Fractions in Lowest Terms

Fractions in lowest terms are discussed in the following steps in order to reduce a fraction.

In order to reduce a fraction to its lowest terms the following steps are:

Step I: Find the HCF (highest common factor) of the numerator (top number) and denominator (bottom number).

Step II: Divide both the numerator and denominator by HCF (highest common factor) obtained in step I to get the equivalent fraction in the lowest terms or in the simplest form.

For Example:

1. Reduce each of the following fractions in lowest term:

(i) ¹⁵/₃₅

The factors of 15 are 1, 3, 5 and 15.

The factors of 35 are 1, 5, 7 and 35.

The common factors of 15 and 35 are 1 and 5.

Therefore, HCF (highest common factor) of 15 and 35 is 5.

Now, 15/35 = (15 ÷ 5)/(35 ÷ 5)

[Dividing numerator and denominator by the HCF (highest common factor) of 15 and 35 is 5].

= ³/₇.

(ii) ⁴⁸/₆₀

The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 24 and 48.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

The common factors of 48 and 60 are 1, 2, 3, 4, 6 and 12.

Therefore, HCF (highest common factor) of 48 and 60 is 12.

Now, 48/60 = (48 ÷ 12)/(60 ÷ 12)

[Dividing numerator and denominator by the HCF (highest common factor) of 48 and 60 is 12].

= ⁴/₅.

(iii) ¹²⁶/₉₀

Let us first compute the HCF (highest common factor) of 126 and 90.

$Fractions in Lowest Terms$

Therefore, HCF (highest common factor) of 126 and 90 is 2 × 3 × 3 = 18.

Now, 126/90 = (126 ÷ 18)/(90 ÷ 18)

[Dividing numerator and denominator by the HCF (highest common factor) of 126 and 90 is 18].

= ⁷/₅

2. Is ¹⁶⁹/₂₈₉ in its simplest form?

We know that a fraction is in lowest term or in simplest form, if the HCF (highest common factor) of numerator (top number) and denominator (bottom number) is 1.

Here, the HCF (highest common factor) of 169 and 289 is 1.

Hence, the fraction 169/289 is in its simplest form.