Answer:
To write equivalent fractions with a common denominator, we need to find the least common multiple (LCM) of the denominators of the fractions and then write each fraction with the LCM as the denominator. Here's a step by step guide:
1. To find the LCM of 3 and 6, we list the multiples of each number and find the smallest one that is common to both:
Multiples of 3: 3, 6, 9, 12, 15, 18, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
The LCM of 3 and 6 is 6, so we write 2/3 and 3/6 with 6 as the denominator:
2/3 = 4/6 and 3/6 = 1/2
2. To find the LCM of 4 and 12, we list the multiples of each number and find the smallest one that is common to both:
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
The LCM of 4 and 12 is 12, so we write 3/4 and 5/12 with 12 as the denominator:
3/4 = 9/12 and 5/12 = 5/12
3. To find the LCM of 5 and 10, we list the multiples of each number and find the smallest one that is common to both:
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
The LCM of 5 and 10 is 10, so we write 3/5 and 7/10 with 10 as the denominator:
3/5 = 6/10 and 7/10 = 7/10
You can use this process to find the LCM and write equivalent fractions with a common denominator for the rest of the problems.