Simplify The Product
After multiplying fractions, the product must be simplified: convert any improper fraction to a mixed number and reduce the fractional part to lowest terms. In Grade 6 Saxon Math Course 1 (Chapter 7: Fractions and Geometric Concepts), students learn that 20/6 simplifies to 3 2/6, which further reduces to 3 1/3 by dividing numerator and denominator by their GCF of 2. The two-step process is: (1) divide the numerator by the denominator to get the whole number and remainder, forming the mixed number; (2) reduce the fractional remainder by its GCF. A fully simplified answer uses no improper fractions and the fraction part is in lowest terms.
Key Concepts
Property After multiplying, the final answer must be simplified. This involves converting any improper fraction into a mixed number and reducing the fractional part to its lowest terms. $$\frac{20}{6} = 3\frac{2}{6} = 3\frac{1}{3}$$.
Examples $\frac{32}{3} = 10\frac{2}{3}$ $\frac{44}{8} = 5\frac{4}{8} = 5\frac{1}{2}$ $\frac{50}{12} = 4\frac{2}{12} = 4\frac{1}{6}$.
Explanation Simplifying is like tidying up your final answer to make it look sharp and be easily understood. An improper fraction like $\frac{25}{4}$ is technically right, but it's clunky. Converting it to a mixed number like $6\frac{1}{4}$ makes it neat and practical. It’s the final flourish that turns a correct answer into a great one.
Common Questions
How do you simplify an improper fraction after multiplying?
Divide the numerator by the denominator. The quotient is the whole number and the remainder becomes the numerator of the fraction part. Then reduce the fraction to lowest terms.
Simplify 20/6 completely.
20 ÷ 6 = 3 remainder 2, giving 3 2/6. Then divide both 2 and 6 by GCF=2 to get 3 1/3.
What does it mean for a fraction to be in lowest terms?
The numerator and denominator share no common factors other than 1. Divide both by their GCF to reach lowest terms.
When is a fraction fully simplified?
When it is written as a mixed number (not an improper fraction) and the fractional part has no common factors between numerator and denominator other than 1.
What is the GCF of 8 and 12, and how does it simplify 8/12?
GCF of 8 and 12 is 4. Divide both by 4: 8/12 = 2/3.