Prompt. Use equivalent fractions to order therse fractions from least to greatest: 2/3,1/2, 4/12, 5/6. Explain the steps you took to find your answer.
What don't you understand about this problem?
the common denominator for all of the fractions would be six.
as long as you multiply or divide the top and the bottom with the same number you do not break any math rules.
2/3=(2*2)/(3*2)=4/6
1/2=(1*3)/(2*3)=3/6
4/12=(4/2)/(12/2)=2/6
and 5/6=5/6
order the common fractions with the lowest to highest numerator.
2/6
3/6
4/6
5/6
To order fractions from least to greatest, we need to find a common denominator for all the fractions. This way, we can compare the numerators and determine their relative values.
Step 1: Find the common denominator
To find the common denominator, we look for the least common multiple (LCM) of the denominators of the given fractions. In this case, the denominators are 3, 2, 12, and 6. The LCM of these numbers is 12.
Step 2: Convert the fractions to have the same denominator
Now, we need to convert each fraction to an equivalent fraction with a denominator of 12. We do this by multiplying both the numerator and denominator of each fraction by a number that would make the denominator equal to 12.
Let's convert each fraction:
- 2/3: Since the denominator is already 3, we need to multiply both the numerator and denominator by 4 to make the denominator 12. So, 2/3 becomes 8/12.
- 1/2: We need to multiply both the numerator and denominator by 6 to get the denominator 12. So, 1/2 becomes 6/12.
- 4/12: The denominator is already 12, so there is no need for any conversion.
- 5/6: We need to multiply both the numerator and denominator by 2 to get the denominator 12. So, 5/6 becomes 10/12.
Now, our new fractions are: 8/12, 6/12, 4/12, and 10/12.
Step 3: Order the fractions
Now that all the fractions have the same denominator, we can compare their numerators to determine their order.
The fractions from least to greatest are:
- 4/12 (which is equivalent to 1/3)
- 6/12 (which is equivalent to 1/2)
- 8/12 (which is equivalent to 2/3)
- 10/12 (which is equivalent to 5/6)
Therefore, the fractions in order from least to greatest are: 1/3 (or 4/12), 1/2 (or 6/12), 2/3 (or 8/12), and 5/6 (or 10/12).