1. Using Rational Numbers How to add, subtract, multiply and divide rational numbers

2.  A rational number is a number that can be written as a simple fraction (i.e. as a ratio).rational number

3. Examples: NumberAs a Fraction 55/1 1.757/4.0011/1000 0.111...1/9

4. In general...  So, a rational number looks like this:  p / q  But q cannot be zero, as that would be dividing by zero.dividing by zero

5. How to Add, Subtract, Multiply and Divide  If the rational number is something simple like 3, or 0.001, then just use mental arithmetic, or your calculator!  But if it is still in the form p / q, then read on to find how to handle it.

6. ½ A rational number is a fraction, so you could also refer to:fraction Adding Fractions,Adding Fractions Subtracting Fractions,Subtracting Fractions Multiplying Fractions andMultiplying Fractions Dividing Fractions But here I will be showing you those operations in a more Algebra-like way.Algebra You might also like to read Fractions in Algebra.Fractions in Algebra

7. I will start with multiplication, as that is the easiest.

8. Multiplication  To multiply two rational numbers, just multiply the tops and bottoms separately, like this:

10. Division  To divide two rational numbers, first flip the second number over (make it a reciprocal) and then do a multiply like above:

12. Addition and Subtraction  I will cover Addition and Subtraction in one go, as they are the same method.  Before you can add or subtract, the rational numbers should have the same bottom number (called a Common Denominator).Common Denominator

13. The easiest way to do this is to  Multiply both parts of each number by the bottom part of the other

14. Like this (note that I use the dot · to mean multiply):

17. Simplest Form

18. Be Careful With "Mixed Fractions"  You may be tempted to write an Improper Fraction (a fraction that is "top-heavy", i.e. where the top number is bigger then the bottom number) as a Mixed Fraction:Improper FractionMixed Fraction

20.  But for mathematics the "Improper" form (such as 7 / 4 ) is actually better.  Because Mixed fractions (such as 1 3 / 4 ) can be confusing when you write them down in a formula, as it can look like a multiplication:

21. Mixed Fraction: What is:1 + 2 1 / 4 ? Is it:1 + 2 + 1 / 4 = 3 1 / 4 ? Or is it:1 + 2 × 1 / 4 = 1 1 / 2 ? Improper Fraction: What is:1 + 9 / 4 ? It is: 4 / 4 + 9 / 4 = 13 / 4