The Standard Algorithm for Fraction Multiplication
The Standard Algorithm for Fraction Multiplication is a Grade 5 math skill in Eureka Math, Chapter 23: Multiplication of a Fraction by a Fraction, where students multiply numerator by numerator and denominator by denominator to compute fraction products, then simplify the result. This algorithm generalizes to multiplying any two rational numbers and is a cornerstone of middle school math.
Key Concepts
To multiply two fractions, multiply the numerators to find the new numerator and multiply the denominators to find the new denominator. $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$.
Common Questions
What is the standard algorithm for multiplying fractions?
Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. For example, 2/3 x 3/5 = (2x3)/(3x5) = 6/15, which simplifies to 2/5.
Do you need a common denominator to multiply fractions?
No. Unlike addition and subtraction, multiplying fractions does not require a common denominator. You simply multiply across the numerators and across the denominators.
Should you simplify before or after multiplying fractions?
You can do either. Simplifying before multiplying (cross-cancellation) keeps numbers smaller during calculation. Simplifying after multiplying means reducing the final product to lowest terms.
What is Eureka Math Grade 5 Chapter 23 about?
Chapter 23 covers Multiplication of a Fraction by a Fraction, building from area models to the standard algorithm for multiplying any two fractions.