find equivalent fraction with a common
denominator 2/3,1/2,5/12
60 is the smallest number evenly divisible by 3, 2, and 12
2/3 = 40/60
1/2 = ?/60
5/12 = ?/60
To find equivalent fractions with a common denominator for the fractions 2/3, 1/2, and 5/12, you need to determine the least common denominator (LCD) for all the fractions and then convert each fraction to that denominator.
Step 1: Find the least common denominator (LCD)
To find the LCD, you need to identify the least common multiple (LCM) of the denominators.
For the given fractions:
Denominator of 2/3 = 3
Denominator of 1/2 = 2
Denominator of 5/12 = 12
The multiples of each denominator are:
Multiples of 3: 3, 6, 9, 12, 15, 18, ...
Multiples of 2: 2, 4, 6, 8, 10, 12, ...
Multiples of 12: 12, 24, 36, ...
From the multiples, you can see that the LCM of 3, 2, and 12 is 12. Therefore, the least common denominator (LCD) for the fractions 2/3, 1/2, and 5/12 is 12.
Step 2: Convert each fraction to the LCD
Now that you have the LCD, you can convert each fraction to that denominator.
For 2/3:
To convert the fraction 2/3 to the denominator 12, multiply both the numerator and denominator by a factor that equals the LCD divided by the current denominator. In this case, the current denominator is 3 and the LCD is 12.
Multiply the numerator (2) by 4 and multiply the denominator (3) by 4:
2/3 * 4/4 = 8/12
So, the equivalent fraction of 2/3 with a denominator of 12 is 8/12.
For 1/2:
To convert the fraction 1/2 to the denominator 12, follow the same process as above.
Multiply the numerator (1) by 6 and multiply the denominator (2) by 6:
1/2 * 6/6 = 6/12
Therefore, the equivalent fraction of 1/2 with a denominator of 12 is 6/12.
For 5/12:
Since the fraction 5/12 already has a denominator of 12, it is already in the desired form. Therefore, there is no need to convert it.
So, the equivalent fractions with a common denominator of 12 are:
2/3 is equivalent to 8/12
1/2 is equivalent to 6/12
5/12 remains the same since it is already in the desired form.