# What are mixed fractions?

A mixed number contains a whole part and a fractional part.

is a mixed number. It contains both a whole part , 3, and a fractional part, 2/5. We read the fraction as “three and two fifths” and this is exactly what we mean.

• =
• Adding a whole number to a fraction is a special case of addition of two fractions. Click on the question mark to see the addition step-by-step:
• =
• We usually skip the intermediate steps. Click on the question mark below to see the improved method:

In writing these mixed numbers as a single fraction, we are writing improper fractions. An improper fraction is any fraction which has a numerator that is greater than the denominator. For example , is an improper fraction. Mixed numbers can always be written as improper fractions.

Think about pies. If we had two pies and 3/8 of a pie, we can figure out how many 1/8-sized pieces we have.

1. 2 3/8 = (2*8 + 3)/8 = 19/8
2. More Examples

## Exercise

Practice changing positive mixed numbers to improper fractions:

Take a few minutes to practise the reverse process – making an improper fraction into a mixed number. Think of a multiple of the denominator that is just smaller than the numerator. This multiple gives you the whole part of the mixed number. The difference between the multiple and the numerator gives you the numerator for the fractional part.

### Example

• Again pies come to mind.
• 17 =
• 17/6 = (12 + 5)/6 = (2*6 + 5)/6 = 2 5/6

## Exercise

For these exercises, convert the improper fraction to a mixed number.

### Signed Mixed Numbers

Consider the mixed fraction . Here the sign applies to all of .

1. That is,
2. Beware: which is in fact
3. In short, you can convert the numeric part of a negative mixed number to an improper fraction in the same way as a positive one, except the improper fraction gets a negative sign.
4. Study a few more examples of changing negative mixed numbers into improper fractions:

## Exercise

Try some of these exercises of changing negative mixed numbers into improper fractions:

Now the reverse process – making a negative improper fraction into a mixed number. Treat a negative improper fraction in the same way as a positive improper fraction giving the result a negative sign.

Ignoring the sign for a moment, think of a multiple of the denominator that is just smaller than the numerator. This multiple gives you the integer part of the mixed number.

The difference between the multiple and the numerator gives the numerator of the fractional part. Remember to include the negative sign on the mixed number.

## Exercise

For these exercises, convert the improper fraction to a mixed number.

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## Converting Fractions to Mixed Numbers

You may recall the example below from a previous lesson.

Example 1

In example 1, we used circles to help us solve the problem. Now look at the next example.

Example 2: At a birthday party, there are 19 cupcakes to be shared equally among 11 guests. What part of the cupcakes will each guest get?

Analysis: We need to divide 19 cupcakes by 11 equal parts. It would be time-consuming to use circles or other shapes to help us solve this problem. Therefore, we need an arithmetic method.

Step 1: Look at the fraction nineteen-elevenths below. Recall that the fraction bar means to divide the numerator by the denominator. This is shown in step 2.

• Step 2:
• Step 3:
• Solution:
• Example 3:
• Step 1:
• Step 2:
• Analysis: We need to divide 37 into 10 equal parts.
• Step 1:
• Step 2:
• Example 5:
• Analysis: We need to divide 37 into 13 equal parts.
• Step 1:
• Step 2:

In each of the examples above, we converted a fraction to a mixed number through long division of its numerator and denominator. Look at example 6 below. What is wrong with this problem?

Example 6:

Analysis: In the fraction seven-eighths, the numerator is less than the denominator. Therefore, seven-eighths is a proper fraction less than 1. We know from a previous lesson that a mixed number is greater than 1.

Answer: Seven-eighths cannot be written as a mixed number because it is a proper fraction.

Example 7: Can these fractions be written as mixed numbers? Explain why or why not.

Analysis: In each fraction above, the numerator is equal to the denominator. Therefore, each of these fractions is an improper fraction equal to 1. But a mixed number is greater than 1.

Answer: These fractions cannot be written as mixed numbers since each is an improper fraction equal to 1.

After reading examples 6 and 7, you may be wondering: Which types of fractions can be written as mixed numbers? To answer this question, let's review an important chart from a previous lesson.

1. Comparison of numerator and denominator: If the numerator denominator, then the fraction > 1.
2. Example:
3. Type of Fraction: improper fraction
4. Write As: mixed number
5. The answer to the question is: Only an improper fraction greater than 1 can be written to a mixed number.
6. Summary: We can convert an improper fraction greater than one to a mixed number through long division of its numerator and denominator.

### Exercises

In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. Note: To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.

 1 Write eleven-fifths as a mixed number.
 2 Write eleven-fourths as a mixed number.
 3 Write thirteen-ninths as a mixed number.
 4 On field day, there are 23 pies to share equally among 7 classes. What part of the pies will each class get?
 5 A teacher gives her class a spelling test worth 35 points. If there are 8 words graded equally, then how many points is each word worth?

## Mixed Number – Definition with Examples

A mixed number is a whole number, and a proper fraction represented together.  It generally represents a number between any two whole numbers.

Look at the given image, it represents a fraction that is greater than 1 but less than 2. It is thus, a mixed number.

Some other examples of mixed numbers are

Parts of a mixed number

A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

Properties of mixed numbers

• It is partly a whole number.
• It is partly a fraction.
• Converting improper fractions to mixed fractions.
• Step 1: Divide the numerator by the denominator.
• Step 2: Write down the quotient as the whole number.
• Step 3: Write down the remainder as the numerator and the divisor as the denominator.
• For example, we follow the given steps to convert 7/3 into a mixed number form.
• Step 1: Divide 7 by 3

Step 2: Write quotient, divisor and remainder in form as in step 2 and step 3 above.

2. One can add mixed numbers by rearranging the whole numbers, adding them separately and adding the leftover fractions individually and in the end combing them all.
3. 1 1⁄2 + 3 3⁄4
4. Adding the whole numbers separately and the fractions separately.
5. For whole numbers:
6. 1+3 = 4
7. For fractions:  Find the LCM and then add

• In the end, adding both the parts together.
• 4+1 1⁄4 =5 1⁄4
• Real life examples

We can check our understanding of mixed fractions by expressing the parts of a whole as mixed fractions while serving a pizza or a pie at home. Leftover pizzas, half-filled glasses of milk form examples of mixed fractions.

 Fun Facts Mixed numbers are also called mixed fractions.

## Mixed Fractions

(Also called “Mixed Numbers“)

 134 (one and three-quarters)
• A Mixed Fraction is a whole number and a proper fraction combined.
• Such as 134

See how each example is made up of a whole number and a proper fraction together? That is why it is called a “mixed” fraction (or mixed number).

### Names

We can give names to every part of a mixed fraction:

### Three Types of Fractions

There are three types of fraction:

### Mixed Fractions or Improper Fractions

We can use either an improper fraction or a mixed fraction to show the same amount.

For example 134 = 74, as shown here:

 134 74 =

### Converting Improper Fractions to Mixed Fractions

To convert an improper fraction to a mixed fraction, follow these steps:

 Divide the numerator by the denominator. Write down the whole number answer Then write down any remainder above the denominator.
1. Divide:
2. 11 ÷ 4 = 2 with a remainder of 3
3. Write down the 2 and then write down the remainder (3) above the denominator (4).
5. 2 34

## Definition and examples mixed fraction | define mixed fraction

A Mixed Fraction is a number with a combination of an integer and a proper fraction.

Mixed fraction is also called as mixed number. An improper fraction can be converted into a mixed fraction and vice versa.

### Examples of Mixed Fraction

23, 46, 19, 5, 12, 29, 8, 42  is a mixed number, in which 5 is an integer and  is a fraction.  is a mixed number, in which – 3 is an integer and  is a fraction.  is an improper fraction as the numerator is greater than the denominator. It can be converted into a mixed fraction as:

So, the mixed number  is equivalent to improper fraction .

### Video Examples: How To Do Mixed Fractions Multiplication

A. 3 +  B.  C.  D.  Correct Answer: C

### Solution:

Step 1: A mixed fraction is a combination of an integer and a proper fraction. Step 2: So,  is a mixed fraction.

## What are improper fractions and mixed numbers?

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## Mixed Numbers Calculator

Do math calculations with mixed numbers (mixed fractions) performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions.

### Mixed Numbers Calculator (also referred to as Mixed Fractions):

This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists.

Enter mixed numbers, whole numbers or fractions in the following formats:

• Mixed numbers: Enter as 1 1/2 which is one and one half or 25 3/32 which is twenty five and three thirty seconds. Keep exactly one space between the whole number and fraction and use a forward slash to input fractions. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789).
• Whole numbers: Up to 3 digits in length.
• Fractions: Enter as 3/4 which is three fourths or 3/100 which is three one hundredths. You can enter up to 3 digits in length for each the numerators and denominators (e.g., 456/789).

1. Convert the mixed numbers to improper fractions
2. Use the algebraic formula for addition of fractions: a/b + c/d = (ad + bc) / bd
3. Reduce fractions and simplify if possible

( dfrac{a}{b} + dfrac{c}{d} = dfrac{(a imes d) + (b imes c)}{b imes d} )

### Example

Add 1 2/6 and 2 1/4

( 1 dfrac{2}{6} + 2 dfrac{1}{4} = dfrac{8}{6} + dfrac{9}{4} ) ( = dfrac{(8 imes 4) + (9 imes 6)}{6 imes 4} ) ( = dfrac{32 + 54}{24} = dfrac{86}{24} = dfrac{43}{12} )

1 2/6 + 2 1/4 = 8/6 + 9/4 = (8*4 + 9*6) / 6*4 = 86 / 24

So we get 86/24 and simplify to 3 7/12

### Subtracting Mixed Numbers using the Subtracting Fractions Formula

1. Convert the mixed numbers to improper fractions
2. Use the algebraic formula for subtraction of fractions: a/b – c/d = (ad – bc) / bd
3. Reduce fractions and simplify if possible

### Subtracting Fractions Formula

( dfrac{a}{b} – dfrac{c}{d} = dfrac{(a imes d) – (b imes c)}{b imes d} )

### Example

• Subtract 2 1/4 from 1 2/6
• 1 2/6 – 2 1/4 = 8/6 – 9/4 = (8*4 – 9*6) / 6*4 = -22 / 24
• Reduce the fraction to get -11/12

### Multiplying Mixed Numbers using the Multiplying Fractions Formula

1. Convert the mixed numbers to improper fractions
2. Use the algebraic formula for multiplying of fractions: a/b * c/d = ac / bd
3. Reduce fractions and simplify if possible

### Multiplying Fractions Formula

( dfrac{a}{b} imes dfrac{c}{d} = dfrac{a imes c}{b imes d} )

### Example

1. multiply 1 2/6 by 2 1/4
2. 1 2/6 * 2 1/4 = 8/6 * 9/4 = 8*9 / 6*4 = 72 / 24
3. Reduce the fraction to get 3/1 and simplify to 3

### Dividing Mixed Numbers using the Dividing Fractions Formula

1. Convert the mixed numbers to improper fractions
2. Use the algebraic formula for division of fractions: a/b ÷ c/d = ad / bc
3. Reduce fractions and simplify if possible

### Dividing Fractions Formula

( dfrac{a}{b} div dfrac{c}{d} = dfrac{a imes d}{b imes c} )

### Example

• divide 1 2/6 by 2 1/4
• 1 2/6 ÷ 2 1/4 = 8/6 ÷ 9/4 = 8*4 / 9*6 = 32 / 54
• Reduce the fraction to get 16/27

### Related Calculators

To perform math operations on simple proper or improper fractions use our Fractions Calculator. This calculator simplifies improper fraction answers into mixed numbers.

1. If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.
2. For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.
3. If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.
4. Note:

This calculator performs the reducing calculation faster than others you might find. The primary reason is that the code utilizes Euclid's Theorem for reducing fractions which can be found at The Math Forum: LCD, LCM.