It would be easier to compare them if they had like denominators. We need to convert these fractions to equivalent fractions with a common denominator in order to compare them more easily. Since nine-twelfths is greater than eight-twelfths, three-fourths is greater than two-thirds.
Therefore, Josephine ate more pie. The example above works out nicely! But how did we know to use 12 as our common denominator? It turns out that the least common denominator is the best choice for comparing fractions.
Definition: The least common denominator LCD of two or more non-zero denominators is the smallest whole number that is divisible by each of the denominators. Remember that " Revisiting example 3, we found that the least common multiple of 3 and 4 is Therefore, the least common denominator of two-thirds and three-fourths is We then converted each fraction into an equivalent fraction with a denominator of 12, so that we could compare them.
In this lesson, we have compared fractions with like denominators and with unlike denominators. Let's see what happens when we compare fractions with like numerators. Look at the shaded rectangles below. The fractions above all have the same numerator. Each of these fractions is called a unit fraction. As the denominator gets larger, the fraction gets smaller. To compare fractions with like numerators, look at the denominators. The fraction with the smaller denominator is the larger fraction.
Let's look at some examples. Since five-thirds has the smaller denominator, it is the larger fraction. Remember, when comparing fractions with like numerators, the fraction with the smaller denominator is the larger fraction.
Let's look at some more examples of comparing fractions with like numerators. Note that the improper fractions in example 11 are equivalent. This is because for each fraction, the numerator is equal to its denominator.
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. Example Problem Determine whether and are equivalent fractions. Multiply the numerator and denominator of by 10 to get 60 in the denominator. Divide the numerator and denominator by the common factor B Incorrect.
C Correct. 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. Comparing Fractions Comparing fractions means determining the larger and the smaller fraction among two parts. How to Compare Fractions? Comparing Fractions with Same Denominators 3. Comparing Fractions with Unlike Denominators 4. Decimal Method of Comparing Fractions 5.
We've re-arranged the fractions from the least to the greatest. When ordering fractions with the same denominators , look at the numerators and compare them 2 at a time. The fractions have the same denominators, so you just need to compare their numerators. This is how we order these fractions from the least to the greatest :.
When ordering fractions with different numerators and denominators , write the fractions as equivalent fractions with like denominators. Tip: Like means "the same". Unlike means "different". Be careful when picking the equivalent fractions to compare!
Make sure that they all have the same denominators. Now that we've found equivalent fractions with matching denominators , it's easy to compare them! Start a 7 day free trial. I know it's because of Class Ace! Membership includes:. Password-Free Login! Scannable auto login passes make it easy for your students to login anywhere even young learners on shared devices.
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