Equation field guide
Fractions: division written vertically
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
The structure of a fraction
The horizontal bar groups the numerator and denominator. In (a + b)/c, the entire sum a + b is divided by c. Parentheses make the intended grouping explicit when a fraction is written on one line.
A denominator of zero is excluded because no number multiplied by zero can produce a nonzero numerator. So 5/0 has no ordinary real-number value.
A concrete interpretation
If a task takes 3 hours and is shared equally among 4 people, 3/4 hour is each person’s share. The same fraction can be a quotient, a part of a whole, or a ratio, depending on the article.
Fractions are numbers in their own right. 1/2, 2/4, and 0.5 are different representations of the same value.
Order matters
a/b is generally different from b/a. For example, 2/5 = 0.4 while 5/2 = 2.5. Swapping numerator and denominator takes the reciprocal.
When a formula has a fraction, identify exactly what belongs above and below the bar before substituting values. This avoids a common precedence error.