Sixth Grade Math Help: Rational Numbers

Rational Number Help

A number is rational if it can be written as a fraction. Of course, this means that all fractions are rational numbers. All of the numbers marked on the number line can be written as fractions, so they are rational as well. Even decimals are considered rational if they have an equivalent fraction, and most decimals do.

Properties of Rational Numbers

In sixth grade, you won't spend much time worrying about whether or not numbers are rational, since most of the numbers you're dealing with are. However, you'll spend lots of time studying the properties of rational numbers. 'Properties' is just a fancy way of saying, 'things that are true of all rational numbers.'

Location on the Number Line

As we mentioned earlier, rational numbers include the positive and negative numbers that are usually labeled on number lines. What you might not realize is that all rational numbers can be located on the number line, even fractions and decimals. For example, 0.5 can be found exactly halfway between zero and one on the number line, and 3.5 is halfway between the three and the four. To locate fractions on the number line, you must convert them to decimals first.

Comparing and Ordering

Since all rational numbers have a home on the number line, this means that we can compare any two rational numbers. When we compare numbers, we either determine that one is greater than the other, or they are equal. We indicate this using the > or < symbol with the open end facing the greater number. One rational number is greater than another if it is farther to the right on the number line. For instance, 8 > 2, 1 > - 1 and -2 > -4. When we compare more than one rational number at a time, this is called ordering. For example, 8 > 2 > 1 > -1 > -2 > -4.

Absolute Value

While rational numbers are compared and ordered based on their relative distance to the right, all rational numbers also have an absolute value that's determined by their physical distance from zero. Even though 1 > -1, both of these numbers have the same absolute value. Absolute value is always stated as a positive number, so the absolute value of 12 is 12, and the absolute value of -12 is also 12.

Directionality

Another property of rational numbers is that they can represent directions. For example, imagine that a miner travels 300 feet underground, and then he climbs 200 feet back toward the surface. To find out how far below ground he ends up relative to the surface, you can add the distance he traveled downward (-300 feet) to the distance he traveled upward (+200 feet). Since -300 + 200 = -100, he ended up 100 feet below the surface.