Dividing Mixed Numbers
Divide mixed numbers in Grade 6 math by first converting them to improper fractions, then applying Keep, Change, Flip to multiply by the reciprocal and simplify the result.
Key Concepts
Property To divide mixed numbers, you must complete two steps. First, rewrite all mixed numbers or whole numbers as improper fractions. Then, to perform the division, multiply the first fraction by the reciprocal of the second fraction.
Examples $3\frac{1}{3} \div 1\frac{1}{2} = \frac{10}{3} \div \frac{3}{2} = \frac{10}{3} \times \frac{2}{3} = \frac{20}{9} = 2\frac{2}{9}$ $2\frac{1}{2} \div 1\frac{2}{3} = \frac{5}{2} \div \frac{5}{3} = \frac{5}{2} \times \frac{3}{5} = \frac{15}{10} = 1\frac{1}{2}$ $8 \div 1\frac{1}{3} = \frac{8}{1} \div \frac{4}{3} = \frac{8}{1} \times \frac{3}{4} = \frac{24}{4} = 6$.
Explanation Think of this as a two part mission! First, you have to get your mixed numbers into their 'improper fraction' disguises. Then, instead of a direct fight (division), you bring in the second number's secret agent twin (its reciprocal) and multiply. It's a clever switcheroo that makes solving the problem much simpler!
Common Questions
How do you divide mixed numbers?
Convert each mixed number to an improper fraction first. Then apply Keep, Change, Flip: keep the first fraction, change ÷ to ×, flip the second fraction. Multiply across and simplify the result.
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. For example, 2 3/4 = (2×4 + 3)/4 = 11/4.
Why must you convert mixed numbers before dividing?
You cannot apply the Keep, Change, Flip method to mixed numbers directly. Converting to improper fractions first puts the entire value over one denominator, making the division straightforward.
How do you convert an improper fraction answer back to a mixed number?
Divide the numerator by the denominator. The quotient is the whole number part, and the remainder over the denominator is the fraction part. For example, 17/4 = 4 remainder 1 = 4 1/4.