What Is A Unit Fraction?

What Is A Unit Fraction:

A unit fraction is a number that can be expressed as a proper fraction with one whole, and the denominator is 1.

e.g:- ½ = 2/4, ¼ = 4/9, ⅛ = 8/9, etc.

The definition of a unit fraction tells us that it can be expressed in terms of its numerator divided by its denominator.

In other words, we have:

In mathematics, the symbol for “or” is … so this equation may also be written as:

as shown below: 

A formula is an expression that provides detailed information about a particular problem or situation. An excellent example of this is the following famous geometry recipe related to circles: Area of Circle = π × (radius)2. This equation tells us how to work out the area of a process if we know its radius.

e.g.:- If the circumference of a circular plate is 18 cm, what is its radius?

To find the radius, plugin for “C” and solve for “r.” The answer will be 6 cm.

Since unit fractions are ratios between whole numbers, they may also be expressed as proportions. We have already seen this with equivalence proofs so far, so it won’t be necessary to re-visit them again here. It should also be noted that the following two equations are equivalent:

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i) A/B = 1/X

ii) B = X/A

i) A/B = 1/X

ii) B = X/A

For example, let’s have a look at the following question: 

If ½ is of ¼, what is the value of x?

To solve this problem, first, write down both of the equations. The second equation can be written as two separate equations where “x” appears on each side of the equal sign. This gives us:

1/4 = x/½  and ½ = × ¼

Now solve for x by multiplying both sides of the equation by four, so we get 4x=1 which means x=1/. Now recall how fractional multiplication works, i.e., multiply both top and bottom by the denominator, so the new fractions are all in lowest terms.

This gives us 1/8 = x, the final answer to the question.

One way of thinking about a unit fraction is a “building block” for other fractions. In other words, we can use unit fractions to create more complex fractions by multiplying (or dividing) them together. For example, let’s take the fraction ¾ and see how we can make new fractions from it.

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We can create the fraction ¾ by multiplying 3 unit fractions together, i.e., 1/3, 2/3, and 3/3.

Similarly, we can create the fraction ¼ by dividing 3 unit fractions together, i.e., 1/3, 2/3, and 3/3.

In general, we can create a fraction of n in unit fractions by multiplying together the first n natural numbers, i.e., 1, 2, 3, 4… etc. The product of these unit fractions will be the fraction of n.

One example is to show that 1⁄6 = 6⁄1x: 

(1/6) * (6/1) = (1*6)/(6*1) = (6)/(1) = 6 – Therefore we know that 1⁄6= 6⁄1x and vice versa.

The next example is to show that 8⁄9 + 7⁄9 = 15⁄9: –

8/9  + 7/9 = (8+7)/9 = 15/9 – Therefore we know that 8⁄9 + 7⁄9 = 15⁄9.

Lastly, let’s show that 1² + 2² = 3²: –

We can use the same method as the previous example to show that 1² + 2² = 3². In this case, we have:

1/1  + 2/1  = (1+2)/1 = 3/1 = 3 – Therefore we know that 1² + 2² = 3².

Now that we understand what a unit is and how unit fractions can be used to create other bits, we will explore the concept of a unitary operation.

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A unitary operation is any process that reduces a fraction or complex number down to its simplest form by multiplying or dividing both the top and bottom of the fraction or number by the same multiplier, divisor, or factor. In this case, it means reducing all denominators in a fraction down to 1 to simplify them. For example, 4⁄9 = 4/9 but 9 = 1.

Similarly, 3² can also be reduced because 3*3 = 9 and 2² can also be reduced because 2*2 = 4, while 1² cannot be reduced since 1*1=1.

For two numbers to be in a unitary relationship, one must represent the inverse of the other – this is to say that their product will equal 1. We can determine whether two fractions are in a unitary relationship by multiplying them and seeing if their product equals 1. If it is, then they are unitarily related.

For example: 

2/3  × 3/2  = (2*3)/(3*2) = 6/6 = 1

– This means that 2⁄3 and 3⁄2 are in a unitary relationship since 1 represents the multiplicative inverse of either fraction (i.e., x * 1 =1).

Now let’s look at some examples involving negative numbers.

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