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Mixed numbers and improper fractions, converted and calculated step by step.
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The Coddy math course teaches the method itself - you work each step on an interactive board and get told exactly where a move went wrong.
A mixed number like 2 3/4 is a whole part and a fraction written side by side, and the invisible sign between them is a plus. That makes it easy to read and awkward to calculate with: you cannot multiply 2 3/4 by 1 1/3 by multiplying the whole parts and the fractions separately, and if you try you get 2 1/4 instead of 3 2/3.
So almost every mixed-number question starts with the same move: turn each one into an improper fraction, multiply the whole part by the denominator and add the top. 2 3/4 becomes 11/4. From there it is an ordinary fraction question, and at the end you convert back. That first and last step are what this page is really for - they are where the marks are lost.
It is exact throughout, and it gets negatives right. -2 3/4 is one negative quantity, not minus two plus three quarters, so it is -11/4 and not -5/4. That distinction is quietly wrong in a surprising number of calculators, and it changes the answer to every question containing a negative mixed number.
Each number has three boxes: the whole part, then the numerator and denominator. Leave the whole box empty for a plain fraction, or the fraction boxes empty for a whole number.
Plus, minus, times or divide. The conversion to improper fractions happens first in every case, and you can see it in the first step.
The improper fraction and the mixed number are both given, because different questions ask for different ones. The decimal and percentage are there too.
The first and last steps are the conversions. If your own answer differs from this one, that is nearly always where it went wrong.
The two conversions, and what each operation needs once you have done them.
| Task | How | Example |
|---|---|---|
| Mixed to improper | whole × denominator + top | 2 3/4 = (8+3)/4 = 11/4 |
| Improper to mixed | divide, keep the remainder on top | 11/4 = 2 3/4 |
| Negative mixed to improper | the sign covers both parts | -2 3/4 = -11/4 |
| Add | convert, common denominator, add | 2 1/2 + 1 3/4 = 5/2 + 7/4 = 17/4 = 4 1/4 |
| Subtract | convert, common denominator, subtract | 4 1/3 - 1 5/6 = 13/3 - 11/6 = 5/2 = 2 1/2 |
| Multiply | convert, multiply across | 2 1/4 × 1 1/3 = 9/4 × 4/3 = 3 |
| Divide | convert, multiply by the reciprocal | 3 1/3 ÷ 1 1/6 = 10/3 × 6/7 = 20/7 = 2 6/7 |
Convert first: 5/2 and 7/4. The common denominator is 4, so 10/4 + 7/4 = 17/4, which is 4 1/4. You could also add the whole parts to get 3 and the fractions to get 5/4, then carry the extra whole - same answer, and worth knowing, but it is a rule that only works for addition.
As improper fractions this is 9/4 × 4/3 = 36/12 = 3, exactly. Multiplying the whole parts and the fractions separately would have given 2 1/12, which is not close - this is the example that convinces people the conversion is not optional.
Convert to 10/3 ÷ 7/6, flip the second and multiply: 10/3 × 6/7 = 60/21 = 20/7 = 2 6/7. Two conversions, one reciprocal, and one reduction - and the page shows all four lines.
-2 3/4 is -(2 + 3/4) = -11/4, so the sum is -11/4 + 2/4 = -9/4 = -2 1/4. Reading the sign as applying only to the 2 would give -5/4, which is a different number - this is the one place a mixed number can be misread rather than miscalculated.
