Writing Mixed Numbers as Improper Fractions
Converting a mixed number to an improper fraction requires multiplying the whole number by the denominator, adding the numerator, and placing the result over the original denominator. In Grade 6 Saxon Math Course 1 (Chapter 7: Fractions and Geometric Concepts), students use this conversion as the required first step before multiplying or dividing mixed numbers. For 2¾: (2 × 4) + 3 = 11, giving 11/4. Students also reverse the process: divide the numerator by the denominator—the quotient is the whole number and the remainder becomes the new numerator—to convert back to a mixed number.
Key Concepts
New Concept To convert a mixed number to an improper fraction, multiply the denominator by the whole number, add the numerator, and keep the original denominator. $$ 3\frac{1}{2} = \frac{(2 \times 3) + 1}{2} = \frac{7}{2} $$ What’s next This is a foundational skill for working with fractions. Next, you'll apply this technique in worked examples and practice problems, including multiplication.
Common Questions
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, then add the numerator. Place this total over the original denominator. Example: 3 2/5 → (3×5)+2 = 17, so the improper fraction is 17/5.
Why convert mixed numbers to improper fractions?
Multiplication and division of fractions require improper fractions. Mixed numbers cannot be directly multiplied or divided using standard fraction algorithms.
How do you convert an improper fraction back to a mixed number?
Divide the numerator by the denominator. The quotient is the whole number; the remainder is the new numerator over the original denominator. For 13/4: 13÷4=3 R1, giving 3 1/4.
Convert 4 3/7 to an improper fraction.
(4×7)+3 = 31, so 4 3/7 = 31/7.
What distinguishes a proper fraction, improper fraction, and mixed number?
Proper fraction: numerator < denominator (e.g., 3/5). Improper fraction: numerator ≥ denominator (e.g., 8/5). Mixed number: whole number plus proper fraction (e.g., 1 3/5).