Determining which fraction is largest

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. So, each fraction is equivalent to 1. We have looked at many examples in this lesson. Let's try to summarize what we have learned. How To Compare: Look at the numerators. The larger fraction is the one with the greater numerator. How To Compare: Convert each fraction to an equivalent fraction with a common denominator.

How To Compare: Look at the denominators. Summary: In this lesson, we learned how to compare fractions with like denominators, with unlike denominators, and with like numerators. To compare fractions with unlike denominators, use the LCD to write equivalent fractions with a common denominator; then compare the numerators.

By signing up, you agree to receive useful information and to our privacy policy. Shop Math Games. Skip to main content. Search form Search. Drake: Josh: Analysis:? These fractions have like denominators, so we can compare the numerators. Josephine: Penelope: Solution: Since nine-twelfths is greater than eight-twelfths, three-fourths is greater than two-thirds. Josephine: Penelope: Procedure: To compare fractions with unlike denominators, follow these steps: 1.

Use the LCD to write equivalent fractions with a common denominator. Compare the numerators: The larger fraction is the one with the greater numerator. Let's look at some more examples of comparing fractions with unlike denominators. Now you see that contains 4 parts of 12, and contains 3 parts of So, is greater than.

As long as the denominators are the same, the fraction with the greater numerator is the greater fraction, as it contains more parts of the whole. The fraction with the lesser numerator is the lesser fraction as it contains fewer parts of the whole. These symbols are inequality symbols. One way to help you remember the distinction between the two symbols is to think that the smaller end of the symbol points to the lesser number.

Comparing Fractions. To compare two fractions:. 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. Instead of rewriting them in terms of a common denominator, the fastest way to compare fractions is to convert them into decimal numbers.

How do you rewrite a fraction as a decimal number? As we learned way back when we talked about the connection between fractions and division , all you have to do is divide the numerator of the fraction by its denominator this is often easiest and quickest to do with the help of a calculator. Just as we found earlier using the common denominator method, the fact that the decimal 0.

Whether you prefer to rewrite them in terms of a common denominator and compare their numerators or simply convert them into easily comparable decimal numbers, writing fractions in ascending or descending order is a relatively straightforward task. Finally, please send your math questions my way via Facebook , Twitter , or email at mathdude quickanddirtytips. Thanks for reading, math fans! He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.