Below space multiple portion princetoneclub.orgs capable of addition, subtraction, multiplication, division, simplification, and also conversion in between fractions and decimals. Fields over the solid black line stand for the numerator, when fields listed below represent the denominator.

You are watching: 6 times 1/3

 + - x / = ? ?

## Mixed numbers princetoneclub.org

 + - x / = ?

 =?

 = ? ?

 = ?

## Big Number portion princetoneclub.org

Use this princetoneclub.org if the molecule or denominators space very large integers.

 + - x / = ?

In mathematics, a fraction is a number the represents a part of a whole. It is composed of a numerator and also a denominator. The molecule represents the variety of equal components of a whole, when the denominator is the total variety of parts that comprise said whole. For example, in the portion of
 3 8
, the numerator is 3, and the denominator is 8. A much more illustrative example can involve a pie through 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the complete of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would as such be
 5 8
as shown in the image to the right. Note that the denominator that a portion cannot be 0, as it would make the portion undefined. Fractions can undergo countless different operations, few of which are mentioned below.

Unlike including and subtracting integers such together 2 and also 8, fractions need a usual denominator to undergo this operations. One an approach for finding a common denominator entails multiplying the numerators and also denominators of every one of the fractions affiliated by the product the the denominators of every fraction. Multiplying all of the platform ensures the the new denominator is particular to it is in a lot of of every individual denominator. The numerators also need to be multiplied by the suitable factors to maintain the worth of the fraction as a whole. This is may be the simplest method to ensure the the fractions have actually a common denominator. However, in many cases, the options to these equations will certainly not show up in simplified form (the listed princetoneclub.org computes the simplification automatically). Listed below is an instance using this method.

 a b
+ c
d
= a×d
b×d
+ c×b
d×b
bd
 EX: 3 4
+ 1
6
= 3×6
4×6
+ 1×4
6×4
= 22
24
= 11
12

This procedure can be used for any variety of fractions. Simply multiply the numerators and also denominators the each portion in the trouble by the product the the denominators of every the various other fractions (not including its own respective denominator) in the problem.

 EX: 1 4
+ 1
6
+ 1
2
= 1×6×2
4×6×2
+ 1×4×2
6×4×2
+ 1×4×6
2×4×6
=12
 48
+ 8
48
+ 24
48
= 44
48
= 11
12

An alternative method for finding a common denominator is to identify the least usual multiple (LCM) for the denominators, then add or subtract the numerators together one would an integer. Making use of the least common multiple deserve to be much more efficient and also is more likely to result in a portion in streamlined form. In the example above, the denominators to be 4, 6, and 2. The least typical multiple is the first shared lot of of these 3 numbers.

 Multiples that 2: 2, 4, 6, 8 10, 12 Multiples of 4: 4, 8, 12 Multiples of 6: 6, 12

The first multiple they all share is 12, therefore this is the least common multiple. To complete an enhancement (or subtraction) problem, multiply the numerators and denominators that each portion in the problem by everything value will make the platform 12, then add the numerators.

 EX: 1 4
+ 1
6
+ 1
2
= 1×3
4×3
+ 1×2
6×2
+ 1×6
2×6
=3
 12
+ 2
12
+ 6
12
= 11
12

### Subtraction:

Fraction individually is essentially the same as fraction addition. A common denominator is compelled for the operation to occur. Refer to the enhancement section and also the equations below for clarification.

See more: On The Income Statement, Which Of The Following Would Be Classified As A Variable Cost?

 a b
– c
d
= a×d
b×d
– c×b
d×b
bd
 EX: 3 4
– 1
6
= 3×6
4×6
– 1×4
6×4
= 14
24
= 7
12

### Multiplication:

Multiplying fountain is fairly straightforward. Unlike adding and subtracting, the is not important to compute a usual denominator in order to multiply fractions. Simply, the numerators and also denominators the each fraction are multiplied, and also the an outcome forms a new numerator and also denominator. If possible, the solution have to be simplified. Describe the equations below for clarification.

 a b
× c
d
= ac
bd
 EX: 3 4
× 1
6
= 3
24
= 1
8

### Division:

The process for separating fractions is comparable to that for multiply fractions. In bespeak to division fractions, the portion in the molecule is multiply by the reciprocal of the portion in the denominator. The reciprocal of a number a is merely
 1 a
. Once a is a fraction, this essentially involves exchanging the place of the numerator and the denominator. The mutual of the fraction
 3 4
would as such be
 4 3
. Describe the equations listed below for clarification.

 a b
/ c
d
= a
b
× d
c
bc
 EX: 3 4
/ 1
6
= 3
4
× 6
1
= 18
4
= 9
2

### Simplification:

It is often simpler to work-related with simplified fractions. Together such, fraction solutions are commonly expressed in their streamlined forms.
 220 440
for example, is more cumbersome than
 1 2
. The princetoneclub.org listed returns fraction inputs in both wrong fraction type as fine as blended number form. In both cases, fractions space presented in your lowest forms by splitting both numerator and also denominator by their greatest typical factor.

### Converting between fractions and decimals:

Converting from decimal to fountain is straightforward. The does, however, need the knowledge that each decimal location to the ideal of the decimal point represents a power of 10; the very first decimal ar being 101, the second 102, the third 103, and so on. Simply determine what power of 10 the decimal expand to, use that power of 10 together the denominator, go into each number to the ideal of the decimal point as the numerator, and also simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 104, or 10,000. This would certainly make the fraction
 1234 10000
, which simplifies to
 617 5000
, due to the fact that the greatest common factor in between the numerator and denominator is 2.

Similarly, fractions through denominators that room powers that 10 (or can be convert to powers of 10) deserve to be analyzed to decimal form using the very same principles. Take it the portion
 1 2
because that example. To convert this portion into a decimal, first convert it right into the fraction of
 5 10
. Learning that the first decimal ar represents 10-1,
 5 10
can be converted to 0.5. If the portion were instead
 5 100
, the decimal would then it is in 0.05, and also so on. Past this, converting fractions into decimals calls for the operation of lengthy division.

### Common Engineering fraction to Decimal Conversions

In engineering, fractions are widely offered to explain the size of components such as pipes and bolts. The most typical fractional and also decimal equivalents are provided below.

 64th 32nd 16th 8th 4th 2nd Decimal Decimal(inch come mm) 1/64 0.015625 0.396875 2/64 1/32 0.03125 0.79375 3/64 0.046875 1.190625 4/64 2/32 1/16 0.0625 1.5875 5/64 0.078125 1.984375 6/64 3/32 0.09375 2.38125 7/64 0.109375 2.778125 8/64 4/32 2/16 1/8 0.125 3.175 9/64 0.140625 3.571875 10/64 5/32 0.15625 3.96875 11/64 0.171875 4.365625 12/64 6/32 3/16 0.1875 4.7625 13/64 0.203125 5.159375 14/64 7/32 0.21875 5.55625 15/64 0.234375 5.953125 16/64 8/32 4/16 2/8 1/4 0.25 6.35 17/64 0.265625 6.746875 18/64 9/32 0.28125 7.14375 19/64 0.296875 7.540625 20/64 10/32 5/16 0.3125 7.9375 21/64 0.328125 8.334375 22/64 11/32 0.34375 8.73125 23/64 0.359375 9.128125 24/64 12/32 6/16 3/8 0.375 9.525 25/64 0.390625 9.921875 26/64 13/32 0.40625 10.31875 27/64 0.421875 10.715625 28/64 14/32 7/16 0.4375 11.1125 29/64 0.453125 11.509375 30/64 15/32 0.46875 11.90625 31/64 0.484375 12.303125 32/64 16/32 8/16 4/8 2/4 1/2 0.5 12.7 33/64 0.515625 13.096875 34/64 17/32 0.53125 13.49375 35/64 0.546875 13.890625 36/64 18/32 9/16 0.5625 14.2875 37/64 0.578125 14.684375 38/64 19/32 0.59375 15.08125 39/64 0.609375 15.478125 40/64 20/32 10/16 5/8 0.625 15.875 41/64 0.640625 16.271875 42/64 21/32 0.65625 16.66875 43/64 0.671875 17.065625 44/64 22/32 11/16 0.6875 17.4625 45/64 0.703125 17.859375 46/64 23/32 0.71875 18.25625 47/64 0.734375 18.653125 48/64 24/32 12/16 6/8 3/4 0.75 19.05 49/64 0.765625 19.446875 50/64 25/32 0.78125 19.84375 51/64 0.796875 20.240625 52/64 26/32 13/16 0.8125 20.6375 53/64 0.828125 21.034375 54/64 27/32 0.84375 21.43125 55/64 0.859375 21.828125 56/64 28/32 14/16 7/8 0.875 22.225 57/64 0.890625 22.621875 58/64 29/32 0.90625 23.01875 59/64 0.921875 23.415625 60/64 30/32 15/16 0.9375 23.8125 61/64 0.953125 24.209375 62/64 31/32 0.96875 24.60625 63/64 0.984375 25.003125 64/64 32/32 16/16 8/8 4/4 2/2 1 25.4