Multiplying a Whole Number by a Unit Fraction
Grade 4 Eureka Math students learn that multiplying a whole number by a unit fraction is equivalent to repeated addition of that fraction. The rule n × (1/d) = n/d means 4 × (1/3) = 4/3 and 5 × (1/8) = 5/8. On a number line, each multiplication is shown as n equal jumps of size 1/d. This connects fraction multiplication to the foundational meaning of multiplication as repeated addition, and prepares students for multiplying whole numbers by non-unit fractions.
Key Concepts
Multiplying a whole number, $n$, by a unit fraction, $\frac{1}{d}$, is equivalent to repeated addition. This relationship is generalized by the rule: $$n \times \frac{1}{d} = \underbrace{\frac{1}{d} + \frac{1}{d} + \dots + \frac{1}{d}} {n \text{ times}} = \frac{n}{d}$$.
Common Questions
What is a unit fraction?
A unit fraction has a numerator of 1, such as 1/3, 1/4, or 1/8. It represents one equal part of a whole divided into that many parts.
How do you multiply a whole number by a unit fraction?
Place the whole number in the numerator over the fraction's denominator. For example, 4 × (1/3) = 4/3.
How is 4 × (1/3) shown as repeated addition?
It equals 1/3 + 1/3 + 1/3 + 1/3 = 4/3. Each jump on a number line is 1/3, and you make 4 jumps.
What does 5 × (1/8) equal and why?
5 × (1/8) = 5/8, because adding 1/8 five times gives 5 eighths.
How does this connect to multiplying by non-unit fractions?
Once students understand n × (1/d) = n/d, they extend to n × (a/d) = na/d by treating a/d as a groups of 1/d.