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Answer:
Reducing Ratios to Simplest Form
A ratio is the relationship, or comparison, of one amount to another.
To simplify a ratio means to reduce it to its smallest, simplest, terms.
In order to reduce a ratio, or fraction, to its simplest form, it is necessary to find the greatest, or highest, common factor for both terms in the ratio or fraction.
The greatest common factor of two numbers is the largest number that will divide into both terms evenly.
Let's look at an example:
Write this ratio in simplest form
2024
.
First, find the factors of the terms 20 and 24.
The factors of 20 are 1, 2, 4, 5, 10, and 20.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Next, find the highest common factor.
The factors that both 20 and 24 have in common are 1, 2 and 4.
The greatest of those common factors is 4.
Then, divide both terms by 4 to write the ratio in its simplest form.
2024=20÷424÷4=56
The answer is
56
Simplifying ratios can be helpful in determining equivalence.
Equivalent ratios are those that are equal.
Examples
Example 1
Earlier, you were given a problem about Noah and the family cross-country road trip.
Noah was dismayed as he thought about having to ride yet another 300 miles, but that was all that was left of the 2,700 mile trip. Express this distance as a fraction in its simplest terms.
First, write a fraction.
300 miles to go : 2,700 miles total
3002700
Next, recognize the two zeros at the end of each term make 100 a large factor that can be immediately removed.
327
Then, find the greatest common factor to further simplify and reduce both terms by division.
3÷327÷3=19
The answer is
19
Noah's family has only
19
of the total distance yet to go.
Example 2
Simplify this ratio: 14:16
First, write the ratio as a fraction.
1416
Next, determine the common factors.
The factors of 14 are 1, 2, 7, and 14.
The factors of 16 are 1, 2, 4, 8, and 16.
Then, determine the greatest common factor.
Common factors are 1 and 2.
2 is the greatest common factor.