Definition of a mixed number and examples

📚 Quick Study Guide

🔍 A mixed number is a number consisting of a whole number and a proper fraction.
• ➕ For example, $2\frac{3}{4}$ is a mixed number. 2 is the whole number, and $\frac{3}{4}$ is the proper fraction.
💡 To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, add the numerator, and then write the result over the original denominator. For $a\frac{b}{c}$, this gives $\frac{(a \times c) + b}{c}$. 📝 Example: Convert $3\frac{1}{2}$ to an improper fraction: $(3 \times 2) + 1 = 7$, so $3\frac{1}{2} = \frac{7}{2}$. ➗ To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, the remainder is the numerator of the fractional part, and the denominator stays the same. ➗ Example: Convert $\frac{11}{3}$ to a mixed number: $11 \div 3 = 3$ with a remainder of 2, so $\frac{11}{3} = 3\frac{2}{3}$.

➕ Practice Quiz

1. What is the definition of a mixed number?
   1. A fraction with a numerator greater than the denominator.
   2. A whole number.
   3. A number consisting of a whole number and a proper fraction.
   4. A negative number.
2. Which of the following is a mixed number?
   1. $\frac{7}{2}$
   2. 5
   3. $3\frac{1}{4}$
   4. $\frac{1}{2}$
3. Convert the mixed number $2\frac{1}{3}$ to an improper fraction.
   1. $\frac{5}{3}$
   2. $\frac{6}{3}$
   3. $\frac{7}{3}$
   4. $\frac{8}{3}$
4. Convert the improper fraction $\frac{9}{4}$ to a mixed number.
   1. $1\frac{5}{4}$
   2. $2\frac{1}{4}$
   3. $2\frac{2}{4}$
   4. $3\frac{1}{4}$
5. What is the whole number part of the mixed number $5\frac{2}{7}$?
   1. 2
   2. 5
   3. 7
   4. 9
6. Which mixed number is equivalent to $\frac{15}{4}$?
   1. $2\frac{3}{4}$
   2. $3\frac{1}{4}$
   3. $3\frac{3}{4}$
   4. $4\frac{1}{4}$
7. Simplify $4\frac{6}{8}$.
   1. $4\frac{1}{4}$
   2. $4\frac{2}{4}$
   3. $4\frac{3}{4}$
   4. $4\frac{4}{4}$