Related Articles. Article Summary. Determine whether or not the fractions have the same denominator. This is the first step to comparing fractions. The denominator is the number on the bottom of the fraction and the numerator is the number on top. Find a common denominator.
To be able to compare the fractions, you'll need to find a common denominator [3] X Research source so you can figure out which fraction is greater. If you were adding and subtracting fractions with unlike denominators , then it would be best to find the least common denominator for the fractions.
But since you're just comparing the fractions, you can just take a shortcut and multiply the denominators of both fractions to find the common denominator. Change the numerators of the fractions. To do this, you'll need to multiply the numerator of each fraction by the same number that you multiplied the denominator by to get Compare the numerators of the fractions.
The one with the larger numerator is the greater fraction. You don't compare denominators. You convert the dissimilar fractions to equivalent fractions that have identical denominators. Then you compare numerators. In the example given below, when we cross multiply, we get 4 and 6.
Can you explain it to him? The fraction with a greater numerator will be a greater fraction. He is a bit confused. Can you help him? In this method, we find lcm of the denominators of the given fractions, making the denominator the same.
By doing so, we get 18 for both. Comparing fractions means comparing the given fractions in order to tell if one fraction is less than, greater than, or equal to another. When the denominators are the same, the fraction with the lesser numerator is the lesser fraction and the fraction with the greater numerator is the greater fraction.
When the numerators are equal, the fractions are considered equivalent. When the fractions have the same numerator, the fraction with the smaller denominator is greater. The fractions that have different numerators and denominators but are equal in their values are called equivalent fractions. The easiest and the fastest way to compare fractions is to convert them into decimal numbers.
Then arrange the decimal numbers in ascending or descending order. The fraction with a greater decimal value would be a greater fraction. Comparing fractions is an important component, which helps students develop their number sense about fraction size.
Learn Practice Download. This concept can be generalized to any fractions with common numerators—but I had to be convinced of this, as I had never learned it in grade school.
If two fractions have denominators that are easily related such as 4 and 8 , then it is easy to scale one of them up quickly in order to compare them.
This is particularly useful when working with ruler measurement and line plots using halves, fourths, and eighths. If two fractions have numerators that are easily related such as 3 and 6 , then scaling the fraction with the lesser numerator to be equivalent to the greater numerator allows a comparison based on their denominators.
I like to let students use whiteboards for constructions like these, as they can more accurately refine their subdivisions if needed. Circles, squares, and rectangles are popular choices for subdividing in order to compare fractions. While I have had many a debate with teachers about whether to use this method to compare fractions, it must be included on the list.
If the product of the first numerator and the second denominator is greater than the product of the second numerator and the first denominator, then the first fraction is greater than the second.
As you can see, students have many options when comparing fractions. There are even more ways converting to decimals, for instance that will become important in later grades. Contact Us Find a Sales Rep 1. Mathematics Sadlier Math Grades K—6. Core Program Preview Buy.
Full Access Preview Buy. Step 1: Compare denominators. If they are different, rewrite one or both fractions with a common denominator. Step 2: Check the numerators. If the denominators are the same, then the fraction with the greater numerator is the greater fraction. The fraction with the lesser numerator is the lesser fraction.
And, as noted above, if the numerators are equal, the fractions are equivalent. Is , or is? You cannot compare the fractions directly because they have different denominators. You need to find a common denominator for the two fractions. Since 5 is a factor of 20, you can use 20 as the common denominator. Multiply the numerator and denominator by 4 to create an equivalent fraction with a denominator of Compare the two fractions. If , then , since. Which of the following is a true statement?
They are equivalent. Finding a common denominator, you can compare to , and see that , which means. Simplifying , you get the equivalent fraction. You find that , so as well. You can compare two fractions with like denominators by comparing their numerators. The fraction with the greater numerator is the greater fraction, as it contains more parts of the whole. If two fractions have the same denominator, then equal numerators indicate equivalent fractions.
Example Problem Are and equivalent fractions? Answer and are not equivalent fractions.
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