Find equivalent fractions with common denominator and order form least to greatest: 2/3, 1/2, 5/12
The common denominator for the fractions is 12.
2/3 = 8/12 etc.
Convert the others to twelfths also, and arrange in order of increasing numerators.
To find equivalent fractions with a common denominator, you need to determine the least common multiple (LCM) of the denominators involved. Once you have the LCM, you can convert each fraction to an equivalent fraction with that denominator.
In this case, the denominators are 3, 2, and 12. To find the LCM, you can use either the prime factorization method or the listing method.
Prime factorization method:
- The prime factors of 3 are 3.
- The prime factors of 2 are 2.
- The prime factors of 12 are 2, 2, and 3.
To find the LCM:
- Take the highest power of each prime factor that appears in any of the numbers.
- Multiply them together.
In this case, we have 2^2 * 3 = 12. Therefore, the LCM of 3, 2, and 12 is 12.
Now, let's convert each fraction to an equivalent fraction with a denominator of 12:
1. For 2/3:
- Multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 12.
- (2/3) * (4/4) = 8/12
2. For 1/2:
- Multiply both the numerator and denominator by 6 to get an equivalent fraction with a denominator of 12.
- (1/2) * (6/6) = 6/12
3. For 5/12:
- Since the denominator is already 12, there is no need for conversion.
Now, we have the following equivalent fractions with a common denominator of 12:
2/3 = 8/12
1/2 = 6/12
5/12 (already in the desired form)
To order these fractions from least to greatest, we can compare their numerators:
6/12 < 8/12 < 5/12
Therefore, the equivalent fractions in least to greatest order are: 1/2, 2/3, 5/12.