Divide a Mixed Number by a Whole Number
Dividing a mixed number by a whole number in Grade 6 requires converting the mixed number to an improper fraction first, then multiplying by the reciprocal of the whole number. From enVision Mathematics, 2½ ÷ 5 = (5/2) ÷ (5/1) = (5/2) × (1/5) = 5/10 = 1/2. This convert-then-invert-and-multiply procedure works for all mixed number division problems and follows directly from the general rule for dividing fractions: keep the dividend, change the operation to multiplication, flip the divisor.
Key Concepts
Property To divide a mixed number by a whole number, convert the mixed number to an improper fraction and write the whole number as a fraction with a denominator of 1. Then, multiply by the reciprocal of the whole number.
Examples $2\frac{1}{2} \div 5 = \frac{5}{2} \div \frac{5}{1} = \frac{5}{2} \times \frac{1}{5} = \frac{5}{10} = \frac{1}{2}$ $3\frac{1}{3} \div 2 = \frac{10}{3} \div \frac{2}{1} = \frac{10}{3} \times \frac{1}{2} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3}$.
Explanation To divide a mixed number by a whole number, you must first convert both numbers into fractional form. Change the mixed number into an improper fraction. Write the whole number as a fraction by placing it over a denominator of 1. Finally, multiply the first fraction by the reciprocal of the second fraction and simplify the result.
Common Questions
How do you divide a mixed number by a whole number?
Convert the mixed number to an improper fraction, write the whole number as a fraction over 1, then multiply by the reciprocal. For example, 2½ ÷ 5 = (5/2) × (1/5) = 1/2.
Why do you convert to an improper fraction first?
Fractions can only be divided using the keep-change-flip (KCF) rule when both values are fractions. Converting to improper form allows the procedure to apply cleanly.
Can you show another example?
3⅓ ÷ 2 = (10/3) ÷ (2/1) = (10/3) × (1/2) = 10/6 = 5/3 = 1⅔.
What does dividing a mixed number by a whole number mean?
It means splitting the mixed number into equal parts. For example, 2½ ÷ 5 means dividing 2½ into 5 equal pieces, each piece being ½.
Where is this skill taught in enVision Mathematics?
Dividing a mixed number by a whole number is covered in enVision Mathematics, Grade 6, as part of fraction and mixed number division content.
What is the keep-change-flip rule for dividing fractions?
Keep the first fraction, change the ÷ sign to ×, and flip the second fraction (use its reciprocal). Then multiply across numerators and denominators.
What common mistakes do students make?
Students often forget to convert the mixed number to an improper fraction first, or they flip the wrong fraction (flip the dividend instead of the divisor).