{a} \times \frac{1}{b} = \frac{1}{a \times b}$$.
Common Questions
How do you use an area model to multiply unit fractions?
Draw a rectangle. Divide it into rows based on one denominator and columns based on the other. Shade one row and one column and find the overlapping piece. That piece represents the product. For 1/3 x 1/4, the rectangle has 12 pieces and the overlap is 1 piece, so the product is 1/12.
Why does multiplying two fractions less than 1 give a smaller result?
Multiplying by a fraction less than 1 takes only a part of the original amount, making the result smaller. The area model shows this visually as a small shaded region within the whole rectangle.
What is a unit fraction?
A unit fraction has 1 as its numerator, such as 1/2, 1/3, or 1/5. Unit fractions are the building blocks for all fractions, which can be expressed as multiples of unit fractions.
What is Eureka Math Grade 5 Chapter 23 about?
Chapter 23 covers Multiplication of a Fraction by a Fraction, using area models and number lines to develop conceptual understanding before applying the standard multiplication algorithm.