Adam wants to compare the fractions 2/5 , 1/6 and 1/3. He wants to order them from least to greatest and rewrite them so they all have the same denominator. Explain how Adam can rewrite the fraction
Oops I made a mistake on the previous question! Sorry about that....
The common denominator is 30.
http://www.coolmath4kids.com/fractions/fractions-04-equivalent-01.html
No problem! Let's correct the mistake and answer your question.
To compare the fractions 2/5, 1/6, and 1/3, Adam can follow these steps:
Step 1: Find a common denominator:
To rewrite the fractions with the same denominator, Adam needs to find a common denominator for 5, 6, and 3. In this case, the least common multiple (LCM) of these three numbers is 30.
Step 2: Rewrite the fractions with the common denominator:
Multiply the numerator and denominator of each fraction by the necessary factors to obtain a denominator of 30:
2/5 x 6/6 = 12/30
1/6 x 5/5 = 5/30
1/3 x 10/10 = 10/30
Step 3: Order the rewritten fractions:
Now that all the fractions have the same denominator, Adam can easily compare them. In this case, the fractions can be ordered from least to greatest as follows:
5/30 < 10/30 < 12/30
So, the correct order from least to greatest is 1/6, 1/3, and 2/5.
No problem! Let's correct the mistake together. To compare the fractions 2/5, 1/6, and 1/3, Adam needs to order them from least to greatest and rewrite them with the same denominator.
To rewrite fractions with the same denominator, Adam needs to find the least common denominator (LCD) of the fractions. The LCD is the least common multiple (LCM) of the denominators.
Step 1: Find the LCD of 5, 6, and 3
The prime factorization of 5 is 5.
The prime factorization of 6 is 2 x 3.
The prime factorization of 3 is 3.
To find the LCD, we can take the highest exponent of each prime factor: 5 x 2 x 3 = 30.
So, the LCD is 30.
Step 2: Rewrite the fractions with the same denominator
To rewrite the fractions with the same denominator of 30, Adam needs to multiply both the numerator and the denominator of each fraction by the same value that would make the denominator become 30.
For 2/5, he needs to multiply both the numerator and denominator by 6 (since 5 multiplied by 6 equals 30).
Result: (2 x 6) / (5 x 6) = 12/30
For 1/6, he needs to multiply both the numerator and denominator by 5 (since 6 multiplied by 5 equals 30).
Result: (1 x 5) / (6 x 5) = 5/30
For 1/3, he needs to multiply both the numerator and denominator by 10 (since 3 multiplied by 10 equals 30).
Result: (1 x 10) / (3 x 10) = 10/30
Now, Adam has rewritten the fractions with the same denominator.
Step 3: Order the fractions from least to greatest
The fractions, with the same denominator of 30, are: 12/30, 5/30, and 10/30.
To order them from least to greatest, Adam can compare their numerators since the denominators are the same.
The fractions in order from least to greatest are: 5/30, 10/30, 12/30.
Therefore, the correct order of the fractions 2/5, 1/6, and 1/3 (revised question) is 5/30, 10/30, 12/30.