With a 4th grade student under the roof, you can bet we’re spending a lot of time lately talking about fractions, percentages and decimals. And when I say a lot of time, I mean a lot of time.
Fractions are definitely one of those topics that take some time to explain, and the concept of equivalent fractions even more so. Let’s just say trying to explain to a 10 year old how something with completely different numbers, especially ones with many many more digits, might be exactly the same, or even less than a reduced fraction, is not a task for the impatient.
Color me impatient then because my solution to this equivalent fraction conundrum is summed up in this amazing new fraction chart I just whipped up…
This chart shows how the quantity shown by fractions with different denominators relate to each other relative to the number line. This makes all of the equivalent fractions line up neatly, and I’ve shown the decimal equivalents for the most common ones. This has already answered a lot of questions around here and will hopefully save a few more of my remaining hairs.
There are a few different versions of the chart, and because the graphic came out so amazing, I decided to setup poster sized versions as well. Please check them out and let me know what you think in the comments section!
I hope all of you have had a great summer! If you’re just returning to your math drills for the school year, I hope you’ll notice a big change around here at DadsWorksheets! I’ve been busy updating our worksheets starting with switching to PDF files, and a great deal of effort wehnt into giving them a more modern look and feel…
I’m especially pleased with the fraction worksheets… Not only do the new worksheets look amazing, but the answer keys show work with more clarity, adding a few extra steps to the computations to make some of the problems a little easier to understand. You’ll especially appreciate this when working with the multiplying fractions or dividing fractions worksheets, where solving those types of problems can have many steps.
As always, these worksheets show you how to cross-multiply fractions where necessary to get the answer. Cross multiplication is difficult to explain, but having fraction problems that illustrate the steps in the key can be a huge help for kids trying to see where their computations went wrong (or, if you’re an adult, I can tell you from experience they also come in handy more than you might think!)
If you’re starting 3rd, 4th or 5th grade, now’s the time to start learning fraction concepts and these worksheets are a great place to start… I hope you’ll print a few out and let me know what you think in the comments section below!
I’ve received so much positive feedback on the fraction calculator and I really appreciate everyone who’s taken the time to pass along comments and suggestions! If you haven’t had a chance to play with it, please check out the new and improved version!
One thought that came up from users repeatedly was the way the previews represented mixed fractions was a little unintuitive given that the whole part of the fraction was always shown as a numeric value but the fraction had the pie-chart representation. And the concepts didn’t related particularly well to the multiplication and division operations.
To make the preview a little more useful in an instructional setting, I’ve updated it now. In general, small mixed fractions will be shown entirely as pies, with the wholes being shown as one or more complete pies divided by the numerator. If there are more than five wholes, the calculator’s representation reverts back to it’s numeric mixed fraction form.
What this accomplishes for addition and subtraction calculations is to make the representation totally visual, which is much closer to the vision I had in creating this thing.
Now multiplication and division are slightly different beasts, and in the context of the fraction calculator trying to show a meaningful visualization of how the operands translate into the product or quotient, my friend Maria Miller suggested that the right approach was really to express the multiplicands as a visualization times a number (or the dividend divided by a numeric divisor representation for division) since these operations didn’t lend themselves immediately towards the sort of counted forms that addition and subtraction do. If you think about it, this makes sense because these operations are more about repeated operations (multiples of or divisions into) a value, and the visualization of two separate fractions could almost be misleading. Either way try it out with a whole multiplicand or a whole divisor and I think you’ll find the preview is conceptually at least much better.
I still have plans to add steps the calculator is taking to generate the solutions, so for example a break down of how common denominators are determined or how the final mixed fraction might be reduced. It’s definitely a work in progress, but even now I think you’ll agree the calculator is already one of the best fraction teaching tools online!
Percentages are an important part of both math and daily life. We deal with percentages all over the place… Calculating tips, 50% off sales, sales tax, or (dare I mention it in April?) income taxes. All of these areas work with percentages.
This percentage calculator easily allows you to convert a percent to fraction or, in reverse, a fraction to percent. By playing with the various values, you can work out various types of problems (“what percent of a number is some other number” for example), and the spoken-word version of various types of problems is shown in the preview. Working various problems through the calculator will quickly build experience with various types of percentage problems.
Also be sure to check out the various fraction and percentage math worksheets on the site for more practice.
Sometimes, it’s really just all about pie. Who gets how much pie. How many pieces of pie. Fractions of pies. Big fractions for me, please.
When you are learning how to add or subtract fractions, it’s easy enough to get the whole common denominator thing figured out. I mean, if Uncle Billy ate half of the cherry apple, you know you’re only going to have a third of the pie left after you take your traditional one sixth slice. Denominators of two and three and six… It’s just basic pierithmetic.
But multiplying and dividing, that requires skills. Serious skills. And that’s where this fraction calculator might come in handy. Whether you have to deal with mixed fractions or improper fractions, or if you just need a little help with the core operations on simple fractions, this calculator is built just for you. It will reduce and simply anything you put into it, and along the way give you a visual preview to help show what’s going on. Check out the YouTube video in this post for a quick demo, or just go straight to the link below.
Also works great for pizza. Because, you know. Pizza is a pie, too.
Fractions worksheets! I can’t get seem to get enough!
Regular visitors know how much time and energy I’ve put into the fraction worksheets, and their answer keys represent some of the more complex work on the site. If you look at the addition and subtraction worksheets, you’ll find detailed steps that show calculations for reaching common denominators. The fraction multiplication and division worksheets demonstrate the cross cancelling operations leading to answers in their simplest form. All of these worksheets really helped get my older daughter through fractions, and I’m proud to say this is one of the scarier math topics that she has down cold.
But getting started was hard. I’m right at the fractional starting line with my younger daughter, and we needed something to begin with that visualizes exactly what a fraction means. Enter the Graphic Fraction worksheet series I posted today…
These worksheets make a great lead-in to the fraction operations. Let me know what you think in the comments section, and if you like them (or the rest of the site!) please consider clicking the Google “+1” button near the top left of the page.
The fraction worksheets, they keep going and going… and going…
An initial set of drills for converting fractions to decimals has been posted, along with worksheets for converting fractions with slightly larger denominators into decimal equivalents using long division. I keep thinking I’m near the end of the content dealing with fractions, but recent home work has included problems ordering fractions and a few other topics that seem like reasonable candidates for practice, so I may be on this topic for a while.
I’m working on additional worksheets dealing with converting fractions to their decimal equivalents, and then I think we’ll have wrapped up the basic fractions sheets. Having hit adding fractions, subtracting fractions, multiplying fractions and dividing fractions, we should be pretty complete for basic fraction related topics. I’ll do an overview post on all of the fraction content at that point, and then I’ll be (gladly!) moving on to a new topic area.
Going through fractions with my daughter has been tough, and thankfully something ‘clicked’ for her along the way, although frankly I’m not sure what or how. Especially for multiplication and division, it was a topic area where I struggled to get across the relationships between the numbers and not just the procedures (although I admit to repeating the phrase, “Take the reciprocal and multiply” so many times I now mumble it in my sleep.) Regardless of my bumbling efforts, my nearly-5th grader seems to have the concepts down now, and this Dad is relieved.
You can find the new worksheets are at the link below, or navigate the ‘Worksheet’ menu on the side of the page.
The number of new worksheets posted has been a little slow lately, but that doesn’t mean there haven’t been a number of useful changes. The worksheets on the site have all been refreshed and I think you’ll find a number of sheets are more useful.