Ordering fractions. When ordering fractions, you must first look at the denominator. If the denominators of the fraction are the same, then you order them according to the numerators, with the values increasing left to right.
Let’s look at an example. You can see all the denominators are the same, so we’re going to order these fractions by looking at our numerators.
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If you’re ordering them from left to right or from least to greatest, then the smallest number would be our biggest negative number, negative seven-ninths. Our next number would be our next negative number, negative four ninths. Next biggest, would be our first positive number, two-ninths and finally four ninths.
Now let’s look at some fractions that don’t have the same denominator. For these fractions, we could first find the least common denominator, so that we could have all the same denominator and then order them by the numerator. The least common denominator LCD for four, 12, two and six, would be 12. First, we’re going to convert all these fractions to have the denominator of 12. Three-fourths, to convert three-fourths to something over 12, we need to multiply four times three, so we’ll do the same to our numerator. Three times three is nine and four times three is 12, so three-fourths is nine twelfths.
Negative seven-twelfths already has our least common denominator of 12 so we’re going to leave it alone. One-half, two would need to be multiplied by six to get 12, so we would do the same to our numerator, one time six is six, two times six is 12, negative five sixth. Six would need to be multiplied by two to get 12, so we’ll do the same to our numerator. Five times two is 10, six times two is 12 and of course, it’s still negative.
Now we can order our fractions based on their numerators from least to greatest, from left to right. Our smallest number is our biggest negative, which is negative 10 twelfths. Then our next negative, negative seven-twelfths, then six-twelfths and finally nine twelfths would be our largest number.
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