Subtracting Mixed Numerals
Subtracting Mixed Numerals covers taking one mixed numeral from another in NSW Year 7 maths (NESA outcome MA4‑FRC‑C‑01). Rename the fractions with a common denominator, subtract the whole numbers and the fractions, and borrow one whole when the first fraction is too small, as in \(4\frac{1}{5} - 1\frac{3}{5} = 2\frac{3}{5}\).
You will subtract fractions from whole numbers, try the improper fraction method as a second way, check by adding back, and spot errors in someone else's working. Cutting ribbon off a roll, the time left in a film and the missing side of a garden bed are everyday examples. It is part of Year 7 Fractions.
Theory
To subtract mixed numerals, subtract the whole numbers, then subtract the fractions. The fractions must have the same denominator first, and if the first fraction is smaller you borrow a whole. This Year 7 maths page shows each step, another method using improper fractions, and how to check by adding back.
Subtract the whole numbers first and then the fractions: \(5\dfrac{1}{2} - 4\dfrac{1}{4} = (5 - 4) + \dfrac{2}{4} - \dfrac{1}{4} = 1\dfrac{1}{4}\).
Rename with the lowest common denominator (LCD) if the denominators are different.
Borrow if the first fraction is smaller than the second: take \(1\) whole and rename it as a fraction: \(5\dfrac{2}{7} = 4 + \dfrac{7}{7} + \dfrac{2}{7} = 4\dfrac{9}{7}\).
Whole number minus a fraction: write one whole as a fraction: \(5 - \dfrac{2}{3} = 4 + \dfrac{3}{3} - \dfrac{2}{3} = 4\dfrac{1}{3}\).
Borrowing and the improper fraction method:
How to subtract mixed numerals
- Rename the fractions with the LCD.
- Borrow a whole if the first fraction is smaller than the second.
- Subtract the whole numbers, then the fractions.
- Simplify and check by adding back.
| \(5\dfrac{2}{3} - 2\dfrac{1}{4}\) | \(=\) | \(3 + \dfrac{8}{12} - \dfrac{3}{12}\) |
| \(\) | \(=\) | \(3\dfrac{5}{12}\) |
\(3\dfrac{5}{12}\)
\(\dfrac{1}{2} = \dfrac{3}{6}\) is less than \(\dfrac{2}{3} = \dfrac{4}{6}\), so borrow: \(4\dfrac{3}{6} = 3\dfrac{9}{6}\).
| \(3\dfrac{9}{6} - 3\dfrac{4}{6}\) | \(=\) | \(\dfrac{5}{6}\) |
\(\dfrac{5}{6}\). Check: \(\dfrac{5}{6} + 3\dfrac{2}{3} = 4\dfrac{1}{2}\).
(i) \(6\dfrac{7}{10} - 2\dfrac{3}{10}\)
(ii) \(4 - \dfrac{3}{5}\)
| \(6\dfrac{7}{10} - 2\dfrac{3}{10}\) | \(=\) | \(4\dfrac{4}{10} = 4\dfrac{2}{5}\) |
| \(4 - \dfrac{3}{5}\) | \(=\) | \(3 + \dfrac{5}{5} - \dfrac{3}{5} = 3\dfrac{2}{5}\) |
(i) \(4\dfrac{2}{5}\)
(ii) \(3\dfrac{2}{5}\)
| \(5\dfrac{10}{12} - 2\dfrac{3}{12}\) | \(=\) | \(3\dfrac{7}{12}\) |
Check: \(3\dfrac{7}{12} + 2\dfrac{3}{12} = 5\dfrac{10}{12} = 5\dfrac{5}{6}\).
| \(4\dfrac{2}{12} - 1\dfrac{9}{12}\) | \(=\) | \(3\dfrac{14}{12} - 1\dfrac{9}{12}\) |
| \(\) | \(=\) | \(2\dfrac{5}{12}\) |
\(\dfrac{2}{12} < \dfrac{9}{12}\), so borrow \(\dfrac{12}{12}\). The answer is \(2\dfrac{5}{12}\).
| \(\dfrac{1}{3} + 1\dfrac{1}{4}\) | \(=\) | \(\dfrac{4}{12} + 1\dfrac{3}{12} = 1\dfrac{7}{12}\) |
| \(2 - 1\dfrac{7}{12}\) | \(=\) | \(1\dfrac{12}{12} - 1\dfrac{7}{12} = \dfrac{5}{12}\) |
\(\dfrac{1}{12}\) of an hour is \(5\) minutes, so the game lasts \(25\) minutes.
Common pitfalls
Frequently asked questions
How do you subtract mixed numerals?
Rename the fractions with a common denominator, borrow if needed, then subtract the wholes and the fractions.
When do you need to borrow?
When the first fraction is smaller than the one you take away, as in \(4\dfrac{1}{6} - 1\dfrac{3}{4}\).
How do you borrow a whole?
Take \(1\) from the whole number and add it to the fraction: \(4\dfrac{2}{12} = 3\dfrac{14}{12}\).
Is there another method?
Yes. Change both to improper fractions, subtract, then change back.
How do you check a subtraction?
Add the answer to the number you took away. You should get the number you started with.