Final answer:
The correct answer are options b and d. The pairs of fractions that have a least common denominator of 45 are (2/3, 7/15) and (3/45, 3/15). We identify the LCD by finding the smallest number that the denominators of each pair can be multiplied into without a remainder. Options b and d meet this criterion, with their denominators being factors of 45.
Step-by-step explanation:
Least common denominator (LCD) is an important concept in mathematics, specifically when working with fractions. To find which pairs of fractions have an LCD of 45, we need to examine the denominators of each fraction pair and determine if they can all be expressed as equivalent fractions with a denominator of 45.
- Option a: 1/9 and 3/5 have denominators 9 and 5, respectively. Since their LCD needs to be the smallest number that both 9 and 5 can be multiplied into without remainder, and 45 is that number (9*5), this pair does not have an LCD of 45 as they share no common factors.
- Option b: 2/3 and 7/15 have denominators 3 and 15, respectively. The number 3 can be multiplied by 15 to get 45, and 15 is already a factor of 45, thus the LCD of this pair is 45.
- Option c: 5/6 and 3/45 have denominators 6 and 45, respectively. The number 6 is not a factor of 45, thus they do not share an LCD of 45.
- Option d: 3/45 and 3/15 have denominators 45 and 15, respectively. Since 15 can be multiplied by 3 to obtain 45, the LCD for this pair is 45.
Therefore, the pairs of fractions that have a least common denominator of 45 are Option b (2/3, 7/15) and Option d (3/45, 3/15).