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Fractions

    Simplest Form of a Fraction

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6th class > Fractions > Simplest Form of a Fraction

Simplest Form of a Fraction

Given the fraction 3654, let us try to get an equivalent fraction in which the numerator and the denominator have no common factor except 1.

How do we do it?

We see that both 36 and 54 are divisible by .
3654 = 36 ÷ 254 ÷ 2 = .
But 18 and 27 also have common factors other than one.
The common factors are 1, 3, 9; the highest is .
Therefore, 1827 = 18 ÷ 927 ÷ 9 =
Now 2 and 3 have no common factor except 1; we say that the fraction is in the simplest form.

A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.

The shortest way to find the equivalent fraction in the simplest form is to find the HCF of the numerator and denominator, and then divide both of them by the HCF.

Let's try the more examples.

Try these

1. Write the simplest form of :

1575=

  • It can be observed that is the highest common factor of 15 and 75.
  • Divide the numerator and denominator by the highest common factor 15.
  • Hence, we get the fraction is .

1672=

  • It can be observed that is the highest common factor of 16 and 72.
  • Divide the numerator and denominator by the common factor 8.
  • Hence, we get the fraction is .

1751=

  • It can be observed that is the highest common factor of 17 and 51.
  • Divide the numerator and denominator by the common factor 17.
  • Therefore, we get the fraction is .

Let's see simplest form.

2. Is 4964 in its simplest form?

is 4964 in its simplest form ?
, 4964 is in its simplest form.
because 49 and 64 has no common divisor.

EXERCISE