Adding Mixed Numerals
Every question with a fully worked solution.
- Adding Mixed Numerals - Video - How To Add Mixed Fractions With Unlike Denominators Watch
Theory
To add mixed numerals, add the whole numbers first, then add the fractions, then put the two answers together. This Year 7 maths page shows how to rename fractions with the lowest common denominator, how to carry an extra whole when the fractions add to more than \(1\), and how to check with an estimate.
A mixed numeral is a whole number plus a fraction: \(3\dfrac{1}{2} = 3 + \dfrac{1}{2}\). So the wholes and the fractions can be added separately.
Add the whole numbers first, then the fractions: \(3\dfrac{1}{2} + 4\dfrac{1}{4} = 3 + 4 + \dfrac{2}{4} + \dfrac{1}{4} = 7\dfrac{3}{4}\).
If the fractions have different denominators, rename them with the lowest common denominator (LCD) before adding.
If the fractions add to more than one whole, write the improper fraction as a mixed numeral and carry the whole across.
Wholes, then fractions:
How to add mixed numerals
- Add the whole numbers.
- Rename the fractions with the LCD (skip if the denominators match).
- Add the fractions. If the sum is more than \(1\), change it to a mixed numeral and carry the whole.
- Put the whole number and fraction together, simplify, and check with an estimate.
| \(2\dfrac{3}{7} + 1\dfrac{2}{7}\) | \(=\) | \((2 + 1) + \dfrac{3 + 2}{7}\) |
| \(\) | \(=\) | \(3\dfrac{5}{7}\) |
\(3\dfrac{5}{7}\)
| \(3\dfrac{1}{3} + 1\dfrac{1}{2}\) | \(=\) | \(4 + \dfrac{2}{6} + \dfrac{3}{6}\) |
| \(\) | \(=\) | \(4\dfrac{5}{6}\) |
\(4\dfrac{5}{6}\)
| \(\dfrac{7}{10} + \dfrac{9}{10}\) | \(=\) | \(\dfrac{16}{10} = 1\dfrac{3}{5}\) |
| \(6 + 1\dfrac{3}{5}\) | \(=\) | \(7\dfrac{3}{5}\) |
Estimate \(5 + 3 = 8\). The answer is \(7\dfrac{3}{5}\).
| \(\dfrac{1}{6} + \dfrac{3}{4}\) | \(=\) | \(\dfrac{2}{12} + \dfrac{9}{12} = \dfrac{11}{12}\) |
| \(7 + \dfrac{11}{12}\) | \(=\) | \(7\dfrac{11}{12}\) |
\(7\dfrac{11}{12}\)
| \(\dfrac{5}{6} + \dfrac{3}{4}\) | \(=\) | \(\dfrac{10}{12} + \dfrac{9}{12}\) |
| \(\) | \(=\) | \(\dfrac{19}{12} = 1\dfrac{7}{12}\) |
| \(7 + 1\dfrac{7}{12}\) | \(=\) | \(8\dfrac{7}{12}\) |
Estimate \(5 + 4 = 9\). The answer is \(8\dfrac{7}{12}\).
| \(\dfrac{3}{4} + \dfrac{5}{6} + \dfrac{1}{3}\) | \(=\) | \(\dfrac{9}{12} + \dfrac{10}{12} + \dfrac{4}{12}\) |
| \(\) | \(=\) | \(\dfrac{23}{12} = 1\dfrac{11}{12}\) |
| \(6 + 1\dfrac{11}{12}\) | \(=\) | \(7\dfrac{11}{12}\) |
The perimeter is \(7\dfrac{11}{12}\) m.
Common pitfalls
Frequently asked questions
How do you add mixed numerals?
Add the whole numbers, add the fractions (with a common denominator), then combine.
What if the fractions add to more than 1?
Change the improper fraction to a mixed numeral and add the extra whole: \(5 + \dfrac{5}{4} = 6\dfrac{1}{4}\).
Do you need a common denominator?
Yes, for the fraction parts. \(\dfrac{1}{3} + \dfrac{1}{2} = \dfrac{2}{6} + \dfrac{3}{6}\).
How do you check the answer?
Estimate by rounding each mixed numeral to the nearest whole number.
How do you change a fraction of an hour to minutes?
Find that fraction of \(60\). \(\dfrac{5}{6}\) of \(60\) is \(50\) minutes.