You ran 1 3/4 + 23 = 24 3/4 km in total.
Monday: You ran 1 ¾ km, which can be written as 1 + ¾ = 7/4 km.
Tuesday: You ran 23 km.
Now, to find the total distance, we simply add the distances from both days:
Total distance = Distance on Monday + Distance on Tuesday
Total distance = 7/4 km + 23 km
To add these numbers easily, we can first convert the mixed number (7/4) to a whole number and a fraction with the same denominator (23) as the other number. To do this, we multiply the whole part of the mixed number (7) by the denominator of the fractional part (4) and add the numerator (7) to get:
7/4 km = (7 * 4 + 7) / 4 km = 35/4 km
Now, we can add the distances:
Total distance = 35/4 km + 23 km
The easiest way to add these fractions is to find a common denominator, which in this case is the least common multiple of 4 and 23. The LCM of 4 and 23 is 92.
To get 92 in the denominator of the first fraction, we multiply it by 23/23:
35/4 km * 23/23 = 805/92 km
Now, we can add the fractions:
Total distance = 805/92 km + 23 * 23/92 km
Total distance = 805/92 km + 529/92 km
Total distance = 1334/92 km
Therefore, you ran a total of 1334/92 km, which is equal to 14 54/92 km.