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A numerator is the top part of a fraction that expresses a part of a whole. Fractions are simplified into irreducible fractions, and the lowest common denominator is found to compare fractions. The greatest common divisor is used to simplify fractions while maintaining the correct proportions.
A numerator is the top of a fraction, a mathematical expression that expresses a part of a whole. For example, 7/19 is a fraction, with the numerator of that particular fraction being “7”. Similarly, 8/3 is also a fraction. The bottom part of a fraction is known as the denominator, with some people using the term “nominator” to talk about numerators. The numerator describes the number of parts of the whole involved in the fraction.
Fractions can be written with a vertical or horizontal bar, depending on personal taste and convention. In complex equations, fractions are often written with horizontal bars so they’re easy to see. Conventionally, fractions are simplified into what are known as irreducible fractions, so it would be unusual to see a fraction like 3/9, which would be represented as 1/3 instead. The ability to simplify fractions is also important, as it allows people to see the relationship between various fractions and to make equations with fractions. For example, the connection between 8/12 and 3/9 is much easier to see when these fractions are simplified to 2/3 and 1/3.
When people simplify fractions to compare, they start by looking for the least common denominator, the smallest multiple of the denominators involved in the fractions being compared. In the example above, the lowest common denominator is 36, because both 12 and 9 can be multiplied to make 36, 12 three times and nine four times. This example is easy enough to calculate; other fractions can make finding the lowest common denominator much more difficult.
By multiplying the numerator and denominator in the first fraction by three and in the second fraction by four to reach the lowest common denominator while maintaining the correct proportions in the fraction, the fractions could be expressed as 24/36 and 12/36, respectively. These fractions are very complicated, so the next step involves finding the greatest common divisor, the largest number that can be used to divide numerators and denominators while keeping them as integers.
The greatest common divisor in our example appears to be 12. When the numerators and denominators are all divided by 12, the resulting fractions are 2/3 and 1/3. It is important to maintain the relationship between the numerator and denominator, to ensure that the fraction stays the same, which means that any operation performed on a numerator must be performed on a denominator and vice versa. In our example, if someone fails to multiply the numerator by 8/12 when multiplying the denominator, the resulting fraction would be 8/36, a very different fraction than 24/36.
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