In January, Jeff filled his car with 11 1/2 gallons of gas the first week, 13 1/3 gallons the second week, 12 1/4 gallons the third week, and 10 1/6 gallons the fourth week of January. How many gallons of gas did he buy in January?
After you added these amounts together, what answer did you get?
11 1/2 + 13 1/3 + 12 1/4 + 10 1/6 = 23/2 + 40/3 + 49/4 + 61/6 = ?. LCD = 12.
To find the total number of gallons of gas Jeff bought in January, we need to add up the amount of gas he bought each week.
First, let's convert all the mixed fractions to improper fractions.
11 1/2 gallons is the same as 23/2 gallons.
13 1/3 gallons is the same as 40/3 gallons.
12 1/4 gallons is the same as 49/4 gallons.
10 1/6 gallons is the same as 61/6 gallons.
Now, let's add up all the fractions:
23/2 + 40/3 + 49/4 + 61/6
To add these fractions together, we need to find a common denominator. The common denominator for 2, 3, 4, and 6 is 12.
Multiplying the numerator and denominator of the first fraction by 6/6, we get:
(23/2) * (6/6) = 138/12
Multiplying the numerator and denominator of the second fraction by 4/4, we get:
(40/3) * (4/4) = 160/12
Multiplying the numerator and denominator of the third fraction by 3/3, we get:
(49/4) * (3/3) = 147/12
Finally, multiplying the numerator and denominator of the fourth fraction by 2/2, we get:
(61/6) * (2/2) = 122/12
Now, we can add up all the fractions:
138/12 + 160/12 + 147/12 + 122/12 = 567/12
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
567/12 ÷ 3/3 = 189/4
Therefore, Jeff bought 189/4 gallons of gas in January.