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Welcome to the Math Salamanders support page about How to Calculate Fractions of Numbers.

Here you will find information and support about how to find fractions of different numbers.

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Follow these 3 easy steps to get your worksheets printed out perfectly!

Fraction Learning

Fractions is an area that a lot of kids find hard to understand. One of the problems with fractions is that they have different meanings depending on the context.

For example, you can eat half an apple or cut an orange into fourths. But you can also put the number one-half on a number line, measure a line 3 1/2 cm long, or find a fourth of 24.

Once the concept of fractions as numbers and fractions as parts of a whole has been understood, your child will be well on their way to developing a sound understanding of fractions.

How to Calculate Fractions of Numbers Support Page

Here you will find some simple information and advice about how to calculate fractions of numbers.

At the bottom of this page you will also find two printable resource sheets which explain about how to calculate fractions in a little more detail.

Before you start learning to calculate fractions of numbers, you should be able to work out fractions of shapes.

How to find a fraction of a number

Here are the two easy steps for finding the fraction of a number:

Step 1 - Find the unit fraction of the number by dividing the number by the denominator

Step 2 - Multiply by the numerator.

You should have now found your fraction of a number!

Examples

Example 1) Find 5 6 of 24

Step 1)

A unit fraction is a fraction where the numerator is equal to 1.

To find the unit fraction of a number, you need to divide the number by the denominator.

This gives us 1 6 of 24 = 24 ÷ 6 = 4

Step 2)

We need to multiply our answer by the numerator which is 5.

So 5 6 of 24 = ( 1 6 of 24 ) x 5 = 4 x 5 = 20

Example 2) Find 3 7 of 35

Step 1)

The denominator of the first fraction is 7.

This gives us 1 7 of 35 = 35 ÷ 7 = 5

Step 2)

We need to multiply our answer by the numerator which is 3.

So 3 7 of 35 = ( 1 7 of 35 ) x 3 = 5 x 3 = 15

How to calculate fractions - the algebra...

For those of you who like to see things in Algebra...this is what it looks like

If we want to work out a b of a number n

First we divide n by the denominator b (n ÷ b).

This tells us the value of 1 b of n

Next we need to multiply this by the numerator a.

This gives us:

a b of n = (n ÷ b) x a OR (n x a) ÷ b OR n x a b

How do you find fractions printable sheets

This printable support sheet below gives a little more detail about finding fractions of numbers including a step-by-step visual guide to how and why it works.

Fraction of a number worksheets

How to find unit fractions of a number (3rd Grade)

Here you will find a selection of Fraction worksheets designed to help your child understand how to work out unit fractions of different numbers where the numerator is 1.

Using these sheets will help your child to:

develop an understanding of fractions as parts of a whole;

know how to calculate unit fractions of a range of numbers.

All the free Fraction Shape worksheets in this section support the Elementary Math Benchmarks for 3rd Grade.

Learning Fractions

Are you looking for free fraction help or fraction support?

Here you will find a range of fraction help on a variety of fraction topics, from simplest form to converting fractions.

There are fraction videos, worked examples and practice fraction worksheets.

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

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Welcome to the Math Salamanders support page about How to Calculate Fractions of Numbers. Here you will find information and support about how to find fractions of different numbers. How to Print or Save these sheets Follow the 3 easy steps below to get your worksheets printed out perfectly!

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division number stories

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video

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Relationship of Division and Fractions

Explore the connection between division and fractions while dividing up cookies. This video focuses on recognizing patterns when modeling dividing up cookies to share with people.

This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

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Explore the connection between division and fractions while dividing up cookies. This video focuses on recognizing patterns when modeling dividing up cookies to share with people. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers and is part of the Math at the Core: Middle School collection.

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Convert Mixed Numbers & Improper Fractions

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Convert Mixed Numbers & Improper Fractions

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Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally, there are length, area, region, and set models.

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Visually Subtracting Fractions with Unlike Denominators

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Visually Subtracting Fractions with Unlike Denominators

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Khan Academy

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- Let's see if we can figure out with 3/4 minus 5/8 is. And we have 3/4 depicted right over here. You could view this entire bar as a whole, and we see that it is divided into four equal sections, and that three of them are shaded in. So those three that are shaded in, those represent 3/4 of the whole. So you see that right over there, and then this bar down here, you could view this as another whole. This is another whole right over here and you could see this divided into eight equal pieces, and five of them are shaded in. So that represents, that represents the 5/8. So we want to have 3/4, this green shaded area, and we want to take away the 5/8. So how could we do it? And even when you look at it visually, it might jump out at you. Whenever we add or subtract fractions, we like to think in terms of having the same denominator. Are we going to deal in fourths or eighths or 16s, or whatever else? So let's think about having a common denominator. And a good common denominator is going to be a common multiple of the two denominators right over here, and ideally their least common multiple. And one way that I like to tackle that, there's many ways to do it, is look at the larger of the two denominators, look at eight, and then keep looking at increasing multiples of eight until you find one that's also divisible by four, perfectly divisible by four. But with eight, you immediately say, "Well, eight is divisible by four," and that's clearly divisible by itself as well, so eight is actually the least common multiple of four and eight. So you can rewrite both of these, both of these fractions as something over eight. So the 3/4, you can write it as something over eight, and then subtracting from that, the 5/8, if you want to write that as something over eight, well, that's just going to be 5/8. And then you can figure out your actual answer. So how can we rewrite 3/4 to something over eight? Well, there's a couple of ways to think about doing it. One way, look. I had four in the denominator, now I'm going to have twice as many equal sections. I'm multiplied by two, so I'm going to have twice as many of the sections actually shaded in. So times two, 3/4 is the same thing as 6/8. And we can also see that visually. If we're going to have twice as many equal sections, here we have everything in fourths, but I'm going to divide, I'm going to turn this into twice as many equal sections so I have eighths. So let's do that. So let me... So you have this right here. Let me divide that. Let me divide that. Let me divide that, and then let me divide that, and now I went from fourths to eights. I have one, two, three, four, five, six, seven, eight equal sections, and we see that six of them are shaded in, that 3/4 is the same thing as 6/8. But regardless, now we can subtract. We have 6/8 and we want to take away five of the eighths. So we have 6/8, and we want to take away one, two, three, four, five of them, and those five of them correspond to these purple five right over here. We're taking away one, two, three, four, five. We're taking these away. So if you're just looking at the green, we started with 6/8, we're taking away one, two, three, four, five of them, and you can see that corresponds to the 5/8 down here and what are you left with? Well, you're just going to be left with, you're just going to be left with this 1/8 right over there. So it's just going to be 1/8. And you could see that numerically up here. If I have six of something, in this case it's 6/8, and I want to subtract five of that something, in this case 5/8, I'm going to be left with one of that something, or 1/8.

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Visually subtracting fractions: 3/4-5/8 (video) | Khan Academy

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Let's see if we can figure out with 3/4 minus 5/8 is. And we have 3/4 depicted right over here. You could view this entire bar as a whole, and we see that it is divided into four equal sections, and that three of them are shaded in.

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Practice

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teacherled interactive whiteboard ipad teacher classroom resource math maths mathematics education fractions euivalent

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Classroom activity for the interactive whiteboard, android tablet or iPad

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mixed practice

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Visually Adding Fractions with Unlike Denominators

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Visually Adding Fractions with Unlike Denominators

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Khan Academy

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Strategies for adding and subtracting fractions with unlike denominators

Strategies for adding and subtracting fractions with unlike denominators

Video transcript

let's see if we can calculate what 5/6 plus 1/4 is and to help us I have a visual representation of 5/6 and a visual representation of 1/4 notice I have this whole this whole whole I guess you could say broke it up into 1 2 3 4 5 6 sections and we've shaded in five of them so this is 5/6 and then down here we have another hole and we have one out of the four equal sections and so this is 1/4 and I want to add them and I encourage you to any point pause the video and see if you could figure it out on your own well whenever we're adding fractions we like to think in terms of fractions that have the same denominator and these clearly don't have the same denominator but in order to rewrite them with a common denominator we just have to think of a common multiple of 6 and 4 and ideally the smallest common multiple of 6 and 4 and the way that I like to do that is I like to take the larger of the 2 which is 6 and then think about its multiples so I could first think about 6 itself 6 is clearly divisible by 6 but it's not perfectly divisible by 4 so now let's multiply by 2 so then we get to 12 12 is divisible by both 6 and 4 so 12 is a good common denominator here it's a the least common multiple of 6 and 4 so we can rewrite both of these fractions as something over 12 so something over 12 plus something plus something over 12 is equal to now there's a bunch of ways to tackle it but what I want to do is I just want to visualize it here on this on this drawing so if I go if I were to go from if I were to go from 6 equal sections to 12 equal sections which is what I'm doing if I'm going from 6 to the nominator 12 in the denominator I'm essentially multiplying each of these sections by or I'm essentially multiplying the number of sections I have by 2 or I'm taking each of these existing sections and I'm turning them into two sections so let's do that let's do that let me see if I can do it pretty neatly so I could do it a little bit neater than that so it'll look like that and whoops let me do this one I want to divide them fairly close to evenly I'm doing it by eye so it's not going to be perfect so then you have that one and then last on but last but not least you have that one there and then notice I had six sections but now I've doubled the number of sections I've turned the six sections into 12 sections by turning each of the original six into two so now I have one two three four five six seven eight nine ten eleven twelve sections so if I have 12 sections now how many of those twelve are now shaded in instead of having five of the six I now have ten of the twelve that are shaded in so I now have ten 12 five six is the same thing as 10 12 another way you could have thought about that to go from 6 to 12 I had to multiply by 2 so then I have to do the same thing in the numerator 5 times 2 is 10 but hopefully you see that those two fractions are equivalent that I didn't say I didn't change how much is shaded in I just took each of the original six and I turned it into two or I multiplied the total number of sections by 2 to get 12 and then instead of having five six I now have ten twelve shaded in now let's do the same thing with the four with the one-fourth right here I've depicted 1/4 but I want to turn this into something over 12 so to turn it over something in 12 to something over 12 each section has to be turned into three sections so let's do that let's turn each section into three sections so that's one two and three so then I have one two and three I have I think you see where this is going one two and three I have one two and three and so notice all I did is I multiplied before I had four equal sections turned each of those four sections into three sections so now I have 12 equal sections and I did that essentially by multiplying the number of sections I had by three so now what fraction is shaded in well now this original that was one out of the four we can now see is three out of the 12 equal sections it's now three out of the 12 equal sections and so what is this going to be well if I have ten twelfths and I'm adding it to three twelfths well how many 12 stew I have I'm gonna have 13 13 12 and you could see it visually over here as well up here in green I have 10 twelfths shaded in each of these boxes are 1/12 let me write that down each of these boxes are 1/12 that's 1/12 this is 1/12 so how many twelfths do I have shaded in I have the 10 front that are shaded in green and then I have an 11 12 a 12 12 and then finally a 13 the 13 12 is one way to think about it

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Visually adding fractions: 5/6+1/4 (video) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

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Khan Academy

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Sal compares fractions by graphing them a number line and drawing fraction models.

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Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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super tool for comparing fractions

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Classroom activity for the interactive whiteboard, android tablet or iPad

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use bars or circles to create equivalent fractions