Can you explain how to do the following problems?
1. Order these fractions from Greatest to least. 3/12, 5/8, 1/4, 7/8, 4/16
work: find least common denominator
3/12 = 12/48, 5/8 = 30/48, 1/4 = 12/48, 7/8 = 42/48
answer = 7/8, 5/8, since 3/12 and 1/4 are the same, which would be greater?
2.Kelsie worked 172 minutes on homework this week. Her teacher estimates it should take 2 3/4 hours for the work. How much more or less did Kelsie work?
work: 172/60 = 2.86 hours
2.86 - 2.75 = 11 minutes less?
3. A line plot shows 10 beakers measured in Liters. If the liquid is distributed evenly, how much liquid is in each beaker if total liquid is 3 7/8 (three & seven eighths)Liters?
work: (3 7/8)/10 = (3 7/8 * 1/10) = 31/80 = .3875
1. is correct. It doesn't make any difference which 1/4 you put first.
2. I get that Kelsie worked about 7 minutes more.
2.87 - 2.75 = 0.12 hour = 7.2 minutes
3. is correct.
Thanks! I see what I did wrong for #2.
You're welcome.
Sure! Here's the explanation for each problem:
1. To order the fractions from greatest to least (3/12, 5/8, 1/4, 7/8, 4/16), you need to find a common denominator. The least common denominator is 48, so you need to convert each fraction to have a denominator of 48.
To do this, multiply the numerator and denominator of each fraction by the necessary factor to get to 48. For example, for 3/12, multiply both the numerator and denominator by 4 to get 12/48. Do this for all the fractions.
After converting, the fractions become: 3/12 = 12/48, 5/8 = 30/48, 1/4 = 12/48, 7/8 = 42/48, and 4/16 = 12/48.
Now you can compare the numerators: 42/48 is the greatest, followed by 30/48. Since 12/48 and 12/48 are the same, you need to determine which is greater by comparing their numerators. Therefore, the order from greatest to least is 7/8, 5/8, 3/12, 4/16.
2. Kelsie worked 172 minutes on homework this week, and her teacher estimates it should take 2 3/4 hours for the work. To find out how much more or less Kelsie worked, you need to convert the minutes worked to hours.
Divide 172 minutes by 60 to get the equivalent in hours:
172/60 = 2.86 hours
Then, subtract the estimated time (2 3/4 hours) from the actual time worked (2.86 hours):
2.86 - 2.75 = 0.11 hours
Since there are 60 minutes in an hour, multiply 0.11 by 60 to get the difference in minutes:
0.11 * 60 = 6.6 minutes
Therefore, Kelsie worked 6.6 minutes less than her teacher's estimate.
3. In a line plot, you have 10 beakers measured in liters and a total liquid measurement of 3 7/8 liters. To find out how much liquid is in each beaker if it is distributed evenly, divide the total liquid by the number of beakers.
Convert the mixed number (3 7/8) to an improper fraction by multiplying the whole number (3) by the denominator (8), then adding the numerator (7):
3 * 8 + 7 = 24 + 7 = 31
Combine the numerator (31) with the denominator (8) to get the improper fraction:
31/8
To divide by 10, multiply the numerator (31) by 1/10:
31/8 * 1/10 = 31/80
So, each beaker would contain 31/80 liters of liquid when evenly distributed.