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Simplifying, or Reducing the Fraction
Numerator / Denominator
We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.
Numerator/Denominator
You just have to remember those names! (If you forget just think "Down"-ominator)
The definition of a denominator means something that is shared, or is the standard, or the number below the line in a fraction.
An example of a denominator is the red hair color shared by all members of a family.
An example of a denominator is a common level of writing expected in a composition class.
An example of a denominator is the "2" in the fraction "½."
Adding Fractions
It is easy to add fractions with the same denominator (same bottom number):
1/4
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1/4
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=
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2/4
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=
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1/2
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(One-Quarter)
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(One-Quarter)
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(Two-Quarters)
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(One-Half)
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+
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=
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=
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One-quarter plus one-quarter equals two-quarters, equals one-half
Another example:
5/8
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+
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1/8
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=
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6/8
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=
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3/4
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+
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=
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=
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Five-eighths plus one-eighth equals six-eighths, equals three-quarters
Adding Fractions with Different Denominators
But what about when the denominators (the bottom numbers) are not the same?
Three-eighths plus one-quarter equals ... what?
We must somehow make the denominators the same.
In this case it is easy, because we know that 1/4 is the same as 2/8 :
Three-eighths plus two-eighths equals five-eighths
There are two popular methods to make the denominators the same:
Least Common Denominator or
Common Denominator
(They both work nicely, use the one you prefer.)
Definition of Denominator
When an integer is expressed as a fraction, then there appear two numbers separated by a horizontal line. The denominator is the number that appears at the bottom of the horizontal line, whereas the number above the line is the numerator. It is not necessary that only numerical values are expressed in the numerator and denominator form, instead, the variables are also expressed in the same form such as x/y, p/q, m/n, etc., where y, q, and n are the denominators respectively.
A fraction consists of two numbers. Symbolically it is represented by two numbers separated by a horizontal line (–) or slash line (/). The number above the line is the numerator, and the number below the line is the denominator. The term denominator is widely used in ratio and proportion concept.
In the above figure, 4, 2, and 4 are the denominators of 1/4, 1/2, and 3/4 respectively.
The denominator value should not be zero. Because, if the value of the denominator is zero, the fraction value should be undefined. For example, 5/0 is a fraction, which is undefined as the denominator value is zero.
Denominator and Numerator
The denominator indicates the number of equal parts in which the whole thing has to be divided.
The numerator indicates the number of divisions selected out of the total number of equal parts.
This would be better explained with the help of an Example.
3/4 is a fraction in which the denominator 4 represents that 4 equal divisions have to be made.
3 parts selected out of 4 equal parts created out from 1 circle can be represented as 3/4.
Diagrammatic representation of ¾ is as follows:
The diagram clearly shows three equal parts taken out when the whole circle is divided into four equal parts.
What is the Common Denominator?
When two fractions have the same value in the denominator then they are common. They are also called like and unlike fractions based on the similarity between the denominators. Suppose when we perform the arithmetic operations such as addition and subtraction, then the denominator of the fractions should be common or equal. But fractions can be multiplied or divided even though the denominators of the fractions are not the same or common. Let us see some examples here;
1/2 +3/2 = (1+3)/2 = 4/2 = 2
4/7 – 2/7 = (4-2)/7 = 2/7
1/2 x 1/3 = (1 x 1)/(2 x 3) = 1/6
4/5 ÷ 3/7 = 4/5 x 7/3 = (4 x 7)/(5 x 3) = 28/15
Least Common Denominator(LCD)
The least common denominator of two or more non-zero denominators is the smallest whole number that is divisible by each of the denominators.
Frequently Asked Questions on Denominator What is the difference between numerator and denominator?
In a fraction, the top number is called the numerator and the bottom number is called the denominator. For example, ⅘ is a fraction. Here, 4 is the numerator and 5 is the denominator. Similarly, the numerator defines how many parts we have and the bottom number represents how many equal parts the object is divided into.
Can a denominator value be zero?
The denominator value of the fraction cannot be negative, because the fraction value becomes undefined if we have zero in the denominator of a fraction.
What is meant by the common denominator?
If two or more fractions contain the same bottom number, it is considered as the common denominator. We can add or subtract fractions directly if the fractions have a common denominator. For instance, ⅔ and 4/3 are the two fractions, and the common denominator is 3.
What does the denominator represent?
In a fraction, the denominator represents how many equal parts the object/item is divided into, whereas the numerator represents how many parts we have.
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