How to Place Negative Fractions on a Number Line

Negative Fractions with a Common Denominator

• 1

  Put the fractions in ascending order (that is, from least to greatest), according to their respective numerators (their top numbers). Take, for example, these three fractions: -7/8, -1/8 and -5/8. Their ascending order looks like this:

  -7/8, -5/8, -1/8

  This is because -7 is less than -5, which itself is less than -1.

• 2

  Prepare a number line according to the common denominator. Since the denominator in this example is 8, split the space between -1 and 0 into 8 sections, like this:

  -1 -----|-----|-----|-----|-----|-----|-----|----- 0

• 3

  Place the fractions on the number line. Remember that the larger the whole number value of the numerator, the further away it will be from zero and the closer it will be to -1. The number line should look something like this:

  -1 ----- -7/8 -----|----- -5/8 -----|-----|-----|----- -1/8 ----- 0

Negative Fractions with Different Denominators

• 4

  Find the least common multiple (LCM) of the fractions. Use the following fractions as an example:

  -1/2, -2/3, -5/6

  The least common multiple of their denominators would be 12, as it is the smallest number that can be divided by 2, 3 and 6 evenly.

• 5

  Convert the fractions so that the LCM becomes their common denominator. To do this, divide the LCM (which is 12 in this example) by each fraction's denominator, then multiply the result by the numerator. Make the LCM the new denominator. For example, for -1/2:

  12 / 2 = 6

  6 x -1 = -6

  With 12 as the new denominator, -1/2 becomes -6/12. Repeating these steps for the other two fractions yields the following new conversions:

  -2/3 becomes -8/12

  -5/6 becomes -10/12

• 6

  Put the fractions in ascending order according to their respective numerators. In this example, the ascending order of the newly converted fractions looks like this:

  -10/12, -8/12, -6/12

  This is because -10 is less than -8, which itself is less than -6.

• 7

  Prepare a number line according to the common denominator. Because the denominator in this example is 12, split the space between -1 and 0 into 12 sections, like this:

  -1 ---|---|---|---|---|---|---|---|---|---|---|--- 0

• 8

  Place the numbers on the number line. Keep in mind that the larger the whole number value of the numerator, the further away it will be from zero and the closer it will be to -1. The number line should look something like this:

  -1 ---|--- -10/12 ---|--- -8/12 ---|--- -6/12 ---|---|---|---|---|--- 0