May 21, 2024

What Are Lowest Term Fractions | How to reduce fraction to lowest terms fraction

What Are Lowest Term Fractions ?

A “Lowest term Fraction,” also known as a “reduced fraction” or “simplest form fraction,” is a way of expressing a fraction in its most straightforward and smallest form. This means that the numerator   and the denominator of the fraction have no common factors other than 1.  For example \frac{2}{3}

, \frac{2}{7} . \frac{5}{3}  etc. are lowest term fraction.

A fraction in lowest terms is also termed as a fraction in the simplest form.

Lowest term fractions make the fraction  easier to compare, add, subtract, multiply, and divide . It’s a fundamental concept in basic arithmetic and is used extensively in more advanced mathematics and everyday situations involving ratios and proportions.

Reduce the fraction to lowest terms

If the numerator and denominator of a fraction are relatively prime numbers, that is, if they have no factors in common besides one, the fraction is said to be written in the lowest term. In other words, if the HCF of the numerator and denominator is 1, the fraction is said to be in its lowest terms or form.

Reducing fractions to lowest terms refers to simplifying the fractions such that the numerator and denominator become coprime (relatively prime).

The shortest way to find the lowest term fraction  is, find the HCF of the numerator and denominator, and then divide
both of them by the HCF.
Example: Consider   \frac{36}{24}. The HCF of 36 and 24 is 12.

Therefore, \frac{36}{24}\frac{36\div 12}{24\div 12}   =  \frac{3}{2}

The fraction \frac{3}{2} is in the lowest form. Thus, HCF helps us to reduce a fraction to its lowest form.

Another way to reduce the fractions in lowest terms is dividing both numerator and denominator by their  Common Factors. Continue this process until the only common factor is 1.  This method is simple but time-consuming. It uses several steps to get to the answer.

To check the given fraction is in lowest term or not , find the HCF of numerator and denominator. If the HCF is 1 , then the given fraction is in its lowest term. 

Example :  Reduce \frac{48}{60} in lowest terms.

lowest term fraction    ( 6 is factor of both 48 and 60 )

\frac{8}{10}= \frac{8\div 2}{10\div 2}= \frac{4}{5}    ( 2 is factor of both 8 and 10 )

Since, 1 is the only common factor between 4 and 5.  Hence the fraction  \frac{4}{5}  is in its lowest term.

Reducing fractions to lowest terms examples(Lowest term fraction examples)

(i) Reduce the  fraction \frac{105}{70} to their lowest term.
Solution:
The HCF of 105 and 70 is 35.

Therefore, \frac{105}{70}\frac{105\div 35}{70\div 35}   =  \frac{3}{2}

The fraction \frac{3}{2} is in the lowest form.

(ii) state \frac{2}{5}=\frac{10}{15} is true or false ? 
Solution: The HCF of 10 and 15 is 5.

Therefore, \frac{10}{15}=\frac{10\div 5}{15\div 5} = \frac{2}{3}

Hence the given statement is false .

(iii)  state \frac{35}{42}=\frac{5}{6} is true or false ?
Solution: 
The HCF of 35 and 42 is 7.

Therefore, \frac{35}{42}=\frac{35\div 7}{42\div 7} = \frac{5}{6}

Hence the given statement is true .

(iv) Is  \frac{49}{64} in lowest term ?
Solution :
Since, 1 is the only common factor between 49 and 64. The HCF  of 49 and 64 is 1.
Hence the fraction  \frac{49}{64} is in its lowest term.

(v) Reduce the given fractions  to their lowest terms:

(a)\frac{8}{10}

\frac{8}{10}=\frac{8\div 2}{10\div 2}=\frac{4}{5}

(b)  \frac{50}{75} 

\frac{50}{75}=\frac{50\div 25}{75\div 25}=\frac{2}{3}

(c)  \frac{18}{81}

\frac{18}{81}=\frac{18\div 9}{81\div 9}=\frac{2}{9}

(d) \frac{40}{120} 

\frac{40}{120}=\frac{40\div 40}{120\div 40}=\frac{1}{3}

(e) \frac{105}{70}

\frac{105}{70}=\frac{105\div 35}{70\div 35}=\frac{3}{2}

Conclusion :

If the numerator and denominator of a fraction are relatively prime numbers, that is, if they have no factors in common besides one, the fraction is said to be lowest term fraction. In other words, if the HCF of the numerator and denominator is 1, the fraction is said to be in its lowest terms or form.  Finding the HCF of the numerator and denominator and dividing both of them by it is the fastest technique to determine the fraction with the lowest term.

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