Ordering Numbers Math Example 5

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Example 5

medium
Insert a rational number between 25\frac{2}{5} and 35\frac{3}{5}.

Solution

  1. 1
    Find the midpoint: 12(25+35)=12⋅1=12\frac{1}{2}\left(\frac{2}{5} + \frac{3}{5}\right) = \frac{1}{2} \cdot 1 = \frac{1}{2}.
  2. 2
    Check: 25=0.4<0.5=12<0.6=35\frac{2}{5} = 0.4 < 0.5 = \frac{1}{2} < 0.6 = \frac{3}{5}. ✓

Answer

12 lies between 25 and 35\frac{1}{2} \text{ lies between } \frac{2}{5} \text{ and } \frac{3}{5}
The midpoint of two rationals is always rational and always lies strictly between them. This is one of infinitely many numbers between these two fractions — the rationals are dense.

About Ordering Numbers

Ordering numbers is the process of arranging numbers in sequence from smallest to largest (ascending order) or largest to smallest (descending order). To order numbers, compare them using place value, common denominators, or convert to the same form (e.g. all decimals).

Learn more about Ordering Numbers →

More Ordering Numbers Examples

Example 1 easy

Arrange from least to greatest: [formula], [formula], [formula], [formula].

Example 2 medium

Order from greatest to least: [formula], [formula], [formula], [formula].

Example 3 medium

Order from least to greatest: [formula], [formula], [formula], [formula].

Example 4 easy

Write three integers in order such that each is exactly 5 less than the previous.

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