Express the following as rational numbers with denominator 3: a. -46/69 b. 94/141 c. -72/108
Answer (1)
To express fractions with a denominator of 3 , you need to convert each of the given fractions to have a common denominator of 3 . This can involve simplifying the fraction first and then finding an equivalent fraction:
Simplify the Fraction -46/69: To simplify − 69 46 , identify the greatest common divisor (GCD) of 46 and 69 . The GCD is 23 . Simplifying, we divide both numerator and denominator by 23 :
− 69 46 = − 69 ÷ 23 46 ÷ 23 = − 3 2
The fraction − 3 2 already has the denominator of 3 .
Simplify the Fraction 94/141: Determine the GCD of 94 and 141 . The GCD is 47 . Simplifying by dividing both the numerator and the denominator by 47 :
141 94 = 141 ÷ 47 94 ÷ 47 = 3 2
The fraction 3 2 already has the denominator of 3 .
Simplify the Fraction -72/108: Determine the GCD of 72 and 108 . The GCD is 36 . Simplifying by dividing both the numerator and the denominator by 36 :
− 108 72 = − 108 ÷ 36 72 ÷ 36 = − 3 2
The fraction − 3 2 already has the denominator of 3 .
Each of these fractions simplifies to a fraction with a denominator of 3 , which was our goal. If you have any more questions or need further explanation, feel free to ask!
