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Improper Fractions

If you've worked with fractions that look like 9 7 or 17 3 , you've encountered improper fractions. Unlike a proper fraction, which has a numerator that is smaller than the denominator, an improper fraction has an equal or larger numerator than the denominator. Let's take a closer look at improper fractions and their relationship with mixed numbers.

Improper fractions and mixed numbers

Improper fractions are another way of writing mixed numbers:

As you can see, the improper fraction 7 6 is actually the mixed number 1 1 6 .

Since both mixed numbers and improper fractions are common in math problems, knowing how to convert one to the other is important.

Converting improper fractions into mixed numbers

Let's convert the improper fraction 19 9 into a mixed number. First, divide the denominator into the numerator. Then, write the fraction as a sum of the whole part plus the remaining fraction.

19 9 = 2 + 1 9 = 2 1 9

Converting mixed numbers into improper fractions

Now, let's convert the mixed number 7 2 3 into an improper fraction. First, write the mixed number as a sum of a whole number and a proper fraction. Then, write the two parts with a common denominator. Finally, add the fractions.

7 + 2 3 = 21 3 + 2 3 = 23 3

Practice questions on improper fractions

a. Turn 1 3 5 into an improper fraction.

1 + 3 5 = 5 5 + 3 5 = 8 5

b. Turn 26 7 into a mixed number.

26 7 = 3 + 5 7 = 3 5 7

c. Turn 2 5 6 into an improper fraction

2 + 5 6 = 12 6 + 5 6 = 17 6

d. Turn 33 4 into a mixed number.

33 4 = 8 + 1 4 = 8 1 4

Topics related to the Improper Fractions

Dividing Fractions

Operations with Fractions

Equivalent Fractions

Flashcards covering the Improper Fractions

4th Grade Math Flashcards

Common Core: 4th Grade Math Flashcards

Practice tests covering the Improper Fractions

Common Core: 4th Grade Math Diagnostic Tests

4th Grade Math Practice Tests

Get a better understanding of improper fractions

If your student wants help understanding improper fractions or needs assistance with converting them into mixed numbers, tutoring is a great option. A skilled private educator can help your student understand assignments and even refresh their knowledge while preparing for a test. Discover the perks of tutoring and how your student can benefit by reaching out to the Educational Directors at Varsity Tutors today.

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