Multiplying Mixed Numbers
Multiplying mixed numbers in Grade 8 Saxon Math Course 3 requires converting mixed numbers to improper fractions, multiplying numerators and denominators, then simplifying the result back to a mixed number if needed. Students practice this operation in the context of area calculations, scaling recipes, and other real-world scenarios. Proficiency with mixed number multiplication supports work with rational numbers in algebra.
Key Concepts
Property First, rewrite each mixed number as an improper fraction. Then, multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. Finally, simplify the resulting fraction if possible.
Examples $$2\frac{1}{2} \times 1\frac{1}{5} \rightarrow \frac{5}{2} \times \frac{6}{5} = \frac{30}{10} = 3$$ $$3\frac{1}{3} \times 1\frac{1}{2} \rightarrow \frac{10}{3} \times \frac{3}{2} = \frac{\cancel{10}^5}{\cancel{3} 1} \times \frac{\cancel{3}^1}{\cancel{2} 1} = \frac{5}{1} = 5$$.
Explanation Multiplying mixed numbers is a two step dance! First, you have to change your fancy mixed numbers into their simpler improper fraction outfits. Once they're dressed for the party, it's easy: top times top, and bottom times bottom. Then just simplify your answer so it looks sharp, maybe by changing it back into a mixed number.
Common Questions
How do you multiply mixed numbers?
Convert each mixed number to an improper fraction. Multiply numerators together and denominators together. Simplify the result and convert back to a mixed number if needed.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator. This becomes the new numerator, with the same denominator. For example, 2 3/4 = (2x4+3)/4 = 11/4.
How do you multiply 1 1/2 by 2 2/3?
Convert: 3/2 x 8/3. Multiply: 24/6 = 4. The product is 4.
Can you simplify before multiplying mixed numbers?
Yes. After converting to improper fractions, look for common factors between any numerator and any denominator and simplify (cross-cancel) before multiplying to keep numbers smaller.
How does Saxon Math Course 3 teach multiplying mixed numbers?
Saxon Math Course 3 teaches the convert-multiply-simplify sequence with plentiful practice problems, applying mixed number multiplication in geometric area and real-world measurement contexts.