What are the kinds of Fraction?

Question

Plaese post a computation and give an example so that I can understand how to compute or post a website related to my question.

Addition of Fraction
Sutraction of Fraction
Multiplication of Fraction
Division of Fraction

Answer 1

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FRACTION TYPES
There are 3 different types of fractions:

Proper Fractions Numerator < Denominator
Proper fractions have the nominator part smaller than the denominator part,
for example , or .
Improper Fractions Numerator > Denominator or Numerator = Denominator,
Improper fractions have the nominator part greater or equal to the denominator part,
for exampleor .
Mixed Fractions
Mixed fractions have a whole number plus a fraction, for example 2or 123 .

Answer 2

Simple:
Addition:

(a/b) + (c/d)= (ad+cb)/(bd)

In order to add fractions you must have a common denominator, therefore you must cross mutliply and then add.

Subtraction:

(a/b)-(c/d)= (ad-cb)/(bd)

Same as addition but you are subtracting.

Mutliplication:

(a/b)x(c/d)= (ac/bd)

Multiple straight across.

Division:

(a/b)/(c/d)= (ad/bc)

Cross multiply.

Answer 3

Arithmetic with fractions

Fractions, like whole numbers, obey the commutative, associative, and distributive laws, and the rule against division by zero.
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Addition and subtraction
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Adding fractions

Adding fractions can be tricky. The first rule of addition is that you can only add like quantities, and so, while it is easy to add halves and halves or thirds and thirds, you cannot add halves and thirds unless you find a way to make them like quantities.

The quickest way to add fractions is to multiply the denominators, and then change both fractions to equal fractions over that denominator. For example,

1⁄2 + 2⁄3 = 3⁄6 + 4⁄6 = 7⁄6.

This always works, but sometimes there is a smaller denominator that will also work (a least common denominator). For example, to add 3⁄4 + 5⁄12, we can use the denominator 48, but we could also use the smaller denominator 12, which is the least common multiple of 4 and 12.

3⁄4 + 5⁄12 = 9⁄12 + 5⁄12 = 14⁄12.

(This answer can be reduced to 7⁄6.)
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Subtracting fractions

The process for subtracting fractions is, in essence, the same as that of adding them: find a common denominator, and change each fraction to an equivalent fraction with the chosen common denominator. The resulting fraction will have that denominator, and its numerator will be the result of subtracting the numerators of the original fractions. For instance,

2⁄3 − 1⁄2 = 2⁄2 × 2⁄3 − 3⁄3 × 1⁄2 = 4⁄6 − 3⁄6 = 1⁄6.

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Multiplication and division
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Multiplication
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By whole numbers

If you consider the cake example above, if you have a quarter of the cake, and you multiple the amount by three, then you end up with three quarters. We can write this numerically as follows:

3 \times {1 \over 4} = {3 \over 4}

As another example, suppose that five people work for three hours out of a seven hour day (ie. for three seventh of the work day). In total, they will have worked for 15 hours (5 x 3 hours each), or 15 sevenths of a day. Since 7 seventh of a day is a whole day, 14 sevenths is two days, then in total, they will have worked for 2 days and a seventh of day. Numerically:

5 \times {3 \over 7} = {15 \over 7} = 2{1 \over 7}

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By fractions

If you consider the cake example above, if you have a quarter of the cake, and you multiply the amount by a third, then you end up with a twelfth of the cake. In other words, a third of a quarter (or a third times a quarter), is a twelfth. Why? Because we are splitting each quarter into three pieces, and four quarters times three makes 12 parts (or twelfths). We can write this numerically as follows:

{1 \over 3} \times {1 \over 4} = {1 \over 12}

As another example, suppose that five people do an equal amount work that totals three hours out of a seven hour day. Each person will have done a fifth of the work, so they will have worked for a fifth of three sevenths of a day. Numerically:

{1 \over 5} \times {3 \over 7} = {3 \over 35}

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General rule

You may have noticed that when we multiply fractions, we simply multiply the two numerators (the top numbers), and multiply the two denominators) (the bottom numbers). For example:

{5 \over 6} \times {7 \over 8} = {5 \times 7 \over 6 \times 8} = {35 \over 48}

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By mixed numbers

When multiplying mixed numbers, it's best to convert the whole part of the mixed number into a fraction. For example:

3 \times 2{3 \over 4} = 3 \times \left ({{8 \over 4} + {3 \over 4}} \right ) = 3 \times {11 \over 4} = {33 \over 4} = 8{1 \over 4}

In other words, 2{3 \over 4} is the same as \left ({{8 \over 4} + {3 \over 4}} \right ), making 11 quarters in total (because 2 cakes, each split into quarters makes 8 quarters total). And 33 quarters is 8{1 \over 4} since 8 cakes, each made of quarters, is 32 quarters in total.
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Division

To divide by a fraction, simply multiply by the reciprocal of that fraction.

5 \div {1 \over 2} = 5 \times {2 \over 1} = 5 \times 2 = 10

{2 \over 3} \div {2 \over 5} = {2 \over 3} \times {5 \over 2} = {10 \over 6} = {5 \over 3}

To understand why this works, consider that a/b divided by c/d equals acd/bcd divided by c/d which equals ad/bc multiplied by c/d divided by c/d. Since any number divided by itself is 1, we get ad/bc.

Answer 4

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