My daughter had a math question about finding how far someone walked using multiplication of fractions.
The distance was $1 \frac 78$ and he walked $\frac 23$ of the way. The problem wanted to know how far he walked. How does multiplying fractions give you that answer?
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To help understand this we can look at fractions as just another way of writing a percentage. For your example this guy walks 2/3 of the distance. This is the same as 66.6...% (or .666...) of 1 and 7/8 miles. To get the answer we simply multiply .666 x 1 and 7/8 to get 1.25 miles.
So we can see multiplying the 'fraction' with the 'distance' is the same as multiplying the 'percentage of the distance walked (fraction)' by the 'distance'.
Hope this helps!
$1+\cfrac 78=\cfrac {15}8$. One third of this is $\cfrac 58$. Two thirds is $\cfrac {10}8=1+\cfrac 14$.
Note that this can be summarised as $\cfrac {15}8\cdot \cfrac 23=\cfrac 54=1+\cfrac 14$. That is why multiplying the factions works.