Using Rational NumbersHow to add, subtract, multiply and divide rational numbers

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

Examples:

Number As a Fraction

5 5/1

1.75 7/4

.001 1/1000

0.111... 1/9

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

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.

½

A rational number is a fraction, so you could also refer to:

• Adding Fractions,• Subtracting Fractions,

• Multiplying Fractions and

• Dividing Fractions But here I will be showing you those operations in a

more Algebra-like way.You might also like to read Fractions in Algebra.

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

Multiplication To multiply two rational numbers, just multiply the tops and

bottoms separately, like this:

=

Division To divide two rational numbers, first flip the second number

over (make it a reciprocal) and then do a multiply like above:

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).

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

other

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

12+25=12𝑥55+25𝑥22=510

+410

=5+410

=910

And an example of subtraction (I skipped the middle step to make it quicker):

Simplest Form Sometimes you will have a rational number like:

== Now it is in the "simplest form".

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:

For example 7/4 = 1  3/4, shown here:

Improper Fraction Mixed Fraction 1

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:

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