How to Simplify a Ratio
Look at the ratio., Factor out the first number., Factor out the second number., Find the greatest common factor., Divide both sides by the greatest common factor., Write down the final answer.
Step-by-Step Guide
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Step 1: Look at the ratio.
A ratio is an expression used to compare two quantities.
A simplified ratio should be taken as is, but if a ratio has not been simplified already, you should do so now to make the quantities easier to compare and understand.
In order to simplify a ratio, you will need to divide both sides by the same number.Example: 15:21 Note that neither number in this example is a prime number.
Since that is the case, you'll need to factor out both numbers to determine whether or not the two terms have any like factors that can be used in the simplification process. -
Step 2: Factor out the first number.
A factor is a whole number that you can divide the term by evenly, giving you another whole number.
Both terms in the ratio must share at least one factor (other than the number 1), but before you can determine if the two terms share a factor, you must discover what the factors of each term are.
Example:
The number 15 has four factors: 1, 3, 5, 15 15 / 1 = 15 15 / 3 = 5 , In a separate space, list all the factors of the ratio's second term.
For the time being, do not worry about the factors of the first term and only focus on factoring this second term.
Example:
The number 21 has four factors: 1, 3, 7, 21 21 / 1 = 21 21 / 3 = 7 , Look at the factors for both terms in your ratio.
Circle, list, or otherwise identify all numbers that appear in both lists.
If the only shared factor is 1, then the ratio is already in its simplified form and no further work needs to be done.
If the two terms of the ratio have other shared factors, however, sort through them and identify the highest number.
This number is your greatest common factor (GCF).
Example:
Both 15 and 21 share two common factors: 1 and 3 The GCF for the two numbers of your original ratio is
3. , Since both terms of your original ratio share the GCF, you should be able to divide both sides separately and come up with whole numbers as a result.
Both sides must be divided by the GCF; do not only divide one side.
Example:
Both 15 and 21 must be divided by
3. 15 / 3 = 5 21 / 3 = 7 , You should be left with a new terms on both sides of the ratio.
Your new ratio is equivalent to the original ratio, meaning that the quantities of both forms are in the same proportion.Also note that the quantities on both sides of your new ratio should not share any common factors between them.
Example: 5:7 -
Step 3: Factor out the second number.
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Step 4: Find the greatest common factor.
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Step 5: Divide both sides by the greatest common factor.
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Step 6: Write down the final answer.
Detailed Guide
A ratio is an expression used to compare two quantities.
A simplified ratio should be taken as is, but if a ratio has not been simplified already, you should do so now to make the quantities easier to compare and understand.
In order to simplify a ratio, you will need to divide both sides by the same number.Example: 15:21 Note that neither number in this example is a prime number.
Since that is the case, you'll need to factor out both numbers to determine whether or not the two terms have any like factors that can be used in the simplification process.
A factor is a whole number that you can divide the term by evenly, giving you another whole number.
Both terms in the ratio must share at least one factor (other than the number 1), but before you can determine if the two terms share a factor, you must discover what the factors of each term are.
Example:
The number 15 has four factors: 1, 3, 5, 15 15 / 1 = 15 15 / 3 = 5 , In a separate space, list all the factors of the ratio's second term.
For the time being, do not worry about the factors of the first term and only focus on factoring this second term.
Example:
The number 21 has four factors: 1, 3, 7, 21 21 / 1 = 21 21 / 3 = 7 , Look at the factors for both terms in your ratio.
Circle, list, or otherwise identify all numbers that appear in both lists.
If the only shared factor is 1, then the ratio is already in its simplified form and no further work needs to be done.
If the two terms of the ratio have other shared factors, however, sort through them and identify the highest number.
This number is your greatest common factor (GCF).
Example:
Both 15 and 21 share two common factors: 1 and 3 The GCF for the two numbers of your original ratio is
3. , Since both terms of your original ratio share the GCF, you should be able to divide both sides separately and come up with whole numbers as a result.
Both sides must be divided by the GCF; do not only divide one side.
Example:
Both 15 and 21 must be divided by
3. 15 / 3 = 5 21 / 3 = 7 , You should be left with a new terms on both sides of the ratio.
Your new ratio is equivalent to the original ratio, meaning that the quantities of both forms are in the same proportion.Also note that the quantities on both sides of your new ratio should not share any common factors between them.
Example: 5:7
About the Author
Jose Young
With a background in education and learning, Jose Young brings 9 years of hands-on experience to every article. Jose believes in making complex topics accessible to everyone.
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