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Ordering Fractions and Mixed Numbers

Ordering Fractions and Mixed Numbers

We can use the inequality symbols to order fractions. Remember that \(a>b\) means that \(a\) is to the right of \(b\) on the number line. As we move from left to right on a number line, the values increase.

Example

Order each of the following pairs of numbers, using \(<\) or \(>:\)

  1. \(-\frac{2}{3}\_\_\_-1\)
  2. \(-3\frac{1}{2}\_\_\_-3\)
  3. \(-\frac{3}{7}\_\_\_-\frac{3}{8}\)
  4. \(-2\_\_\_\frac{-16}{9}\)

Solution

\(-\frac{2}{3}>-1\)

A number line is shown. The integers from negative 3 to 3 are labeled. Negative 1 is marked with a red dot. Between negative 1 and 0, negative 2 thirds is labeled and marked with a red dot.

\(-3\frac{1}{2}<-3\)

A number line is shown. The integers from negative 4 to 4 are labeled. There is a red dot at negative 3. Between negative 4 and negative 3, negative 3 and one half is labeled and marked with a red dot.

\(-\frac{3}{7}\phantom{\rule{0.2em}{0ex}}\text{<}\phantom{\rule{0.2em}{0ex}}-\frac{3}{8}\)

A number line is shown. The numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3 are labeled. Between negative 1 and 0, negative 3 sevenths and negative 3 eighths are labeled and marked with red dots.

\(-2<\frac{-16}{9}\)

A number line is shown. The numbers negative 3, negative 2, negative 1, 0, 1, 2, and 3 are labeled. There is a red dot at negative 2. Between negative 2 and negative 1, negative 16 over 9 is labeled and marked with a red dot.

 


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