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Reduction of ordinary fractions

Lecture



Using fractions, the same part of the whole object can be written in different ways.

The figure shaded half a circle (1/2).

Reduction of ordinary fractions

If the same circle is divided into 4 parts, then the same half of the circle can be represented as 2/4.

If the same circle is divided into 8 parts, then the same half of the circle can be represented as 4/8.

Thus, all these fractions are equal.

Reduction of ordinary fractions

We received fraction 2/4 from fraction 1/2, multiplying its numerator and denominator by 2.

Reduction of ordinary fractions

And to get 4/8, we have multiplied the numerator and denominator 1/2 by 4.

Reduction of ordinary fractions

For convenience, an additional factor is recorded on the sloping line on the right above the fraction.

Reduction of ordinary fractions

Let us return once more to our fractions and write them in a different order.

Reduction of ordinary fractions

A fraction equal to this can be obtained if the numerator and denominator of the fraction are simultaneously divided into the same number that is not equal to zero.

Such a fraction conversion is called fraction reduction .

Fraction reduction is usually written as follows.

The numerator and denominator are crossed out with lines, and next to them the results of dividing (particular) the numerator and denominator by the same number are written.

The number that divided the numerator and denominator, keep in mind.

Reduction of ordinary fractions

In our example, we reduced (that is, we divided both the numerator and the denominator) a fraction for a two, which we kept in mind.

Fraction reduction can be carried out sequentially.

Reduction of ordinary fractions

The main property of the fraction

We formulate the main property of a fraction.

If the numerator and denominator of a fraction are multiplied or divided by the same number that is not equal to zero, then you will get a fraction equal to this one.

We write this property in the form of letter expressions.

Reduction of ordinary fractions where a, b and k are natural numbers.

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Arithmetic

Terms: Arithmetic