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Algebra Fractions

Algebra fractions are proportions

, we said.

To understand fractions you must however work with them.

Moreover, no matter how you see them, all fractions boils down to numbers which you can use for instance by digitizing them in a calculator.

These numbers can have decimals or not, can be comprised from 0 to 1 (= proper fractions such as 1/2) or greater than 1 (= improper fractions like 6/3) and be positive or negative.

Another very common way of naming fractions is using the word percentage and the symbol %.
We are used for instance to "sales" of say 50% in supermarkets (you can also try this example....)

Finally, you write a fraction in the following way

two thirds


A number on TOP and a number at the BOTTOM with a line inbetween.

The top is also called Numerator, the bottom, Denominator but this is not so important. The numerator is a cardinal number word ("1", "2", "3", etc..), the denominator is a ordinal (sequential) number word ( "third", "forth", "fifth", exception is "half" which clearly indicate a part of the whole, a (sub)divided unity).

This way of writing means the following:

two thirds


How many parts
(in our case we are counting 2 parts)

What is being counted
(in our case we are counting "thirds")



  • The numbers must not be considered separately. In other words, "Top" and "Bottom" are not a separate values! 2/3 is ONE number.
  • 1/4 is not greater than 1/2 (because 4 is greater than 2, one might think). Think of a clock. A break of 1/2 hour (i.d. 30 minutes) is not a smaller time slice of a break of 1/4 of an hour(15 minutes) .
  • Finally, although we have not yet started with algebra fractions really, remember that INTUITIVELY 1/2 + 1/2 is not equal to 1/4 (because 2+2=4) but to the whole, i.d. 1. Two halves of an apple make ONE apple. So, 1/2 + 1/2=1.

One more things. Number like those just described, with a "top" and a "bottom" are called rational numbers, because, as we said, they represent a ratio! But these rational number do no only serve as a representation of a ration. Check here to learn more on rational numbers!



Take pictures of "fractions" around you!

Hint: this is a view from my balcony. You can see the roof of the school which my children attend and other houses and trees in the backgrounds.Can you see the "fractions"?

solar panels as an example of fractions

The solar panels can be seen as a set of objects.

solar panels as and example of fractions

A singular solar panel is divided into equal sub-parts, the tiny rectagles.

solar panels subdivided in equal subparts as an example of fractions

There are also other fractions in the main pictures . Which ones?

Answer: sʍopuıʍ ǝɥʇ




A fraction is something difficult to understand

You need to work with them and have a practical experience

All fractions are in the ends numbers (digits) that you can enter in a calculator



Now, you can start working with fractions if you like.

You can do it by using three ways of looking at them, three exercises: as an area model, a linear model or a set model.


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From algebra fractions back to the algebra homework help webpage

Source: Elementary and Middle School Mathematics: Teaching Developmentally (7th Edition)




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