How do i convert improper fractions to mixed numbers

Solution

Step 1: Convert a mixed number from an improper fractionWe must divide the dividend by the divisor in order to change an improper fraction to a mixed number. After division, the acquired quotient becomes the whole numerals, the remainder becomes the new numerator, and the denominator remains the same, resulting in a mixed number.The classification of fractions is,Proper Fraction – Numerator < Denominator Improper Fraction – Numerator > DenominatorMixed Fraction – Whole number + Proper fractionStep 2: Process to change an improper fraction to a mixed number.A fraction with the divisor always lower than the dividend is called an improper fraction or polynomial fraction. Like 92 is an improper fraction.A mixed fraction, also known as a mixed integers, is made up of a whole number and a correct fraction, like 417 is a mixed number, where 4 is the whole number and 17 is a proper fraction.To convert a mixed number from an improper fraction, divide the numerator by the divisor and compute the remnant and quotient. The quotient is now the positive integers of the finalized mixed fraction, the remnant is the dividend, and the divisor is unchanged.For example,Change the improper fraction into a mixed number: 114.As we can see the number 114, when we dividing 11 by 4, it gives 2 as quotient and 3 as remainder.So,It can be written as, 234.Thus, the mixed fraction of improper fraction 114 is 234.

Video transcript

Write 7/4 as a mixed number. So right now it's an improper fraction. 7 is larger than 4. Let's write it is a mixed number. So first I'm just going to show you a fairly straightforward way of doing it and then we're going to think a little bit about what it actually means. So to figure out what 7/4 represents as a mixed number, let me write it in different colors. So this is going to be equal to-- the easiest way I do it is you say, well, you divide 4 it 7. If we're dealing with fourths, 4 goes into 7 a total of one time. Let me do this in another color. 1 times 4 is 4. And then what is our remainder? 7 minus 4 is 3. So if we wanted to write this in plain-- well, let me just do the problem, and then we'll think about what it means in a second. So you see that 4 goes into 7 one time, so you have one whole here, and then how much do you have left over? Well, you have 3 left over, and that comes from right over there. That is the remainder when you divide 4 into 7. 3 left over, but it's 3 of your 4, or 3/4 left over. So that's the way we just converted it from an improper fraction to a mixed number. Now, it might seem a little bit like voodoo what I just did. I divided 4 into 7, it goes one time, and then the remainder is 3, so I got 1 and 3/4. But why does that make sense? Why does that actually makes sense? So let's draw fourths. Let's draw literally 7 fourths and maybe it'll become clear. So let's do a little square as a fourth. So let's say I have a square like that, and that is 1/4. Now, let's think about what seven of those mean, so let me copy and paste that. Copy and then paste it. So here I have 2 one-fourths, or you could see I have 2/4. Now I have 3 one-fourths. Now, I have 4 one-fourths. Now this is a whole, right? I have 4 one-fourths. This is a whole. So let me start on another whole. So now I have 5. Now I have 6 one-fourths, and now I have 7 one-fourths. Now, what does this look like? So all I did is I rewrote 7/4, or 7 one-fourths. I just kind of drew it for you. Now, what does this represent? Well, I have 4 fourths here, so this is 4/4. This right here is 3/4. Notice, 7/4 is 4/4 with 3/4 left over. So let me write it this way. 7/4 is 4/4 with 3/4 left over. Now what is 4/4? 4/4 is one whole. So you have one whole with 3/4 left over, so you end up with 1 and 3/4. So that is the 3/4 part and that is your one whole. Hopefully that makes sense and hopefully you understand why it connects. Because you say, well, how many wholes do you have? When you're dividing the 4 into the 7 and getting the one, you're essentially saying how many wholes? So the number of wholes, or you can imagine, the number of whole pies. And then how many pieces do we have left over? Well, we have 3 pieces and each piece is 1/4, so we have 3/4 left over. So we have one whole pie and three pieces, which are each a fourth left over.

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An improper fraction is a fraction with a larger "top" than "bottom," like 5/2. Mixed numbers are a whole number and a fraction together, like 21/2. It's usually easier to imagine 21/2 pizzas than "five halves" of a pizza, so it's useful to be able to switch between them.[1] Division is the fastest way to do this, but there is an easier method included if you're having trouble with the first one.

Things You Should Know

• Use division; rewrite the improper fraction as a long division problem, then find the remainder and write the mixed number from your results.
• Without division, write down the fraction and recall all the fractions that equal 1—which is any number divided by itself.
• Split the fraction into two parts; find the second part and then simplify the fraction, repeating until you have the right number.

1. 

   1

   Start with an improper fraction. We'll use 15/4 for our example. This is an improper fraction because the numerator, 15, is greater than the denominator, 4.

   • If you're not comfortable with fractions or division yet, start with the example below instead.

2. 

   2

   Rewrite it as a division problem. Write the fraction as a long division problem.[2] Always write the numerator divided by the denominator. In our example, this is 15 ÷ 4.

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3. 

   3

   Begin solving the division problem. Review long division first if you're not sure what to do.[3] This example will be easier to follow if you write out the long division problem as you read it:

   • Compare 4 to the first digit, 1. 4 doesn't go into 1, so we need to include the next digit.
   • Compare 4 to the first two digits, 15. How many times does 4 go into 15? If you're not sure, guess and see if you're right using multiplication.
   • The answer is 3, so write 3 on the answer line, above the 5.

4. 

   4

   Find the remainder. Unless the numbers divide perfectly, there will be a remainder left over. Here's how to find the remainder in a long division problem:[4]

   • Multiply the answer by the divisor (the number on the left). In our example, that's 3 x 4.
   • Write the result underneath the dividend (the number underneath the division bracket). In our example, 3 x 4 = 12, so write 12 underneath the 15.
   • Subtract the result from the dividend: 15 - 12 = 3. This is the remainder

5. 

   5

   Write the mixed number using your results. A mixed number is a whole number, plus a proper fraction. After solving your division problem, you have everything you need to write this mixed number:[5]

   • The whole number is your answer to the division problem. In this case, that's 3.
   • The numerator of the fraction is your remainder. In this case, that's also 3.
   • The denominator of the fraction is the same as the denominator in the original fraction. In this case, that's 4.
   • Write this as one mixed number: 33/4.

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1. 

   1

   Write down the fraction. An improper fraction is any fraction with a top number larger than the bottom number. For example, 3/2 is an improper fraction, because 3 is larger than 2.

   • The top number of a fraction is called the numerator. The bottom number is called the denominator.
   • This method will take a long time for large fractions. If the numerator is much larger than the bottom number, the division method above is much faster.

2. 

   2

   Remember which fractions equal one. Did you know that 2 ÷ 2 = 1? Or that 4 ÷ 4 = 1? In fact, any number divided by itself equals one. Fractions are exactly the same. 2/2 = 1, and 4/4 = 1, and even 397/397 equals 1!

3. 

   3

   Split the fraction into two parts. That sounded like an easy way to turn a fraction into a whole number. Let's see if we can do that for part of our improper fraction:

   • For 3/2, the denominator (lower number) is 2.
   • 2/2 is an easy fraction to simplify, because the top and bottom numbers are the same. We want to take this out of the larger fraction, and find out what we have left behind.
   • Write this down: 3/2 = 2/2 + ?/2.

4. 

   4

   Find the second part. How do we turn that question mark into a number? If you don't know how to add and subtract fractions, don't worry. When the denominators (bottom numbers) are the same, we can ignore them and turn the problem into ordinary addition. Here's a step by step guide for our example, 3/2 = 2/2 + ?/2:

   • Look at just the numerators (top numbers). They say 3 = 2 + "?". what number can we write instead of that question mark to solve the problem? What number can you add to 2 to get 3?
   • The answer is 1, because 3 = 2 + 1.
   • When you get the answer, write the equation again, including the denominators: 3/2 = 2/2 + 1/2.

5. 

   5

   Simplify the fraction.[6] Now we know our improper fraction is the same as 2/2 + 1/2. We also know that 2/2 = 1, just like any fraction with the same top and bottom number. That means you can cross out 2/2, and write 1 instead. Now we have 1 + 1/2, which is a mixed number! For this example, the problem is solved.

   • Once you've found the solution, you don't need to write the + symbol anymore. Just write 11/2.
   • A mixed number is a whole number plus a proper fraction.[7]

6. 

   6

   Repeat these instructions if the fraction is still improper. Sometimes, the fraction part of your answer will still be improper, with a numerator larger than the denominator. In this case, you can start again with that fraction, turning it into another mixed number. Don't forget to add the "1" back when you're done. Here's an example, turning 7/3 into a mixed fraction:

   • 7/3 = 3/3 + ?/3
   • 7 = 3 + ?
   • 7 = 3 + 4
   • 7/3 = 3/3 + 4/3
   • 7/3 = 1 + 4/3
   • That fraction is improper, so ignore the 1 for now and do the same thing: 4/3 = 3/3 + ?/3
   • 4 = 3 + ?
   • 4 = 3 + 1
   • 4/3 = 3/3 + 1/3
   • 4/3 = 1 + 1/3
   • That fraction is proper, so we're done. Remember to add the 1 we ignored earlier: 1 + 1 + 1/3 = 21/3.

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Add New Question

• Question

  How can I change 12/3 to a whole number?

  

  Divide 12 by 3 and you'll find that the answer is 4. When you see that type of slash, think the division sign instead.

• Question

  How do I convert 9/8 to a mixed number?

  

  See how many times 8 goes into 9, which is once. This number is your whole number, with a remainder of 1; therefore. the mixed number fraction would be 1 and 1/8.

• Question

  How do I write 7 3/4 as an improper fraction?

  

  To convert a mixed number into an improper fraction, multiply the whole number by the denominator, then add the numerator. Place this result over the denominator to get your improper fraction. So, to convert 7 3/4: 7*4 = 28. 28 + 3 = 31. 31/4 is your answer.

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To turn an improper fraction into a mixed number, just divide the numerator by the denominator. For example, if your improper fraction is 15/4, you would divide 15 by 4 to get 3.75. Just remember to write your answer in mixed-number format, using the original denominator for the fraction. So in this case, your improper fraction would be the mixed number 3¾. To learn how to turn an improper fraction into a mixed number without using division, scroll down!

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