Basics Of Fractions

Last Updated on April 11, 2024.

When we deal with fractions, please realize that every fraction has a numerator and a denominator.

And the numerator is on top, while the denominator is on the bottom.

This lesson is provided by Onsego GED Prep.

Video Transcription

Let’s take a look at the basics of fractions. Again, fractions are made up of two \((2)\) numbers, two integers, one on top, one on the bottom, and they’re separated by a line. You can also see fractions written as numbers divided by a slash.

In those cases, the numbers to the left are the “top” while the numbers on the “bottom” are on the right. Top numbers are called the numerators, while the bottom numbers are called the denominators.

The top numbers represent the number of segments that you have while the bottom numbers represent the number of equal segments there could be. You can also see a whole number placed to the left of the fraction.

If you’re dealing with that kind of big number, those fractions are called mixed numbers. Mixed numbers are whole numbers with fractions.

Here are some examples:

\( \frac{4}{9}\) \( (\frac{four}{ninth})\)

 

• We have four \((4)\) segments.

• We could have nine\((9)\) equal parts.

• Four \((4)\) is the numerator here, and nine \((9)\) is the denominator here.

\(3\, \frac{4}{9}\) \(\,(three \,and \,\frac{four}{ninth},\, mixed \,number)\)

 

• We have three\((3)\) whole objects, plus

• We have four \((4)\) segments of a whole object.

• We could have nine \((9)\) equal segments of that whole object.

• \(3\) (three) is the whole number, \(4\) (four) is the numerator, and \(9\) (nine) is the denominator.

Parts of a Whole

A fraction is a number that’s representing a number of equal-sized segments. If we’re talking about halves, that means that we took some object and then split it into two \((2)\) equal parts.

When we’re working with thirds, then we have three \((3)\) equal segments. Any number, or any object, may be broken into whatever number of equal segments. You may come across a fraction problem that has, for example, one thousand seventy-thirds.

Finding Common Factors

With a lot of functions with fractions, you will need to search for common factors. Often, you may have to simplify the fraction like turning \( \frac{6}{8}\) into \( \frac{3}{4}\). Then, you must know that two \((2)\) is actually a common factor for the fraction’s numerator and the denominator.

You may be using factors when adding or subtracting fractions. Adding these fractions \( \frac{3}{5}\) and \( \frac{7}{10}\) may cause some difficulty, but when you’re multiplying the first value \( (\frac{3}{5})\)by factor two \((2)\), you’ll end with \( \frac{6}{10}\).

Now, is adding \( \frac{6}{10}\) and \( \frac{7}{10}\) difficult?

That is as easy as pie. The correct answer is the improper fraction of \( \frac{13}{10}\) (or the mixed number of \(1\, \frac{3}{10}\)).

A factor is a natural number that may evenly divide into both numerators and denominators.

A fraction like \( \frac{17}{25}\) doesn’t have any common factors at all, and it can in no way be reduced.

A fraction like \( \frac{16}{24}\), though, is totally different.

In \( \frac{16}{24}\), the numerator and the denominator are sharing the factors \(2; \,4;\,\) and \(8\).

So reducing that fraction will result in \( \frac{2}{3}\). You just have divided both the top and the bottom value by \(8\). If you are using common factors more frequently, you’ll get used to them.