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Mixed Numbers

A mixed number is expressed as the sum of a whole number and a fraction (ex. 5 1 3 ). Mixed numbers give a good idea of the size of a number. But when it comes to making calculations, improper fractions are usually easier to work with. If you encounter a mixed number, you'll want to know how to convert it into an improper fraction, and vice versa. Let's go over these steps.

Writing a mixed number as an improper fraction

Improper fractions are alternate expressions of mixed numbers. For example, the mixed number 2 4 5 can also be written as 14 5 . But what steps should you take to turn a mixed number into an improper fraction? Let's find out.

Write the mixed number 3 1 4 as an improper fraction.

First, we'll write the mixed number as a sum of a whole number and a proper fraction:

3 + 1 4

Then, we'll write the two parts with a common denominator.

12 4 + 1 4

Now, add the fractions.

12 4 + 1 4 = 13 4

13 4 is the improper fraction equivalent of 3 1 4 .

Writing a mixed number as an improper fraction using the shortcut method

Now that you've learned how to write a mixed number as an improper fraction, let's go over the shortcut method, which can give you the same answer much faster.

Write 3 1 4 as an improper fraction.

First, multiply the whole part by the denominator of the fractional part.

3 × 4 = 12

Next, add the numerator of the fractional part. This is the numerator of the improper fraction.

12 + 1 = 13

Another way to find the numerator is to write the following: 3 4 + 1 = 13 .

Keep the same denominator, 4, and you have the improper fraction 13 4 .

Writing an improper fraction as a mixed number

Now, let's try writing the improper fraction 27 5 as a mixed number.

First, divide the numerator by the denominator.

27 ÷ 5 = 5 R 2

We have a quotient of 5, and a remainder of 2.

We'll use the quotient as the whole part of the mixed number and the remainder as the numerator of the fractional part. Keep the denominator the same.

27 5 = 25 5 + 2 5 = 5 2 5

Practice questions on mixed numbers

a. Write 5 5 6 as an improper fraction.

5 + 5 6 = 30 6 + 5 6

Answer: 35 6

b. Write 7 1 8 as an improper fraction.

7 + 1 8 = 56 8 + 1 8

Answer: 57 8

c. Write 2 6 7 as an improper fraction using the shortcut method.

Numerator: 2 ( 7 ) + 6 = 20 . Denominator: 7.

Answer: 20 7

d. Write 14 3 as a mixed number.

To write 14 3 as a mixed number, we perform the division:

14 ÷ 3 = 4 R 2

The quotient is 4 and the remainder is 2. The denominator remains as 3.

So, 14 3 can be expressed as the sum of the whole number quotient and the fraction with the same denominator:

14 3 = 12 3 + 2 3

Therefore, the answer is 4 2 3 .

e. Write 47 7 as a mixed number.

47 ÷ 7 = 6 R 5

Quotient: 6. Remainder: 5. Denominator: 7.

47 7 = 42 7 + 5 7

Answer: 6 5 7

Topics related to the Mixed Numbers

Least Common Denominators (LCDs)

Place Value

Associative Property

Flashcards covering the Mixed Numbers

5th Grade Math Flashcards

Common Core: 5th Grade Math Flashcards

Practice tests covering the Mixed Numbers

MAP 5th Grade Math Practice Tests

Common Core: 5th Grade Math Diagnostic Tests

Get a better understanding of mixed numbers

If your student is learning about mixed numbers for the first time, they might feel challenged by the process of writing them as improper fractions -- or writing improper fractions as mixed numbers. Tutoring can help whether your student is working on homework, preparing for an exam, or simply wants to strengthen their knowledge of mixed numbers. A qualified personal educator has the expertise to boost your student's confidence as a math learner. Learn more about the perks of private instruction by contacting the Educational Directors at Varsity Tutors today.

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