Multiplying a Whole Number by a Fraction
Multiplying a Whole Number by a Fraction is a Grade 4 math skill that formalizes the connection between repeated addition and multiplication. When you multiply a whole number n by fraction a/b, the result is (n x a)/b — only the numerator changes. For example, 6 x 2/5 = 12/5. Students also use unit fraction thinking: 6 x 2/5 = 6 x 2 x (1/5) = 12 x (1/5) = 12/5. Covered in the fraction chapters of Eureka Math Grade 4, this skill is the first step toward the general fraction multiplication algorithm fully developed in 5th grade.
Key Concepts
To multiply a whole number ($n$) by a fraction ($\frac{a}{b}$), multiply the whole number by the numerator ($a$) and keep the denominator ($b$) the same. $$n \times \frac{a}{b} = \frac{n \times a}{b}$$.
Common Questions
How do I multiply a whole number by a fraction?
Multiply the whole number by the numerator and keep the denominator the same. For example, 4 x 3/7 = (4 x 3)/7 = 12/7. The denominator stays unchanged because the size of each fractional piece does not change — only the count of pieces grows.
Why does multiplying by a fraction give a larger numerator but the same denominator?
The denominator names the size of each piece. Multiplying by a whole number means taking more of those same-sized pieces. More pieces means a larger numerator, but the piece size (denominator) is unchanged.
How do I use unit fractions to multiply 6 x 2/5?
Rewrite 2/5 as 2 x (1/5). Now: 6 x 2 x (1/5) = 12 x (1/5) = 12/5. This unit fraction approach shows multiplication as counting unit fractional pieces, connecting to the repeated addition model.
What is 5 x 3/4?
5 x 3/4 = (5 x 3)/4 = 15/4. This improper fraction equals 3 3/4 as a mixed number. You can verify using repeated addition: 3/4 + 3/4 + 3/4 + 3/4 + 3/4 = 15/4.
How does multiplying a fraction by a whole number prepare for Grade 5?
In Grade 5, students extend this to fraction times fraction. The formula n x (a/b) = (n x a)/b is a special case of (a/b) x (c/d) = (a x c)/(b x d). Grade 4 builds the pattern with whole numbers before the full algorithm is introduced.
What grade covers multiplying whole numbers by fractions?
Multiplying a whole number by a fraction is a Grade 4 skill developed in the fraction chapters of Eureka Math Grade 4. Students use repeated addition, unit fractions, and the multiplication rule to build fluency.