Ordering from least to greatest
1/9, 2/15, 3/21
You can do this two ways.
1. Change these fractions to equivalent fractions with a common denominator of 450.
or
2. Change these fractions to equivalent decimals by dividing the numerator by the denominator.
Let's line up these fractions from least to greatest, just like organizing a clown parade.
First, we have the clowns preparing the circus snacks. In this case, the snacks are fractions.
The first clown brings 1/9 slices of pie for everyone. That's a generous offer, but still the smallest portion.
Next up is the clown with 2/15 slices. They're being considerate but still not as much as the previous clown in terms of portion size.
Finally, the last clown in line brings 3/21 slices, and they're trying their best to share, but it's still the biggest portion compared to the others.
So, in our clown parade-style ordering, from least to greatest, we have:
1/9, 2/15, 3/21
To order the fractions from least to greatest, we can compare their values by finding the least common denominator (LCD) and converting them to a common denominator.
The least common denominator of 9, 15, and 21 is 63.
1/9 = (1/9) * (7/7) = 7/63
2/15 = (2/15) * (9/9) = 18/135 = 2/15
3/21 = (3/21) * (3/3) = 9/63
Now, we can see that the fractions in order from least to greatest are:
7/63, 2/15, 9/63
To order the given fractions from least to greatest, we can compare their values by finding a common denominator and then comparing the numerators.
Step 1: Find a common denominator
The denominators in the given fractions are 9, 15, and 21. To find a common denominator, we need to find the least common multiple (LCM) of these numbers.
Factors of 9: 1, 3, 9
Factors of 15: 1, 3, 5, 15
Factors of 21: 1, 3, 7, 21
The least common multiple (LCM) of 9, 15, and 21 is 3 x 5 x 7 = 105. Therefore, we can rewrite the fractions with a common denominator of 105.
Step 2: Rewrite the fractions with the common denominator
1/9 = (1/9) x (105/105) = 105/945
2/15 = (2/15) x (7/7) = 14/105
3/21 = (3/21) x (5/5) = 15/105
Now, we have the fractions with a common denominator:
105/945, 14/105, 15/105
Step 3: Compare the numerators
Since the denominators are the same, we can directly compare the numerators to determine the order.
105/945 < 14/105 < 15/105
Therefore, the correct order from least to greatest is:
1/9 < 2/15 < 3/21