Converting Between Improper Fractions and Mixed Numbers

Unless you’re using a calculator, converting between improper fractions and mixed numbers is an essential skill. On the math GED®, one of these problems is likely to occur in your no calculator portion in the exam.

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Why Converting Between Improper Fractions and Mixed Numbers Matters

Without a calculator, performing math on a mixed number is complicated. By converting it into an improper fraction, you will better be able to handle the problem. Additionally, using improper fractions can be helpful when you are looking for a common denominator.

Converting between improper fractions and mixed numbers is also essential since some problems may present you with diverse mediums. While it is possible to convert decimals into fractions, convincing the fractions to play nicely is another story.

A Fraction and Mixed Number Review

Fraction Structure Diagram

The top value in a fraction is called the numerator, while the bottom value is called a denominator. When the denominator is bigger than the numerator, the fraction is proper. However, when the numerator is bigger than the denominator, the fraction is improper.

mixed number structure

You can convert any improper fraction into a mixed number. A mixed number consists of a fraction and a value of wholes placed to the left. Your math GED® exam considers mixed numbers as the proper answer form in multiple-choice questions.

The Steps of Converting Between Improper Fractions and Mixed Numbers

Converting between mixed numbers and improper fractions

Once you get the steps down, converting should not take you long. Let’s start by going from a mixed number to an improper fraction.

The first step involved taking the value in the whole number spot and multiplying it against the denominator of the fraction. This action tells you how many pieces that the whole number represented. Then you add the answer you got to the numerator of the original fraction. Using the same denominator, rewrite the fraction, and you’re done.

Converting back to a mixed number from an improper fraction is trickier. If possible, reduce the fraction. Then, take the numerator and divide that by the denominator. The number in the answer slot goes in the whole value place, then the number at the bottom of the subtraction goes in the numerator spot. The denominator of the fraction does not change.

Examples of Converting Between Improper Fractions and Mixed Numbers

Let’s work through some examples of the steps for converting between improper fractions and mixed numbers, beginning with mixed to improper.

For our first problem, we need to convert 1¾. The first step is to take the 1 from the wholes spot and multiply it by 4, which is the denominator. That gives us 4. Then we add that 4 to the 3 in the numerator spot. This addition makes our final improper fraction 7/4.

Mixed numbers to Improper fractions example 1

Now let’s try a little bigger, 74/5. We’ll use the same steps, starting with multiplying the whole 7 against the denominator 5. This operation gives us 35. Then we add the 35 to the numerator 4, which provides us with 39. Our final conversion is 39/5.

mixed numbers to improper fractions example 2

Let’s go the other direction now by converting 10/3 to a mixed number. We will begin by dividing 10 by 3 using longhand division. This operation gives us 3 in the answer spot and 1 at the bottom of the problem. Our final answer would be 31/3.

Improper fractions to mixed numbers example 1

Alright, for our last example, let’s convert 100/10. Out first step is to divide 100 by 10. That gives us 10 in the answer spot of the division problem, and 0 down the bottom. Since 0 is at the bottom of the problem, there is no need for a fraction in the final answer. This problem comes out as 10 even.

Improper fractions to mixed numbers example 2

One Last Trick

Any whole number can become a fraction quickly, provided it’s not already a mixed number. All you need to do is place a 1 in the denominator position, and the whole number becomes the numerator. This trick allows you to work with whole numbers and fractions together.