3

Comparing Numbers

Positives and Negatives

As with integers, there are positive and negative rational numbers. You can use a number line to understand how rational numbers are related to each other.

Which number is greater, –1.5 or –3?

Step 1: One way to compare numbers is to look at the numbers on a number line.

Find the numbers you are comparing on the number line.

Step 2: On a number line, numbers are greater as you move right. This means the numbers are in least to greatest order from left to right. Which number is greater (or farther to the right)?

–1.5 is greater than –3.

Use the symbols <, >, or = to compare 3/4 and 1/2.

Step 1: Fractions are one type of rational number. To compare fractions with different denominators, first rewrite them so they have the same denominator.

To change a denominator of 2 to a denominator of 4, multiply the numerator and denominator by 2.

Step 2: Compare the like fractions 3/4 and 2/4 by comparing the numerators.

TEST TIME: Explain Your Answer

The temperature Tuesday was –4°F. The temperature Wednesday was 2°F. Reagan said it was colder Wednesday because 2 is less than 4. Is she correct? Explain.

This problem asks if Reagan is correct. It also asks for an explanation. Be sure to include all of the required answers.

Solution: Reagan is not correct. She is correct in knowing that a lower temperature is colder than a higher temperature. However, she did not understand that the temperature on Tuesday was a negative number, and negative numbers always have a lower value than positive numbers. It would have helped Reagan if she had looked at a thermometer to compare the temperatures. –4°F is lower on the thermometer and therefore colder than 2°F.

–4 is less than 2, so Tuesday was colder than Wednesday.

Definitions

equal sign (=): The two numbers or expressions on opposites sides of this sign have the same value.

less than sign (<): The number or expression on the left has a value that is less than the number or expression on the right.

greater than sign (>): The number or expression on the left has a value that is greater than the number or expression on the right.

TEST TIME: Multiple Choice

Which set puts the numbers 3, –6, –4, and 0 in order from least to greatest?

You can use what you know about positive and negative numbers. Negative numbers are always less than positive numbers. Zero is the dividing point between positive and negative numbers. Answers a and d both have positive numbers listed before negative, so they are not the correct answers. A negative number has a lesser value when the number part is “bigger.” –6 has a “bigger” number part than –4, so it has a lesser value and should be listed first.

Solution: Answer c is the correct answer.

Test-Taking Hint

Some multiple choice questions can be solved by eliminating choices that are obviously incorrect.