In this publication, we will consider the main property of an ordinary fraction, studied in the school algebra curriculum in grades 6-8. We will also analyze examples of solving problems for a better understanding of the theoretical material.
Formulation of the basic property of a fraction
If the numerator and denominator are multiplied (or divided) by the same natural number, then the value of the fraction will remain unchanged.
=
=
Examples of tasks
Task 1
:
,
,
,
,
.
Solution
are equal
и
, because:
=
, that is, the numerator and denominator are multiplied by the number 5.
=
, i.e. numerator and denominator divided by 2.
Task 2
equals a fraction
.
Solution
may equal
only if its numerator and denominator are multiplied/divided by the same number.
We know the denominators of both fractions, so we can easily find the missing factor (or divisor) by dividing one value by another: 21: 7 = 3.
Therefore, the quotient of dividing the numerators must also be equal to three:
In 3: x = 3
x = 1
.