On the number line, fractions keep going past 1. So some fractions land exactly on whole numbers.
Why it works
$\frac{3}{3}$ is all 3 of the 3 equal parts: the whole thing, so $\frac{3}{3} = 1$. Six thirds is two wholes, so $\frac{6}{3} = 2$. And $\frac{5}{1}$ means each whole is just 1 part; 5 of those parts are 5 wholes, so $\frac{5}{1} = 5$. A fraction and a whole number can name the same point.
Key idea
When the numerator and denominator are equal, the fraction is 1: $\frac{4}{4} = 1$. Every $b$ pieces of $\frac{1}{b}$ make one whole. And any whole number can be written over 1: $5 = \frac{5}{1}$.
Worked example: One whole
What is $\frac{4}{4}$?
- 4 fourths is all 4 equal parts of the whole.
Answer: $1$
Worked example: Two wholes
What whole number is $\frac{8}{4}$?
- Every 4 fourths make 1.
- 8 fourths make 2 wholes.
Answer: $2$
Worked example: Write a whole number as a fraction
Write 3 as a fraction with denominator 4.
- One whole is 4 fourths.
- 3 wholes is $3 \times 4 = 12$ fourths.
Answer: $3 = \frac{12}{4}$
Common mistake
Believing a fraction is always less than 1. $\frac{5}{4}$ is one whole and one more fourth, more than 1. Check with bars: a single bar holds only 4 fourths, so $\frac{5}{4}$ needs a second bar.