Please I need help with math

Question

A driver is monitoring his cars gasoline consumption for 3 weeksweeks.if the car consumes 3 7/8 gasoline the first week 2 5:6 gallons the second week and 2 2/3 gallon the third week what is the average weekly consumption write solution in mixed numbers

Answer 1

The "average weekly consumption" can be thought of as the [Total Fuel Used] / [Total Number of Weeks].

 

The total fuel used is simply the sum of the fuel used in each week.

 

Total Fuel Used (TFU) = 3 7/8 + 2 5/6 + 2 2/3

 

To calculate TFU, let's convert the values to improper fractions:

3 7/8 = (3*8+7)/8 = 31/8

2 5/6 = (2*6+5)/6 = 17/6

2 2/3 = (2*3+2)/3 = 8/3

 

To add together these three improper fractions, we need to find the Least Common Denominator.  Notice that 8, 6, and 3 (the denominators of the above fractions) are all factors of 24.  So we can convert each fraction into one whose denominator is 24.

31/8 * (3/3) = 93/24

17/6 * (4/4) = 68/24

8/3 * (8/8) = 64/24

 

We now add the fractions with the common denominator by adding their numerators.

93/24 + 68/24 + 64/24 = (93 + 68 + 64)/24 = 225/24

 

The above result (225/24) represents the total fuel used.  The Average Weekly Consumption is that number divided by the total number of weeks, which is 3 in this problem.

(225/24)/3 = (225/24) * (1/3) = 225/72

 

That result (225/72) is the average weekly consumption.  But the problem says to write the answer as a mixed fraction.  So we divide 225 by 72:

225/72 = 3 with a remainder of 9

 

Therefore, average weekly consumption is 3 9/72.  But the fractional part of that answer can be reduced.  Notice that 9/72 = 1/8

 

The answer to the problem is therefore 3 1/8.

 

Notice that 3 1/8 is between the maximum (3 7/8) and minimum (2 2/3) of the values stated in the problem.  That gives me confidence that we have found the correct answer.

 

Hope this helps,

Paul

 

Answer 2

Hi Jennifer--

 

First thing to do here is to get all the fraction parts of the mixed numbers to speak the same language--that is, find their common denominator. You need one number that 8, 6, and 3 all go into.

 

That would be 24, right? Now, give all the fraction parts of the mixed numbers the denominator of 24. And whatever you needed to multiply each denominator by to make it 24, multiply that fraction's numerator by the same amount. (For example, your 3 7/8 is going to become 3 21/24.)

 

So now each mixed number's fraction denominator is 24, and you've also multiplied out the numerators accordingly, yes?

 

NOW, to find the average fuel consumption...

 

First, add up all the whole numbers: 3 + 2 + 2 = 7 gallons so far.

 

But we need to think of those 7 wholes as a gigantic pile of little 24ths instead. So multiply 7 wholes x 24 pieces, which gives you

 

168 little pieces, otherwise known as 168 / 24ths...

 

NOW, you have to add on the OTHER 24ths, the ones you made in the fractions themselves. They were 21/24, 20/24, and 16/24, which add up to... 57/24 (don't worry that it's an improper fraction. Right now that's good!)

 

Add 57/24 to 168/24 and you get 225/24. SO,

 

your TOTAL consumption for the 3 weeks is 225/24 gallons. BUT you need to find the per-week average, so you need to divide...

 

225 divided by 3 to get the average number of 24ths...

 

225 / 3 = 75.  SOOO on average, you used 75/24 gallons per week. BUT...

 

You need to simplify AND make this a mixed number. SO... divide the numerator and the denominator by their greatest common factor, which is just 3, and you get 25/8

 

Then do 25 / 8 = ??  this will give you a mixed number, which is your weekly average--and you answer. :-)

 

(Pssst... it's 3 1/8.)

 

I know this is long--hope it's helpful, too!

 

Matt in New York