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❶Multiplication of rational numbers Multiplication has very much the same properties of addition.

## Simplifying Rational Expressions

Examples of integers include 25, three and Decimals are not integers. Integers are rational numbers because any integer can be written as a fraction by putting it over one. Since rational numbers are numbers that can be written as fractions, it's no surprise that fractions are rational numbers.

Mixed fractions are rational because they can be converted into improper fractions. Decimals that have a definite ending point are rational numbers, because they have an equivalent fraction. The only decimals that are not rational are decimals that continue infinitely and follow no particular pattern. Because some decimals continue forever in a random manner, mathematicians have not been able to pinpoint an equivalent fraction for them. Examples of decimals that fit this description are pi 3.

They are considered irrational numbers. Some decimals that continue forever, like 0. The difference between these decimals and the irrational decimals, like pi , is that they go on forever in a predictable pattern. Because of this, it is possible to write them as fractions.

If you divide one by three, you'll see that the division problem never ends! Although it's not necessary to actually convert a decimal to a fraction in order to determine if it's rational, it's helpful to know how to do this. For simple decimals that just go to the tenths place, you can determine what their equivalent fraction is by putting the number in the tenths place over ten, and then simplifying it if necessary.

This means that 0. You can extend this process to any decimal that has a definite ending point. For example, you could write 0.

Some square roots that are perfect squares , like the square root of 25, are rational numbers because they are equal to an integer that can be written as a fraction. Mathematicians have proven that some square roots, like the square root of two and the square root of three, are not rational numbers.

They're irrational because they're equal to decimals that continue forever and don't follow a pattern. Numbers that are not rational are irrational. Most of the numbers you'll encounter in daily life are rational, but here's a quick reference of commonly used irrational numbers:. Here are two math games to give students a competitive incentive for getting a handle on their numbers.

Division can be confusing, especially when working with larger numbers. Read on to learn how to help your fifth grader remember how to divide many different lengths of numbers.

What's a Rational Number? Integers Integers include all of the whole numbers, which are the numbers from zero to infinity. Fractions Since rational numbers are numbers that can be written as fractions, it's no surprise that fractions are rational numbers.

Decimals Decimals that have a definite ending point are rational numbers, because they have an equivalent fraction. Repeating Decimals Some decimals that continue forever, like 0. Converting Decimals to Fractions Although it's not necessary to actually convert a decimal to a fraction in order to determine if it's rational, it's helpful to know how to do this. Rational Numbers Sort by: A helpful scientific calculator that runs in your web browser window.

Excellent site showing examples of algebra, trig, calculus, differential equations, and linear algebra. Paul's Online Math Notes. Some worked example problems that point out many common errors students make when solving them. Pauls Online Math Notes. This page describes the sets of numbers, natural, whole, integers, rational, irrational and real numbers. Gives examples and organizes the information well. The Real Number System.

Resources Math Algebra Rational Numbers.

## Main Topics

Integers are rational numbers because any integer can be written as a fraction by putting it over one. For example, 5/1 = 5 and -9/1 = This even works with zero, since 0/1 = 0.

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Rational numbers are numbers that can be expressed as a fraction, a/b, when b is not equal to zero. Both a and b are integers, and rational numbers can be either positive or .