Learning

Why might you need to rationalize a denominator? In mathematics the term denominator refers to the bottom number in a fraction. You may be wondering in what circumstances may you need to look at rationalizing a denominator, the bottom number in the fraction which you’re working with.

The answer is that if you ever discover a radical expression in your denominator, you’ll need to get to work on rationalizing your denominator.

Do you need to rationalize your numerator if it contains a radical expression?

If you’re curious about whether you need to rationalize your fraction if you discover a radical expression in the top number of your fraction, which is your numerator, your answer is no. There is absolutely no reason to remove a radical expression from your fraction.

How to rationalize your denominator:

To rationalize the denominator you’ll need to multiply your fraction by either a single term or a set of terms which will be able to remove the radical expression in your denominator, which you’re intent on getting rid of. If you believe that you’d find step by step instructions on removing radial expressions from denominators, simply follow the instructions below.

1. Identify the radical expression

Your first step should be to identify the radical expression in your denominator, which you’ll then work on eliminating from your fraction. What is a common example of a radical expression that you may find in one of your denominators? An example of a radical expression, that you may find in one of your denominators is a square root.

2. Find a suitable number to multiply both your numerator and your denominator with

Once you’ve identified your radical expression, such as a square root, it’s time to try and identify a number which you can successfully multiply your top number and your bottom number of your fraction with.

3. Now multiply the numerator and denominator by the radical which you would like to remove from your fraction

If you happen to be rationalizing a fraction which features a monomial, ensure that you your numerator and your denominator are both multiplied by the same number. As what you’re doing is multiplying your factors by 1.

4. Simplify your fraction

Now that you’ve completed the 3 steps listed above, it’s the right time to simplify your fraction.

How to rationalize a binomial denominator:

If you’re trying to remove a radical expression from a binomial denominator instead of a monomial denominator, simply follow the instructions listed below, in order to discover your answer.

1. Assess the components of your fraction

Start off by assessing the components of your fraction as if your fraction contains a sum of two terms in your denominator which are irrational, you won’t be able to multiply your fraction properly.

2 Multiple the conjugate of your denominator by your fraction

3. Simply your fraction

Rationalize the denominator calculator:

Alternatively, if you’d like to rationalize your fraction is a fraction of the time, it’s well worth using a calculator to solve your equation for you.

Hopefully you now have a clear understanding of how to go about rationalizing denominators in fractions, in order to get rid of radicals such as square roots.

If you’re interested in being able to solve two step equations without any issues, simply learn how to use the simple, fuss free, two step equation which is outlined below.

How to confidently solve two step equations with integers:

Step one:

Shift all your data that doesn’t have the variable, which you’re looking to the opposite side of your equation.

Step two:

Remember that whatever you do to one side of your equation, you’ll need to do to the opposite to the other side of your equation. As an example if you use a + side on the left side of your equation, you’ll need to place a – side on the right side of your equation.

An example of a simple two step equation:

If you’re still not confident about your ability to use a two step equation in order to be able to solve a simple equation, it may help to work through an example exercise. Let’s start off with a fairly simple equation, that is fairly easy to solve but will allow you to confidently test out your knowledge of both of the two steps which you read about above.

The test equation which we will be working with is 4x+3=7. To find the value of x, make sure to follow the directions which were explained in the previous paragraph.

Step one:

As you know your first step should be to shift all of your data that doesn’t have the variable which you’re looking for, to the opposite side of your equation. In our example you need to subtract three from both sides of your equation. You should have written down 4x+3-3=7-3, which should then give you 4x=4.

Step two:

Now you’ll need to go about diving each side of your formula by 4. The process which you should write down now is 4x/4=4/4 and x=1. If the answer which you worked out is different, simply go back to step one and double check all of the processes which you used, to make sure that you didn’t make a simple error, which you’ll easily be able to correct.

An extra example to work through:

In order to cement the information which you have just learned, it’s a great idea to work through one more example. This time the two step equation which you’ll need to solve is 3x to the power of 3+4=28. To find the value of x, simply work through the simple two step instructions, which you have been learning to follow.

Step one:

Again, begin by isolating the given variable in your equation. You should have written down 3x to the power of 4-4=28-4 and 3x to the power of 4=24.

Step two:

Lastly to find the value of x you’ll need to divide each side by 3. Your notes should now show 3x to the power of 3/3=24/3. X to the power of 3=8. Now write down the cube root for each side and you should get your answer, x=2.

Again, if you didn’t obtain the same answer, simply work through the two step by step instructions listed above again.

If you’re wondering what does corresponding mean in math, simply continue reading to discover a simple easy to understand answer.

What does corresponding mean in math?

Simply put the term corresponding in math refers to objects such as angles which appear in the same exact place, in two similar situations.

What are corresponding angles and how do you go about figuring out the value of corresponding angles?

The mathematical term corresponding angles is commonly used to refer to matching angles. What are corresponding angles? When two straight lines are crossed by a third line, which is known as a traversal line, the angles in each matching corner are referred to as corresponding angles. Corresponding angles are always the same size as each other.
As an example if one angle in a matching corner is 118 degrees, the angle is the corresponding matching corner of the second line will also be 118 degrees.
How to find corresponding angles?
If you label each angle from left to right and top to bottom, you can find corresponding angles by looking at the place of each angle. Angle a and angle e, will be corresponding angles. Angle b and angle f will be matching corresponding angles, angle c and angle g will also be corresponding angles and lastly angle d and angle h will also be even, corresponding angles.
What happens if two lines are crossed by parallel lines?
As a second example, if two straight lines, which do not touch are both crossed by two parallel lines, which each cross one of the two straight lines but don’t intersect each other, you’ll also be able to work out various corresponding angles.
In this example, again assuming that each angle is labelled from a to b, going left to right and top to bottom, angle a and angle e are corresponding angles, angle b and angle h are corresponding angles, angle c and angle f are corresponding angles and angle d and angle h are also corresponding angles.
While it may take a couple of minutes to understand the rules which govern corresponding angles, once you’re able to find out one corresponding angle, you should have no issues figuring out corresponding angles in the future.
Are there any other circumstances in maths in which the term corresponding is frequently used?
Yes, the term corresponding is often used to describe properties of congruent triangles. What is a congruent triangle? A congruent triangle is a common type of triangle where each side is exactly the same length as the other two angles. Congruent triangles also feature three internal angles a right angle and two congruent or equal angles.
As congruent triangles feature equal lines and angles, congruent triangles can also be said to feature corresponding lines and corresponding angles. If you’re ever trying to explain the term corresponding in maths to a friend, it’s a great idea to use this particular example, to illustrate the points which you want to make.
Hopefully you’re now confident about how the term corresponding is used in mathematics and how you can effortlessly figure out corresponding angles.

If you’re interested in learning about some of the features of regular polygons, simply continue reading to discover valuable information on a wide variety of polygons. Examples of which include a 10 sided polygon and a 100 sided polygon.

What is a 10 sided polygon called?

A 10 sided polygon is most commonly referred to as a decagon, although they are sometimes also referred to as a 10-gon.

What are the key features of a decagon?

A decagon is a regular polygon as it has 10 equal sides. All of a decagon’s internal angles each add up to 144 degrees. As a decagon’s internal angles are less than 180 degrees, a decagon can accurately be described as being a convex polygon.

What is a 9 sided polygon called?

A 9 sided polygon is called a nonogan.

What are the key features of a nonagon?

A nonagon has nine equal sides and as such is also a regular polygon. Just like a decagon a nonagon is also classed as a convex polygon as each of the congruent interior angles of a decagon measures 140 degrees and as mentioned above to be classified as an obtuse polygon a polygon needs to feature interior angles which measure at least 180 degrees.

What is an 8 sided polygon called?

An 8 sided polygon is referred to as an octagon. If you’ve ever watched a UFC, mixed martial arts event you’ll know that each fight takes place within an octagonal shaped ring which features 8 equal sides.

What are some of the key features of an octagon?

An octagon features 8 sides as well as 8 interior angles. Each interior angle inside an octagon measures exactly 135 degrees. An octagon is also a convex polygon.

What is a 7 sided polygon called?

A 7 sided polygon is most commonly referred to as a heptagon. However, a 7 sided polygon is also sometimes referred to as a septagon as “sept” is a latin prefix which is linked to the number 7. Whereas the term heptagon has Greek roots as the prefix “hepta” is connected with the number 7. If you’re curious the “agon” is also Greek and roughly translates to angle. So in Greek the term heptagon translates to 7 angles.

What are some of the key features of a heptagon?

By now you may have guessed that a heptagon has 7 congruent sides and 7 interior angles. Like all of the polygons listed above a heptagon is also a convex polygon as its interior angels each measure 123.57 degrees.

What is a 100 sided polygon called?

While we’ve been discussing polygons which have 10 or less sides, there are polygons which have a far greater number of edges. For starters, a regular polygon which boasts 100 edges is referred to simply as a hectogon. Although you can also accurately call a 100 sided polygon a hectatontogon.

What is a 10000 sided polygon called?

While it can be difficult to picture what a 10000 sided polygon would look like a 10000 sided polygon is referred to as myriagon. Like all of the polygons listed above a 10000 sided polygon is also a convex polygon.

Hopefully, you’re now intrigued enough to learn about more different types of polygons.

If you’re unsure about the difference between rational and irrational numbers, keep reading to discover a simple guide to understanding the key differences between rational and irrational numbers.

What is the difference between rational and irrational numbers?

The primary difference between irrational numbers and rational numbers is that a rational number can be easily expressed as a whole fraction.

A rational number can always be turned into a fraction, which has both a full numerator number and a full denominator number. While an irrational number can’t be expressed as a whole fraction and can’t be written down as a simple ratio of two integers.

Are there any other noticeable differences between rational and irrational numbers.
Yes, while irrational numbers can’t be written down as simple, whole fractions, irrational numbers can easily be expressed as decimal numbers.
Furthermore an irrational number features endless non repeating digits after it’s decimal point. An example of an irrational number is pi which is most commonly shortened to 3.14159. Keep in mind that it is impossible to express a never ending decimal number such as pi with a simple fraction.
To cement the knowledge that you’ve just read, another example of a recurring infinite decimal number, which can be referred to accurately as a rational number is the golden ratio, which is sometimes shortened to 2.7182818.
Everything you need to know about the major differences between rational and irrational numbers:

1. There are infinite irrational numbers
You may be surprised to hear that there is at least one irrational number between any two rational numbers.

2. Every whole number is a rational number.

If you’re confused about whether the number zero is a rational number, the answer is yes because zero and any other whole number can be divided by the number one, which makes zero a rational number.

3. Decimal numbers tend to be irrational numbers, however there are exceptions

Decimal numbers such as pi also tend to be irrational numbers as they aren’t whole numbers and therefore can’t be divided using a whole numerator and a whole denominator.

However there are exceptions. As an example, recurring decimal numbers such as 0.26262626 are rational numbers.

If in doubt, remember that decimals which are infinite and don’t feature a number sequence are irrational numbers, while decimal numbers which feature recurring numbers such as 0.26262626 are always classed as rational numbers.

4. Negative whole numbers are also classified as being rational numbers

If you were confused by negative whole numbers and whether they are rational numbers or irrational numbers the answer is that negative numbers such as -6 can still be easily divided by themselves and therefore can be expressed by whole fractions and are rational numbers.

5. Square roots can also be irrational numbers

Another example of a common irrational number which has not been discussed above are square roots, which can also be irrational numbers.

After reading the definitions and tips which were listed above, you should now be confident about being able to class both rational numbers and irrational numbers.