Matemáticas
What Is a Mixed Number?
A mixed number is a whole number and a fraction written together, and it means add: 2 3/4 is 2 + 3/4, or 11/4. It never means 2 multiplied by 3/4.
Mixed number
A mixed number is a whole number written next to a proper fraction, meaning the two added together — 2 3/4 means 2 + 3/4.
- También llamado
- mixed fraction
- Dónde lo encuentra el alumnado
- Grade 4 to 6, introduced alongside improper fractions, and then used constantly in measurement — 1 1/2 hours, 3 1/4 metres — long after the topic has been left behind.
La respuesta corta
A mixed number is a whole number and a proper fraction written side by side, such as 2 3/4, and it means the two added together: 2 + 3/4. Written as an improper fraction it is 11/4. It does not mean 2 multiplied by 3/4, which is the commonest misreading of the notation.
Un ejemplo
2 3/4 = 2 + 3/4 = 8/4 + 3/4 = 11/4
The second step is the one usually skipped, and it is where the meaning lives. Each whole is four quarters, so two wholes are eight quarters; add the three already there and eleven quarters is the total. Written as the rule multiply the whole by the denominator and add the numerator, it is the same arithmetic with the reason removed.
2 3/4 as a count of quarters
The denominator has already decided that we are counting in quarters, so the only question is how many quarters there are altogether. Two wholes contribute four each, which is eight, and three are already written down, giving eleven quarters: 11/4.
Running it backwards is the same count. Eleven quarters, taken four at a time, makes two wholes with three quarters remaining, which is 2 3/4. A student who counts rather than recites will never apply the rule to the wrong pair of numbers, which is the usual way marks are lost here. The same count handles any of them: 5 2/3 holds five wholes worth three thirds each, which is fifteen thirds, plus the two already written, giving 17/3.
Where mixed numbers cost marks
Three places, all avoidable. In algebra, never write a mixed number: 2 1/2 x cannot be read reliably, so use 5/2 x or 2.5x instead. In multiplication and division, convert to an improper fraction first, because the whole number and the fraction cannot be handled separately without care.
On a calculator, typing 2 + 3 ÷ 4 gives 2.75 and typing 23 ÷ 4 gives 5.75, so the mixed-number key or a pair of brackets is not optional. And a negative mixed number carries its sign across both parts: −2 3/4 means −(2 + 3/4), which is −11/4, not −2 + 3/4.
Preguntas frecuentes
Is 2 3/4 the same as 11/4?
Yes, exactly. They are two ways of writing one number, and neither is more accurate. 2 3/4 counts the wholes first and the leftover quarters afterwards; 11/4 counts every quarter in one go. Which you use depends on what the next step is.
Why is a mixed number not a multiplication?
Because the notation predates the algebraic convention and was never reconciled with it. In a mixed number the plus sign has simply been left out. It is the only common place in school mathematics where two symbols written together are added, and knowing that it is an exception is most of the battle.
Can a mixed number be negative?
Yes, and the sign applies to the whole thing. −2 3/4 means −(2 + 3/4), which is −11/4 or −2.75. Reading it as −2 + 3/4 gives −1.25, a different number entirely. Converting to an improper fraction before doing anything else removes the risk.
Which form should I give as my answer?
Whichever the question asks for. If it does not say, both are correct, because they name the same number. In context, mixed numbers read more naturally for time and measurement, while improper fractions are what you want if any further calculation is coming.
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