What is 1 3 of 12

Calculating the fraction of a whole number is a very useful skill to learn that helps students to understand the nature of numbers and their interactions. In this article, we'll explain how to calculate 1/3 of 12 with step-by-step-examples.

Calculating the Answer as a Number

The simple rule to remember whenever you want to find a fraction of an amount is to divide the amount by the fraction's denominator, and then multiply that answer by the fraction. Using this rule, you'll be able to work out the fractional amount of the original number. Let's work it out together.

First we take the amount, 12, and divide it by the denominator, 3:

12 ÷ 3 = 4

Next, we take the answer, 4, and multiply it by the numerator, 1:

4 × 1 = 4

As you can see, the answer to the question "what is 1/3 of 12?" as a number is 4.

Increase or Decrease an Amount by a Fraction

What if you wanted to increase or decrease 12 by 1/3? Once you have calculated the answer above, 4, you deduct that amount from the whole number to decrease it by 1/3 and you add it to increase:

Increase = 12 + 4 = 16

Decrease = 12 - 4 = 8

Calculating the Answer as a Fraction

Sometimes, you might want to show your answer as another fraction. In that case, we can do the following.

First, we take the whole number and turn it into a fraction by using 1 as the fraction denominator:

12 1

Now that we have two fractions, we can multiply the numerators and denominators together to get our answer in fraction form:

1 × 12 3 × 1 = 12 3

We can simplify this new fraction down to lower terms. To do that we need to know something in math which is called the GCD, or greatest common divisor.

I won't go through the steps of finding the GCD here as we'll cover it in a future article, but for now all you need to know is that the greatest common divisor of 12 and 3 is 3.

Using the GCD, we can divide the new numerator (12) and the denominator (3) by 3 to simplify the fraction:

12 ÷ 3 = 4

3 ÷ 3 = 1

Finally, we can put the fraction answer together:

4 1

Now you might have noticed that the fraction we have has a numerator that is larger than the denominator. This is called a mixed or improper fraction and means that there is a whole number involved. We can simplify this down to a mixed number.

We'll put together a blog post on converting improper fractions to a mixed number to explain those steps in more detail, but for the purposes of this article, we'll go ahead and just give you the mixed number answer:

Hopefully this article helps you to understand how you can work with fractions of whole numbers and work this out quickly for yourself whenever you need it.

Practice Fraction of Number Worksheets

Like most math problems, finding the fraction of a number is something that will get much easier for you the more you practice the problems and the more you practice, the more you understand.

Whether you are a student, a parent, or a teacher, you can create your own fractions of a whole number worksheets using our fraction of a number worksheet generator. This completely free tool will let you create completely randomized, differentiated, fraction of a number problems to help you with your learning and understanding of fractions.

Practice Fractions of a Number Using Examples

If you want to continue learning about how to calculate the fraction of a whole number, take a look at the quick calculations and random calculations in the sidebar to the right of this blog post.

We have listed some of the most common fractions in the quick calculation section, and a selection of completely random fractions as well, to help you work through a number of problems.

Each article will show you, step-by-step, how to work out the fraction of any whole number and will help students to really learn and understand this process.

Calculate Another Fraction of a Number

Enter your fraction in the A and B boxes, and your whole number in the C box below and click "Calculate" to calculate the fraction of the number.

Please use the tool below to link back to this page or cite/reference us in anything you use the information for. Your support helps us to continue providing content!

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

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Mixed Numbers Calculator

Simplify Fractions Calculator

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Decimal to Fraction Calculator

Fraction to Decimal Calculator

Big Number Fraction Calculator

Use this calculator if the numerators or denominators are very big integers.

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In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total 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 therefore be

as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

Multiples of 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, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Division:

The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply

. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction

would therefore be

. Refer to the equations below for clarification.

Simplification:

It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome than

. The calculator provided returns fraction inputs in both improper fraction form as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and 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 make the fraction

, which simplifies to

, since the greatest common factor between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction

for example. To convert this fraction into a decimal, first convert it into the fraction of

. Knowing that the first decimal place represents 10-1,

can be converted to 0.5. If the fraction were instead

, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.

64th	32nd	16th	8th	4th	2nd	Decimal	Decimal (inch to 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

How do you find 1/3 of a number?

Thirds are calculated by dividing by 3. For example: One third of 24 =1/3 of 24 = 24/3 = 8. One third of 33 =1/3 of 33 = 33/3 = 11.

What is 3 out of 12 as a fraction?

The simplified fraction of 312 is 14 . Since 3 is a factor of 12, we divide the numerator and denominator each by 3. This gives us a numerator of 1 and an denominator of 4, making our simplified fraction 14 .