How can fractions be compared

The largest improper fraction will now have the largest numerator. Two improper fractions can only be compared if they have the same denominator on the bottom. Improper fractions are simply fractions that have a larger numerator on top than their denominator on the bottom. The common denominator of these fractions is Here is another example of comparing the size of two improper fractions.

Both fractions have the same denominator and can now be ordered. Comparing Unlike Fractions using Decimals Converting unlike fractions to decimals is a method that can be used to compare the size of them.

Fractions can be turned into decimals by dividing the numerator by the denominator. The larger the decimal number, the larger the fraction. The larger decimal number is 0. Now try our lesson on Adding Fractions with Unlike Denominators where we learn how to add two fractions.

Adding Fractions with Unlike Denominators. When comparing two fractions with like denominators, the larger fraction is the one with the greater numerator. Let's look at some more examples of comparing fractions with like denominators. Example 3: Josephine ate three-fourths of a pie and Penelope ate two-thirds of a pie. If both pies are the same size, then which girl ate more pie? These fractions have unlike denominators and unlike numerators.

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. Their drawings can be in the form of area models or models on a number line. Students will then need other strategies as they move from a concert understanding to an abstract understanding of fractions.

Below are 4 strategies students can use to explain their thinking as they compare fractions. A free download is located at the bottom of this blog post. Each fraction is referring to two pieces, but the pieces are different size s. Two-thirds is referring to larger pieces.

Two-sixths is referring to smaller pieces. Two-thirds is greater, because it's referring to two larger pieces. The numerators and denominators are the same. Answer Yes, and are equivalent fractions. Note: In the example above you could have used the common factor of 20 to simplify directly to. To determine whether or not two fractions are equivalent:.

Step 1: Rewrite one or both of the fractions so that they have common denominators. Step 2: Compare the numerators to see if they have the same value. If so, then the fractions are equivalent. Which of the following fraction pairs are equivalent? Although the same numbers, 5 and 7, are used in each fraction, the numerators and denominators are not equal, so the fractions cannot be equivalent.

The correct answer is. This means the fractions are not equivalent. Take the fraction and multiply both the numerator and denominator by 4. You are left with the fraction. This means that the two fractions are equivalent. The numerators of the two fractions are the same, but the denominators are different.

When given two or more fractions, it is often useful to know which fraction is greater than or less than the other. For example, if the discount in one store is off the original price and the discount in another store is off the original price, which store is offering a better deal?

To answer this question, and others like it, you can compare fractions. To determine which fraction is greater, you need to find a common denominator. You can then compare the fractions directly. Since 3 and 4 are both factors of 12, you will divide the whole into 12 parts, create equivalent fractions for and , and then compare.

Now you see that contains 4 parts of 12, and contains 3 parts of So, is greater than.