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🔟elementary algebra review

Mixed Numbers

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

A mixed number is a representation of a quantity that combines a whole number and a proper fraction. It is a way to express a number that is not a simple whole number or a simple fraction.

5 Must Know Facts For Your Next Test

  1. Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator of the fraction and adding the numerator, then placing this over the denominator.
  2. When adding or subtracting mixed numbers, you can first convert them to improper fractions, perform the operation, and then convert the result back to a mixed number.
  3. Multiplying mixed numbers involves first converting them to improper fractions, multiplying the numerators, and then multiplying the denominators.
  4. Dividing mixed numbers involves first converting them to improper fractions, and then dividing the numerators and multiplying the denominators.
  5. Mixed numbers are useful in representing quantities that are not whole numbers, such as measurements, recipes, and other real-world applications.

Review Questions

  • How can a mixed number be converted to an improper fraction?
    • To convert a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction, and then add the numerator. This result is placed over the original denominator. For example, the mixed number 2$\frac{3}{4}$ can be converted to the improper fraction $\frac{11}{4}$.
  • Describe the process of adding or subtracting mixed numbers.
    • When adding or subtracting mixed numbers, you can first convert them to improper fractions, perform the operation, and then convert the result back to a mixed number. This allows you to work with the fractions more easily. For example, to add 2$\frac{1}{3}$ and 3$\frac{2}{3}$, you would convert them to $\frac{7}{3}$ and $\frac{11}{3}$, add the numerators to get $\frac{18}{3}$, and then convert the result back to the mixed number 6$\frac{0}{3}$ or 6.
  • Explain how to multiply and divide mixed numbers.
    • To multiply mixed numbers, you first convert them to improper fractions, multiply the numerators, and then multiply the denominators. For example, to multiply 2$\frac{1}{2}$ and 3$\frac{1}{4}$, you would convert them to $\frac{5}{2}$ and $\frac{13}{4}$, multiply the numerators to get $\frac{65}{8}$, and then convert the result back to the mixed number 8$\frac{1}{8}$. To divide mixed numbers, you follow a similar process of converting to improper fractions, dividing the numerators, and multiplying the denominators.

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