What is the LCD of 1/3 and 3/4 ?
The Correct Answer and Explanation is :
To find the least common denominator (LCD) of the fractions ( \frac{1}{3} ) and ( \frac{3}{4} ), we need to find the least common multiple (LCM) of the denominators 3 and 4.
Steps to find the LCD:
- List the multiples of each denominator:
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, …
- Multiples of 4: 4, 8, 12, 16, 20, 24, …
- Identify the least common multiple:
The smallest multiple common to both 3 and 4 is 12. Therefore, the LCD of 3 and 4 is 12.
Converting the fractions to have the same denominator:
- For ( \frac{1}{3} ), we need to convert it to a fraction with a denominator of 12. To do this, we multiply both the numerator and denominator by 4 (since ( 3 \times 4 = 12 )): [
\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
] - For ( \frac{3}{4} ), we need to convert it to a fraction with a denominator of 12. To do this, we multiply both the numerator and denominator by 3 (since ( 4 \times 3 = 12 )): [
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
]
Conclusion:
- The LCD of ( \frac{1}{3} ) and ( \frac{3}{4} ) is 12.
- The fractions ( \frac{1}{3} ) and ( \frac{3}{4} ) can be rewritten with a denominator of 12 as ( \frac{4}{12} ) and ( \frac{9}{12} ), respectively.
This process of finding the LCD and converting the fractions allows us to compare or perform operations like addition or subtraction on fractions with different denominators.