Organizing IdeaNumber — Number sense is developed through understanding the ways numbers describe the world.
Guiding QuestionHow can the symmetry of the number line contribute to a sense of number?
Learning OutcomeStudents analyze positive and negative numbers.
This lesson covers: the three equivalent ways to write a negative fraction: −(a/b), (−a)/b, and a/(−b); why all three expressions represent the same value; placing negative fractions on the number line.
Build a negative fraction
Use the arrows to choose a numerator and denominator. All three forms below are always equal — try changing the numbers to see.
−
3
4
minus in front
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negative numerator
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negative denominator
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drag or click the number line to change the fraction
Why three forms?
A negative fraction means you are dividing a negative quantity, or dividing into a negative number of parts.
Either way you end up at the same point on the number line.
Think about −(3/4): you take the fraction 3/4 and make it negative.
In (−3)/4: the numerator is already negative, so dividing by a positive 4 gives a negative result.
In 3/(−4): dividing a positive 3 into −4 equal parts also gives a negative.
All three land on exactly the same spot: −0.75.
The rule: a single negative sign can sit in front of the fraction, in the numerator, or in the denominator — the value is the same.
Two negatives (one in the numerator and one in the denominator) cancel out and make a positive fraction.
Challenge: Find the Equivalent Forms
The fraction below is shown in one form. Select all options that represent exactly the same value — there are always two correct answers.