Subtract fractions - From a whole
Theory
To subtract a fraction from a whole number, rename one whole as a fraction with the same denominator, then subtract the numerators. One whole is \(\dfrac{n}{n}\), so \(1=\dfrac{5}{5}\).
A whole number can be written as a fraction: one whole equals the denominator over itself, such as \(1=\dfrac{5}{5}\) or \(1=\dfrac{8}{8}\).
Renaming a whole means rewriting it with the denominator you need, so both fractions match before subtracting.
When the fractions share a denominator, only the numerators are subtracted; the denominator stays the same.
One whole is renamed to match the denominator being subtracted.
| Whole | Renamed |
|---|---|
| \(1\) | \(\dfrac{3}{3}\) |
| \(1\) | \(\dfrac{5}{5}\) |
| \(2\) | \(1\dfrac{3}{3}\) |
| \(4\) | \(3\dfrac{3}{3}\) |
How to subtract a fraction from a whole
- Rename one whole using the denominator of the fraction.
- Keep any other wholes unchanged.
- Subtract the numerators; the denominator stays the same.
Rename the whole as fifths.
| \(1-\dfrac{2}{5}\) | \(=\) | \(\dfrac{5}{5}-\dfrac{2}{5}=\dfrac{3}{5}\) |
Six sixths make one whole.
| \(1-\dfrac{5}{6}\) | \(=\) | \(\dfrac{6}{6}-\dfrac{5}{6}=\dfrac{1}{6}\) |
Rename one whole, keep the other.
| \(2-\dfrac{1}{3}\) | \(=\) | \(1\dfrac{3}{3}-\dfrac{1}{3}=1\dfrac{2}{3}\) |
| \(1-\dfrac{3}{4}\) | \(=\) | \(\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}\) |
There is \(\dfrac{1}{4}\) of the cake left.
Common pitfalls
Frequently asked questions
How do you subtract a fraction from a whole number?
Rename one whole as a fraction with the same denominator, then subtract the numerators. For \(1-\dfrac{2}{5}\), write \(1\) as \(\dfrac{5}{5}\) and take away \(\dfrac{2}{5}\) to get \(\dfrac{3}{5}\).
Why is one whole the same as a fraction?
Splitting one whole into equal parts and taking all of them gives the whole back, so \(\dfrac{5}{5}=1\) and \(\dfrac{8}{8}=1\).
What if there is more than one whole?
Rename just one of the wholes and keep the rest. For \(2-\dfrac{1}{3}\), write \(2\) as \(1\dfrac{3}{3}\), then subtract to get \(1\dfrac{2}{3}\).
Do you subtract the denominators too?
No. When the denominators match, only the numerators are subtracted; the denominator stays the same.