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All courses Math Foundations · MF.SN.1 23 of 60
Compare, order, and locate signed integers and rational numbers on a number line.

Compare two signed numbers

Problem
Compare -4 and -9. Write a true comparison statement using >, <, or =.
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Hint

Notice that both numbers are negative. Think about which one is closer to 0 on a number line.

For negative numbers, the value farther to the right on the number line is greater.

Solution walkthrough

01

Identify the signs

\[-4~\text{and}~-9~\text{are}~\text{both}~\text{negative}~\text{integers}.\]

Since both numbers are negative, the one closer to 0 is the greater number.

02

Place them on a number line

\[-9~<~-4~<~0\]

On a number line, numbers farther right are greater. Negative 4 is to the right of negative 9.

03

Choose the correct symbol

\[-4~>~-9\]

Because -4 is farther right than -9, the correct comparison symbol is >.

04

Write the true comparison statement

\[-4~>~-9\]

This matches the question because it compares the original numbers in the given order and gives a true statement.

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Another way

  1. Think about distance from 0: -4 is 4 units from 0 and -9 is 9 units from 0. Among negative numbers, the one with the smaller distance from 0 is greater, so -4 > -9.

!

Common mistake

A common mistake is saying -9 > -4 because 9 is bigger than 4. That compares absolute values only and ignores that more negative numbers are actually smaller.