10 5 2 3 Fraction

Welcome to our fraction calculator, a really versatile tool. Information technology tin:

➕ add,

➖subtract,

✖️multiply, and

➗carve up
any ii fractions. Moreover, it has the power to simplify a fraction (A.K.A. reduce), as well as tell you lot how to turn a fraction into decimal, and vice versa. If yous're withal not impressed, this tool not only works on standard proper and improper fractions, simply as well on mixed fractions - what more could you enquire for?😁

Every bit usual, we've prepared some introductory reading, which will allow you dig into the globe of fractions🌎. Below y'all'll read about the fraction definition, the types of fractions (proper, improper, mixed), and all those basic operations on unproblematic and mixed fractions. Are yous ready?

What is a fraction? Fraction definition

A fraction represents the number of equal parts of a whole thing.
Y'all can recognize a uncomplicated fraction because it has two numbers separated by line (or slash):

• We call the top number the numerator, and write it above the line. It tells united states of america

How many parts we have

• We call the bottom number denominator, and display it below the line. It means

The total number of parts

In the example above, it's i part out of six slices, which the pie was cut into in total. We read information technology as one-sixth of the whole pie.

Only, of course, the block can be cut differently!

Then, if you cut the pie in 2, then one slice is one-half of the whole. If you cut the pie in three parts, so one slice is ane-third of the whole pie, etc.

Fractions are used all around u.s.a.:

• every fourth dimension you want to express part of a whole detail, which tin can be divided into fifty-fifty pieces: similar a block🍰, a chocolate bar🍫, a watermelon🍉, a pizza🍕, etc;
• when we measure something📏, peculiarly in inches or eights of an inch; and
• your computer screen size 🖥️ is expressed as a ratio, east.g. 16:9 - and it'south also a fraction, merely written in a unlike mode. (For information on how to simplify ratios, check out our ratio figurer!)

What is a proper, improper, and mixed fraction?

And then, at present that you know the fraction definition, let's have a look at the unlike types of fractions. In general, we have three types of fractions: proper, improper and mixed fractions:

1. Proper fraction

In proper fractions, the height number (numerator) is smaller than the bottom number (denominator). It means that it will e'er be less than ane whole thing, e.g.:

🍰 5 slices of block out of a cake that was cut into half-dozen;

🍫 two rows of a chocolate bar out of the whole chocolate bar, which has 5 rows; and

🍊 7 parts of an orangish out of the entire orange, that nosotros cut into 8.

The full general rule, which works for both positive and negative numbers, is that the absolute value of the fraction is less than one:

|numerator/denominator|< 1

2. Improper fraction

And then what is an improper fraction? Information technology's a fraction where the numerator is larger than (or equal to) the denominator. Improper fractions are sometimes chosen top-heavy fractions. Examples of improper fractions are:

🍰 10 slices of cake, when each cake has six slices;

🍫 8 rows of a chocolate bar. A whole chocolate bar has v rows; and

🍊 21 parts of orange, if we cut each orange to eight equal pieces.

3. Mixed fraction

Mixed fractions, also known as mixed numerals or mixed numbers, are another way of expressing an improper fraction.
They are whole numbers (the amount of whole things) and a proper fraction put together. Then, if we'll take a look at the examples from the previous paragraph:

🍰 10 slices of cake, when each cake has 6 slices is the same as → 1 whole block and 4 slices out of 6;

🍫 8 rows of chocolate when the whole chocolate bar has 5 rows → 1 whole chocolate bar and 3 rows out of v; and

🍊 21 parts of orange, if we cut the orange to 8 slices → two whole oranges and v slices out of eight

💡 The well-nigh important things to remember afterward reading this department:
• A proper fraction has a smaller top number (numerator) than its bottom number (denominator);
• An improper fraction's numerator is larger than (or equal to) its denominator; and
• A mixed number consists of a whole number and a proper fraction.

How do you add fractions? ➕ Adding fractions rules

When it comes to adding fractions, there are three scenarios:

1. The denominator (lesser number) is the aforementioned in both fractions - e.grand., ^three/₅ and ¹/₅

This is the most straightforward case; all you need to do is to add together numerators (top numbers) together and leave the denominator as is, e.k:

3/5 + ane/5 = (three + one)/5 = four/v

2. The fractions have unlike denominators - east.m., two/5 and three/10

This is a bit more than of a complicated case - to add these fractions, y'all need to find the common denominator.

• You lot can employ e.g. LCM - the to the lowest degree common multiple to find the common number of your two denominators:

LCM(5,10) = ten

The other choice is to multiply your denominators and reduce the fraction later.

• Then, you need to expand each fraction, to have this common denominator as its bottom number:

Then, you lot should multiply the fraction with the denominator equal to 5 (our i/5) by 2 to become ten (recall that you must multiply both top and lesser numbers):

2/5 = (2 * 2)/(v * ii) = 4/10

Your second fraction has already its denominator equal to 10:

3/x

• Now that your fractions take the aforementioned denominator, you can add them:

four/10 + 3/x = (4 + 3)/x = vii/10

3. Y'all want to add together two mixed fractions - e.m. 2 ³/₅ and 1 ¹/₂

One solution for this kind of problem is to convert the mixed fraction to an improper fraction and sum it equally usual.

• Permit's convert information technology for 2 ³/₅

• Multiply the whole number past the denominator:

2 * 5 = x

• Add together the effect to you numerator:

x + 3 = 13

• That's your new numerator - write information technology on superlative of your denominator:

ii 3/v = 13/v

Analogically, you can find out that 1 ane/two = 3/ii

• Do the standard improver of fractions with uneven denominators:

13/v + 3/2 = 26/10 + xv/x = 41/10

• Finally, yous can convert your issue back into a mixed fraction:

Do long sectionalization with a remainder:

41/10 = 4 R 1

So 41/x = 4 i/10

Of course, our fraction computer deals with all of these scenarios. 😎

If you lot're however wondering how adding fractions works, mayhap this visual volition help?

For an fifty-fifty more thorough explanation, check out our adding fractions reckoner.

How to subtract fractions ➖

If you lot're wondering how to subtract fractions, and you lot've read through the previous department How exercise you add fractions , we have some skillful news for you: information technology's pretty much the same!

1. If you accept fractions with the aforementioned denominator, subtract the numerators:

3/five - 1/5 = (3 - 1)/5 = ii/5

2. When subtracting fractions with dissimilar denominators - ^two/_v and ^three/₁₀ - echo the process from the previous section, just subtracting, non adding in the final step:

• Observe a common denominator - information technology's x.
• Expand the fractions to their equivalent fractions with a common denominator: ⁴/₁₀ and ³/₁₀.
• Subtract the numerators.

two/v - 3/10 = 4/x - 3/10 = 1/10

3. For mixed fractions (2 three/5 and 1 i/ii):

• Change the mixed fractions to improper fractions, as before

2 3/5 = 13/five and ane 1/ii = iii/ii

• Subtract the ii improper fractions with unequal denominators:

13/5 - 3/2 = 26/x - 15/x = xi/10

• Leave it in an improper fraction, or convert it back to a mixed fraction:

11/10 = ane R i so 11/10 = 1 ane/10

You tin can imagine subtraction as taking or eating part of the cake:

That wasn't and so difficult, was it?

How exercise yous multiply fractions ✖️

Multiplying fractions is - fortunately - an effortless operation. It's numerator times numerator over denominator times denominator. Sometimes y'all besides need to simplify the fraction. And that's it!

Take a await at this example:

two/iii * 5/6 = (2 * 5)/(3 * 6) = 10/eighteen

which you tin can then simplify to 5/9

Whenever you deal with mixed fractions, don't forget than yous must e'er write them as an improper number before multiplying:

2 1/2 * iii 1/four = 5/2 * 13/4 = (5 * 13)/(2 * 4) = 65/8 =

eight 1/8

And when multiplying a fraction by a whole number, remember that you can write the whole number as itself divided by ane:

three * v/vii = iii/i * 5/7 = (3 * five)/(1 * seven) = 15/7

If you lot don't know how to deal with fraction reduction, scroll downwardly to the section How to simplify fractions .

Now that yous know how practice you multiply fractions, let's proceed to the next topic, fraction division.

How to split up fractions ➗

Racking your brain over how to divide fractions? Accept no worries! The sectionalization of fractions is quite like to fraction multiplication. The only divergence is that y'all must multiply your beginning number by the reciprocal of the 2nd fraction. It may sound a bit weird, just it's really simple! Have a look at this example:

(ane/2) / (3/5) = 1/2 * 5/iii = (1 * v)/(2 * 3) = 5/6

So, all you need to do is plough the second fraction upside down (which is its reciprocal) and multiply the fractions. Sometimes, you may also demand to do some fraction reduction. And that's all, tadaaa!🎉

How to simplify fractions?

We always like to brand our lives simpler - fifty-fifty in maths. That's why simplifying fractions is such an important thing. It means that we write the fraction in its simplest possible form. Nosotros likewise phone call simplifying fractions reducing fractions.

Simply what does this mean, exactly? Have a look at these examples:

• You'd rather say that 1-fourth (a quarter) of the pizza is left, instead of two-eights, right?
• or one-half of a cake was eaten, non three-sixths

To simplify a fraction, you can utilize two methods:

1. Use a kind of brute force approach: separate the fraction by 2,3,5,7,eleven... until it's impossible to continue the sectionalisation (without a remainder):

42/126 = /:2

21/63 = /:3

7/21 = /:7

1/3

2. Detect the GCF - greatest mutual factor of the numerator and denominator, and and then carve up them by this number:

GCF(42,126) = 42

42/126 = /:42

1/3

Read more about reducing fractions in our dedicated simplify fractions calculator. As well, make sure to have a look at our amazing equivalent fractions calculator, which can find many equivalents to your fraction.

How to convert a decimal into fraction?

If you want to find out how to catechumen a decimal into a fraction, you're in the right identify. Here's a step-by-step guide:

Permit'southward presume you want to catechumen 0.32 to a fraction:

1. Treat your decimal as a numerator. Then, the denominator volition be 1.

2. Movement the decimal dot to the right, till yous just have a whole number:

0.32 → 3.ii → 32

Each movement corresponds to multiplication by 10

0.32 * 10 → 3.ii * x → 32

3. Yous multiplied the numerator by ten * x, and now we need to multiply the denominator by the aforementioned number:

1 * x * 10 = 100

4. You've changed your fraction to a decimal!✨ 0.32 → 32/100

5. Finally, simplify the event. As the greatest mutual cistron for 32 and 100 is four, divide both numerator and denominator by this value:

32/100 = 8/25

And that's it, the fraction in its simplest course. ❤️

But, if yous accept a repeating decimal... that's a unlike story. Have a good read of the section How to convert a repeating decimal to a fraction? , or simply utilize our fraction calculator.

How to turn a fraction into a decimal?

Well, the easiest way to turn a fraction into a decimal is... to utilize a estimator. Be it this fraction calculator, a standard pocket reckoner🖩, or our dedicated tool - the fraction to decimal converter.

Sometimes the fraction is relatively easy to change into decimal without whatever tools - like for 1/2, three/4 (or even 1/8). We believe that you tin figure out how to expand the in a higher place fractions to have ten, 100, 1000, and so on in the denominator, respectively:

• Multiply i/2 by 5, to become x as the denominator:

i/2 = 5/10 = 0.5

• Multiply 3/4 by 25, to get 100 every bit the denominator:

3/4 = 75/100 = 0.75

• Multiply 1/8 past 125, to go 1000 every bit the denominator:

ane/eight = 125/yard = 0.125

But what if y'all don't accept the Internet or a calculator with you lot, but but pen and paper📝? And your fraction doesn't look so easy to aggrandize as the ones higher up? And so, y'all'll probably demand to practise the long division to the decimal places by hand. Good luck! 🤞

10 5 2 3 Fraction,

Source: https://www.omnicalculator.com/math/fraction

Posted by: williamstheastris.blogspot.com

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