Part A:
Order the fractions from least to greatest, show steps
To order fractions from least to greatest, we first need to find a common denominator for all the fractions.
Let's order the fractions 1/4, 2/5, 3/6, and 5/8 from least to greatest.
1/4, 2/5, 3/6, 5/8
First, find a common denominator for all the fractions. The least common multiple of the denominators 4, 5, 6, and 8 is 40.
Now, convert each fraction to have a denominator of 40:
1/4 = 10/40
2/5 = 16/40
3/6 = 20/40
5/8 = 25/40
Now, the fractions in order from least to greatest are:
1/4 = 10/40
2/5 = 16/40
3/6 = 20/40
5/8 = 25/40
Therefore, the fractions in order from least to greatest are:
1/4, 2/5, 3/6, 5/8
56/9, 4/5, 3 1/4, 9/10,14/6
To order the fractions 56/9, 4/5, 3 1/4, 9/10, and 14/6 from least to greatest, we must first convert any mixed numbers to improper fractions.
Convert 3 1/4 to an improper fraction:
3 1/4 = 3 + 1/4 = 12/4 + 1/4 = 13/4
Now we have the fractions: 56/9, 4/5, 13/4, 9/10, 14/6
Next, let's find a common denominator for all the fractions. The least common multiple of the denominators 9, 5, 4, 10, and 6 is 180.
Now, convert each fraction to have a denominator of 180:
56/9 = 1120/180
4/5 = 144/180
13/4 = 585/180
9/10 = 162/180
14/6 = 420/180
Now, the fractions in order from least to greatest are:
4/5 = 144/180
9/10 = 162/180
14/6 = 420/180
56/9 = 1120/180
13/4 = 585/180
Therefore, the fractions in order from least to greatest are:
4/5, 9/10, 14/6, 56/9, 13/4