Answer:
[tex]\frac{8}{15}[/tex] of a mile
Step-by-step explanation:
To find a segment of a fraction, you must first find the LCM of each value's denominator:
LCM - Lowest Common Multiple
The lowest common multiple is the number that shows up first in each number's multiple set.
Example: LCM of 4 and 6
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 6: 6, 12, 18, 24, 30
Because 12 is the first number to show up in each multiple set, 12 is the LCM.
So, to be able to solve this problem easy, do the same with 5 and 3:
5, 10, 15, 20, 25
3, 6, 9, 12, 15
Since 15 is the first number in both sets, 15 is the LCM.
The next step is to multiply [tex]\frac{4}{5}[/tex] by [tex]\frac{x}{x}[/tex], x being the value that can be multiplied with the denominator to equal 15:
[tex]\frac{4}{5}[/tex] × [tex]\frac{3}{3}[/tex] = [tex]\frac{12}{15}[/tex]
To find how much [tex]\frac{2}{3}[/tex] of [tex]\frac{12}{15}[/tex] is, multiply the fractions together:
[tex]\frac{12}{15}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{24}{45}[/tex]
Simplify the fraction by dividing the numerator and denominator by 3.
[tex]\frac{24}{45}[/tex] ÷ [tex]\frac{3}{3}[/tex] = [tex]\frac{8}{15}[/tex]
Because the fraction can't be simplified any further, Aimee has walked a total of [tex]\frac{8}{15}[/tex] of a mile.
