Which fraction is in its lowest terms?
Select one:
a. $3 / 4$
b. $10 / 12$
c. $2 / 2$
d. $6 / 8$
Answer (2)
Determine the greatest common divisor (GCD) of the numerator and denominator for each fraction.
For 3/4 , the g cd ( 3 , 4 ) = 1 .
For 10/12 , the g cd ( 10 , 12 ) = 2 .
For 2/2 , the g cd ( 2 , 2 ) = 2 .
For 6/8 , the g cd ( 6 , 8 ) = 2 .
The fraction with a GCD of 1 is in its lowest terms: 3/4 .
Explanation
Understanding Lowest Terms We need to determine which fraction is in its lowest terms. A fraction is in its lowest terms if the greatest common divisor (GCD) of the numerator and the denominator is 1. We will find the GCD for each fraction.
Analyzing Fraction a For fraction a. 3/4 , the GCD of 3 and 4 is 1.
Analyzing Fraction b For fraction b. 10/12 , the GCD of 10 and 12 is 2.
Analyzing Fraction c For fraction c. 2/2 , the GCD of 2 and 2 is 2.
Analyzing Fraction d For fraction d. 6/8 , the GCD of 6 and 8 is 2.
Identifying the Fraction in Lowest Terms Since the GCD of 3 and 4 is 1, the fraction 3/4 is in its lowest terms.
Final Answer Therefore, the fraction in its lowest terms is 3/4 .
Examples
In real life, simplifying fractions is useful when you want to divide something equally. For example, if you have a pizza cut into 8 slices and you want to give half of it to your friend, you would give them 4/8 of the pizza. Simplifying this fraction, 4/8 , to its lowest terms, 1/2 , makes it easier to understand that your friend is getting half of the pizza. This concept is also useful in cooking, where recipes often involve fractions, and simplifying them can make measuring ingredients easier.
The fraction that is in its lowest terms is 4 3 . This is because its greatest common divisor is 1, meaning it cannot be simplified further. The other fractions either have common factors and can be simplified or equal to 1.
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