Generating Equivalent Fractions by Multiplication
Generating Equivalent Fractions by Multiplication teaches Grade 3 students that multiplying both the numerator and the denominator of a fraction by the same whole number creates an equal fraction. From Eureka Math Grade 3: multiplying 1/2 by 2/2 gives 2/4; multiplying by 3/3 gives 3/6. Formally: (n × a)/(n × b) = a/b. This skill is the inverse of simplifying fractions and is essential for adding fractions with unlike denominators. Understanding that the fraction's value is unchanged — because n/n = 1 — builds multiplicative identity reasoning.
Key Concepts
To generate an equivalent fraction, multiply the numerator and the denominator by the same whole number ($n 1$). $$\frac{a}{b} = \frac{a \times n}{b \times n}$$.
Common Questions
How do you generate an equivalent fraction?
Multiply both the numerator and the denominator by the same non-zero whole number. The value of the fraction does not change.
How do you make 1/2 equivalent to a fraction with denominator 8?
Multiply numerator and denominator by 4: (1×4)/(2×4) = 4/8.
Why does multiplying numerator and denominator by the same number keep the fraction equal?
You are multiplying by n/n = 1, the multiplicative identity. Multiplying by 1 does not change a value.
How is this different from simplifying a fraction?
Simplifying divides numerator and denominator by a common factor to reduce. Generating equivalents multiplies them by the same number to scale up.
Why do you need equivalent fractions?
To add or subtract fractions with different denominators, you first convert them to equivalent fractions with the same (common) denominator.
What Eureka Math grade covers equivalent fractions?
Grade 3, within the fractions domain.