Multiplying a Whole Number and a Unit Fraction
To multiply a whole number n by a unit fraction 1/d, the whole number becomes the numerator of the result while the denominator stays the same, giving n x (1/d) = n/d, as taught in Illustrative Mathematics Grade 5, Chapter 2: Fractions as Quotients and Fraction Multiplication. For example, 5 x 1/8 = 5/8, representing 5 copies of the unit fraction 1/8.
Key Concepts
To multiply a whole number by a unit fraction, the whole number becomes the numerator of the resulting fraction, and the denominator stays the same.
$$n \times \frac{1}{d} = \frac{n}{d}$$.
Common Questions
How do you multiply a whole number by a unit fraction?
The whole number becomes the numerator of the result and the denominator stays the same: n x (1/d) = n/d; for example, 5 x 1/8 = 5/8.
What is a unit fraction?
A unit fraction has 1 as its numerator, like 1/2, 1/3, 1/4, or 1/8; it represents exactly one equal part of a whole.
Why does n x (1/d) = n/d?
Multiplying by 1/d means taking 1/d of n, or finding n copies of a piece that is 1/d of the whole; n copies of 1/d gives n/d.
What are some examples of multiplying whole numbers by unit fractions?
5 x 1/8 = 5/8; 3 x 1/4 = 3/4; 7 x 1/3 = 7/3; in each case, the whole number becomes the numerator over the same denominator.
How is this skill foundational for fraction multiplication?
Multiplying by unit fractions is the building block for multiplying by any fraction; once students understand n x 1/d = n/d, they can extend this to n x a/d = (n x a)/d.