Lesson 8: Mixed Numbers

Property

A mixed number consists of a whole number $a$ and a fraction $\frac{b}{c}$ where $c \neq 0$. It is written as follows.

Examples

• A baker uses $3 \frac{1}{2}$ cups of flour for a recipe. This means three full cups and one half cup.
• A movie is $2 \frac{1}{4}$ hours long. This means it lasts for two full hours and an additional quarter of an hour.
• A child is $4 \frac{1}{3}$ feet tall. This represents four full feet plus one-third of a foot.

Explanation

A mixed number is a simpler way to write an improper fraction. It combines a whole number with a proper fraction, making it easier to understand how many wholes and parts you have, like $2 \frac{1}{2}$ pizzas.

Property

To convert a mixed number to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator to the product found in Step 1.
3. Write the final sum over the original denominator.

Examples

• To convert $3 \frac{1}{4}$: First, multiply $3 \times 4 = 12$. Then, add the numerator, $12 + 1 = 13$. The improper fraction is $\frac{13}{4}$.
• To convert $5 \frac{2}{3}$: First, multiply $5 \times 3 = 15$. Then, add the numerator, $15 + 2 = 17$. The improper fraction is $\frac{17}{3}$.
• To convert $7 \frac{3}{5}$: First, multiply $7 \times 5 = 35$. Then, add the numerator, $35 + 3 = 38$. The improper fraction is $\frac{38}{5}$.

Explanation

To change $2 \frac{1}{4}$ into just fourths, you break down the wholes. Two wholes are eight-fourths ($2 \times 4$). Add the extra one-fourth, and you have nine-fourths in total, which is written as $\frac{9}{4}$.