On Friday Naomi walked 3/4 of a mile.
On Saturday she walked 1 2/3 of a mile
On Sunday she walked 2 3/5 of a mile.
How many miles did she walk in total?
3/4 = 45/60
1 2/3 = 1 40/60
2 3/5 = 2 36/60
Add.
To find the total distance Naomi walked, we need to add up the distances she walked on each day.
On Friday, Naomi walked 3/4 of a mile.
On Saturday, she walked 1 2/3 of a mile.
On Sunday, she walked 2 3/5 of a mile.
First, let's convert the mixed fraction 1 2/3 into an improper fraction. To do this, multiply the whole number (1) by the denominator (3) and then add the numerator (2). This gives us (1 * 3 + 2 = 5), so 1 2/3 is equivalent to 5/3.
Now we can add up the distances:
3/4 + 5/3 + 2 3/5
To add the fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 4, 3, and 5 is 60. So let's rewrite the fractions with a denominator of 60:
3/4 = (3 * 15) / (4 * 15) = 45/60
5/3 = (5 * 20) / (3 * 20) = 100/60
2 3/5 = (2 * 5 * 12) / (5 * 12) + (3 * 12) / 5 = 120/60 + 36/60 = 156/60
Now we can add the fractions:
45/60 + 100/60 + 156/60
Adding the numerators:
(45 + 100 + 156) / 60 = 301/60
The fraction 301/60 is an improper fraction. We can simplify it by dividing the numerator (301) by the denominator (60):
301 ÷ 60 = 5 remainder 1
So the total distance Naomi walked is 5 1/60 of a mile.
Note: It is often helpful to convert mixed fractions to improper fractions before adding or subtracting them, as it makes the calculations easier and ensures accurate results.