I'm not a math educator but I'm curious about this.

Is this always true, or are there some schools/educational programs where students are shown negative numbers before fractions? Why is it done in this order? Is it because rationals are more "real" or useful than negatives?

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    $\begingroup$ A young child can understand the meaning of half a candy bar. The same child wouldn't be able to understand the meaning of negative three candy bars. I don't, not really (I understand the concept of being owed three candy bars, but that is really just an economic usage of the positive number 3). $\endgroup$ Sep 29, 2017 at 19:09
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    $\begingroup$ A young child can understand the meaning of moving 5 squares forward on a game board, or 5 squares backward. The same child might have a hard time understanding the meaning of moving half a square, because there is no such thing as half a square in the board. $\endgroup$
    – user507
    Sep 29, 2017 at 22:05
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    $\begingroup$ What we need here is actual publications on this, not merely opinions of individual users. $\endgroup$ Sep 30, 2017 at 0:25
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    $\begingroup$ Also: Historically fractions were accepted (long) before negatives were. $\endgroup$ Sep 30, 2017 at 1:09
  • $\begingroup$ Here's a link to the UK national curriculum, which requires fractions much earlier than negative numbers: gov.uk/government/publications/… $\endgroup$
    – Jessica B
    Sep 30, 2017 at 6:54

1 Answer 1


In the US, we have the controversial Common Core. A summary of it is available here.

In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers

This is the first place where negative numbers are introduced, clearly after fractions. A comment on the question suggested that "What we need here is actual publications on this, not merely opinions." I agree, to a point. The documents suggest an order, but don't go in to any satisfying detail about why the order should be that way.

This citation confirms that, at least in the US, this is the order. In my opinion, fractions are very natural. A child old enough to talk will quickly see the unfair nature of splitting something any way but 1/2 and 1/2. Money literally (again, in the US) has a coin called a quarter. And when I am talking fractions to teens, they can relate to our circular pizza which the laws of both God and man dictate be cut into 8 equal sections through the center.

The negative numbers are a bit tougher to grasp, again as a commenter suggested, I typically offer an example of money owed. You have \$2, and spend \$3, one of which is borrowed. Your 'balance sheet' says you have -$1.


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