Fractions, Equivalence & Ratios

Whenever we need to describe a part of a whole, whole numbers are not enough. If you cut a pizza into 8 equal slices and eat 3 of them, you have eaten 3 out of 8 equal parts. We write this as the fraction 3/8. The fraction does not represent a single counting number — it represents a relationship between parts and a whole.

Every fraction has two parts, and their names matter. The top number — called the — counts how many parts you actually have. The bottom number — called the — tells you into how many equal parts the whole has been divided. Think of the denominator as the “size of each slice” and the numerator as “how many slices you took”.

An important detail: the parts must be equal. If you cut a pizza into 8 unequal pieces and eat 3, you cannot simply say 3/8 — fractions only work when the whole is divided into equal-sized parts.

Is 11/7 a proper fraction? Think: 11 is greater than 7, so the value is more than 1 whole — it must be an improper fraction. YesNo

Converting between improper fractions and mixed numbers is straightforward. The improper fraction 7/4 means 7 quarters. Now 4 quarters make exactly 1 whole, so 7 quarters = 1 whole + 3 remaining quarters. That leftover is quarters — so 7/4 = 1¾.