Multiplying a Fraction and a Mixed Number
Multiplying a Fraction and a Mixed Number is a Grade 6 math skill from Big Ideas Math, Course 1, Chapter 2: Fractions and Decimals. Students first convert the mixed number to an improper fraction (e.g., 2 1/4 = 9/4), then multiply numerators and denominators separately. For example: 2 1/4 × 1/3 = 9/4 × 1/3 = 9/12 = 3/4. This two-step process — convert then multiply — is the standard method and builds on earlier understanding of mixed numbers and fraction multiplication from Grade 5.
Key Concepts
Property To multiply a fraction and a mixed number, first convert the mixed number into an improper fraction. Then, multiply the numerators and multiply the denominators. $$a \frac{b}{c} \times \frac{d}{e} = \frac{ac+b}{c} \times \frac{d}{e}$$.
Examples $2 \frac{1}{4} \times \frac{1}{3} = \frac{9}{4} \times \frac{1}{3} = \frac{9}{12} = \frac{3}{4}$ $\frac{2}{5} \times 3 \frac{1}{2} = \frac{2}{5} \times \frac{7}{2} = \frac{14}{10} = \frac{7}{5} = 1 \frac{2}{5}$.
Explanation This process combines two key ideas: converting mixed numbers and multiplying fractions. The first step is always to change the mixed number into an improper fraction. Once you have two fractions, you can apply the standard multiplication rule: multiply the numerators together and the denominators together. Remember to simplify your final answer if possible, and convert it back to a mixed number if needed.
Common Questions
How do you multiply a fraction and a mixed number?
Step 1: Convert the mixed number to an improper fraction (multiply the whole number by the denominator and add the numerator). Step 2: Multiply numerators together and denominators together. Step 3: Simplify. Example: 2 1/4 × 1/3 = 9/4 × 1/3 = 9/12 = 3/4.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, then add the numerator. Keep the same denominator. Example: 3 1/2 → (3×2)+1 = 7, so 3 1/2 = 7/2. Another: 2 3/4 → (2×4)+3 = 11, so 2 3/4 = 11/4.
Can you multiply fractions without converting mixed numbers first?
Technically you can multiply the whole number part and fraction part separately, but it's much harder and error-prone. Always converting to improper fractions first keeps the process clean and consistent.
What is a worked example of fraction times mixed number?
2/5 × 3 1/2 = 2/5 × 7/2 = 14/10 = 7/5 = 1 2/5. After multiplying, simplify and convert back to a mixed number if needed.
When do Grade 6 students practice fraction and mixed number multiplication?
This skill is in Big Ideas Math, Course 1, Chapter 2: Fractions and Decimals, covering Grade 6 fraction operations including multiplication and division of fractions and mixed numbers.
What mistakes do students make when multiplying fractions and mixed numbers?
Common mistakes: forgetting to convert the mixed number first, incorrectly converting (adding instead of multiplying the whole number times denominator), and failing to simplify the final answer. Always double-check the conversion step.