Divide a Mixed Number by a Mixed Number
Dividing a mixed number by a mixed number requires three steps: convert both mixed numbers to improper fractions, multiply by the reciprocal of the divisor, then simplify. For 2 and 1/2 / 1 and 1/4: convert to 5/2 / 5/4 = 5/2 x 4/5 = 20/10 = 2. This 6th grade skill from enVision Mathematics Grade 6 is the most complex form of fraction division and appears in measurement contexts like dividing a mixed-number length into mixed-number sections. It requires fluency with improper fractions, reciprocals, and fraction multiplication.
Key Concepts
Property To divide a mixed number by a mixed number, first convert both to improper fractions. Then, multiply the first fraction by the reciprocal of the second fraction.
Examples $3\frac{1}{2} \div 1\frac{1}{4} = \frac{7}{2} \div \frac{5}{4} = \frac{7}{2} \times \frac{4}{5} = \frac{28}{10} = \frac{14}{5} = 2\frac{4}{5}$ $5\frac{1}{3} \div 2\frac{2}{3} = \frac{16}{3} \div \frac{8}{3} = \frac{16}{3} \times \frac{3}{8} = \frac{48}{24} = 2$.
Explanation This process combines two key steps for dividing fractions. First, you must rewrite both mixed numbers as improper fractions. Then, apply the rule for dividing fractions, which is to multiply the dividend by the reciprocal of the divisor. Finally, simplify your result and convert it back to a mixed number or whole number if needed.
Common Questions
How do you divide a mixed number by a mixed number?
Convert both to improper fractions, then multiply the first by the reciprocal of the second. For 2 and 1/2 / 1 and 1/4: 5/2 / 5/4 = 5/2 x 4/5 = 20/10 = 2.
Why must you convert mixed numbers before dividing?
Mixed numbers are not single fractions and cannot be directly flipped to find a reciprocal. Converting to improper fractions gives a single value that can be flipped.
How do you simplify after dividing mixed numbers?
After multiplying, simplify the resulting fraction by finding the GCF of numerator and denominator, then divide both. Convert back to a mixed number if the result is greater than 1.
What grade divides mixed numbers by mixed numbers?
This is a 6th grade skill in enVision Mathematics Grade 6, the culminating step in the fraction division progression that began with unit fractions and simple fractions.
How can you check your answer after dividing mixed numbers?
Multiply your answer by the original divisor mixed number. The result should equal the original dividend. For answer 2 x 1 and 1/4 = 2 x 5/4 = 10/4 = 2 and 1/2. Correct.
What are common mistakes when dividing mixed numbers?
Forgetting to convert to improper fractions first, or flipping the wrong fraction. Always convert both, then flip only the divisor (the number you are dividing by).