On Saturday, Cecelia ran 3 3/7 miles. On Sunday, she ran 4 5/6 miles. How much farther did Cecelia run on Sunday than on Saturday?
simplest form
4 5/6 - 3 3/7 = 59/42 = 1 17/42
Change to common denominator.
4 35/42 - 3 18/42 = 1 17/42
To find the difference in distance that Cecelia ran on Sunday compared to Saturday, we need to subtract the distance she ran on Saturday from the distance she ran on Sunday.
On Saturday, Cecelia ran 3 3/7 miles, which is equivalent to the improper fraction (7 * 3 + 3) / 7 = 24/7 miles.
On Sunday, Cecelia ran 4 5/6 miles, which is equivalent to the improper fraction (6 * 4 + 5) / 6 = 29/6 miles.
To find the difference, we subtract the distance on Saturday from the distance on Sunday:
29/6 - 24/7
To add or subtract fractions, they need to have a common denominator. To find the least common denominator (LCD), we need to find the least common multiple (LCM) of the denominators, which are 6 and 7.
Multiples of 6: 6, 12, 18, 24, 30, ...
Multiples of 7: 7, 14, 21, 28, 35, ...
The smallest common multiple of 6 and 7 is 42.
Now we can rewrite the fractions with the common denominator of 42:
(29/6) * (7/7) = 203/42
(24/7) * (6/6) = 144/42
Next, we subtract the fractions:
203/42 - 144/42
To subtract fractions, the denominators must be the same, so we can directly subtract the numerators:
(203 - 144) / 42 = 59/42
The result is the fraction 59/42. However, we can simplify this fraction further. To simplify, we find the greatest common divisor (GCD) of the numerator and denominator, which is 1.
Dividing both the numerator and denominator by the GCD:
59/42 ÷ 1/1 = (59 ÷ 1) / (42 ÷ 1) = 59/42
Therefore, Cecelia ran 59/42 miles farther on Sunday than on Saturday.