Sometimes a fraction is bigger than one whole. There are two ways to write those amounts — as an improper fraction or as a mixed number — and switching between them is easier than it looks.
A proper fraction is smaller than one whole — its top number is less than its bottom number, like 3/4. An improper fraction is one whole or more — its top is greater than or equal to its bottom, like 7/4. A mixed number writes that same amount as a whole number next to a proper fraction, like 1¾.
Seven quarter-slices of pizza is one whole pizza plus three more slices. 7/4 and 1¾ are just two names for the exact same thing.
To rewrite an improper fraction as a mixed number, see how many whole groups fit inside it. The denominator tells you how many pieces make one whole.
For 7/4, four quarters make one whole. Four fits into seven one time → that's the whole number, 1.
After taking away 4, there are 3 quarters left. That leftover becomes the new top number.
The bottom number stays 4. Put it together: 1 and 3/4.
If the top divides evenly (like 8/4), there's no leftover — it's just a whole number (8/4 = 2). If there's a remainder, that's your fraction part.
Going the other way, turn the whole number back into pieces and add them to the fraction you already have. Multiply, then add.
Denominator × whole number. For 2⅓: 3 × 2 = 6 thirds hidden in the two wholes.
Add the fraction's numerator: 6 + 1 = 7. That's your new top number.
The bottom stays 3, giving 7/3.
Follow the arrows: multiply the bottom by the whole, then add the top. "Bottom times the whole, plus the top, over the same bottom."
Both are correct — you choose based on what you're doing. Mixed numbers are easier to picture in everyday life ("I need 2½ cups of flour"). Improper fractions are usually easier for calculating, especially when you multiply or divide fractions.
When a fraction answer comes out improper, it's often nicest to rewrite it as a mixed number for your final answer — just like simplifying.
Convert each one, then check your answer.
Enter the whole number, then the leftover fraction (the denominator stays the same).
Multiply the denominator by the whole, add the top, and put it over the same denominator.