What is 3/5 as a mixed number

(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

	Divide the numerator by the denominator. Write down the whole number answer Then write down any remainder above the denominator.

Divide:

11 ÷ 4 = 2 with a remainder of 3

Write down the 2 and then write down the remainder (3) above the denominator (4).

Answer:

2 34

That example can be written like this:

Answer:

3 13

Converting Mixed Fractions to Improper Fractions

	Multiply the whole number part by the fraction's denominator. Add that to the numerator Then write the result on top of the denominator.

Multiply the whole number part by the denominator:

3 × 5 = 15

Add that to the numerator:

15 + 2 = 17

Then write that result above the denominator:

175

We can do the numerator in one go:

Are Improper Fractions Bad ?

NO, they aren't bad!

For mathematics they are actually better than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: should the two parts be added or multiplied?

Mixed Fraction:	What is:		1 + 214		?
	Is it:		1 + 2 + 14		= 314 ?
	Or is it:		1 + 2 × 14		= 112 ?
Improper Fraction:	What is:		1 + 94		?
	It is:		44 + 94 = 134

But, for everyday use, people understand mixed fractions better.

Example: It is easier to say "I ate 214 sausages", than "I ate 94 sausages"

We Recommend:

• For Mathematics: Improper Fractions
• For Everyday Use: Mixed Fractions

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Trying to find out how to convert 5/3 into a mixed number or fraction? Have I got the answer for you! In this guide, we'll walk you through the step-by-step process of converting an improper fraction, in this case 5/3, to a mixed number. Read on!

Want to quickly learn or show students how to convert 5/3 to a mixed number? Play this very quick and fun video now!

Before we begin, let's revisit some basic fraction terms so you understand exactly what we're dealing with here:

• Numerator. This is the number above the fraction line. For 5/3, the numerator is 5.
• Denominator. This is the number below the fraction line. For 5/3, the denominator is 3.
• Improper fraction. This is a fraction where the numerator is greater than the denominator.
• Mixed number. This is a way of expressing an improper fraction by simplifying it to whole units and a smaller overall fraction. It's an integer (whole number) and a proper fraction.

Now let's go through the steps needed to convert 5/3 to a mixed number.

Step 1: Find the whole number

We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

5/3= 1.6666666666667 = 1

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (1) and multiply it by the original denominator (3). The result of that multiplication is then subtracted from the original numerator:

5 - (3 x 1) = 2

Step 3: Our mixed fraction

We've now simplified 5/3 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

Step 4: Simplifying our fraction

In this case, our fraction (2/3) can be simplified down further. In order to do that, we need to calculate the GCF (greatest common factor) of those two numbers. You can use our handy GCF calculator to work this out yourself if you want to. We already did that, and the GCF of 2 and 3 is 1.

We can now divide both the new numerator and the denominator by 1 to simplify this fraction down to its lowest terms.

2/1 = 2

3/1 = 3

When we put that together, we can see that our complete answer is:

Hopefully this tutorial has helped you to understand how to convert any improper fraction you have into a mixed fraction, complete with a whole number and a proper fraction. You're free to use our calculator below to work out more, but do try and learn how to do it yourself. It's more fun than it seems, I promise!

Improper Fraction to Mixed Fraction Calculator

This calculator performs basic and advanced operations with mixed numbers, fractions, integers, decimals. Mixed numbers are also called mixed fractions. A mixed number is a whole number and a proper fraction combined, i.e. one and three-quarters. The calculator evaluates the expression or solves the equation with step-by-step calculation progress information. Solve problems with two or more mixed numbers fractions in one expression.