Multiplying Fractions Word Problems (ex 1) - Fraction, Arithmetic, Mathematics Video Lecture - Engineering Mathematics | Best Video for Engineering Mathematics

before leaving on a road trip Tiffani
filled up her gas tank which holds 16
gallons of gas after four hours tiffany
noticed that the gas tank was 7/8 full
let me do that in a different color was
7/8 full how many gallons of gas were
left in the tank and actually doesn't in
any way matter on how many how long she
had to drive so you this is actually
just extra information that you can
ignore for the sake of this problem so
7/8 full another way of reading that is
7/8 if we wanted to put units here
that's 7/8 is number of gallons left
number of gallons left per total number
of gallons per total number of gallons
so this is saying if you take number of
gallons left divided by total number of
gallons it's essentially 7/8 it doesn't
mean that there are 7 gallons left and
there were 8 total gallons it just means
that the ratio between the number of
gallons left and the total is 7/8 and if
we multiply that times 16 total gallons
times 16 total total gallons you see
that the total gallons cancel out with
the total gallons and the only units
your left is number of gallons left and
you're essentially just multiplying 7
eighths multiplying 7 eighths times 16
so this becomes 7 over 8 times 16 and
you could even view that as 16 over 1
and this is the number of gallons left
so these are the only units we have left
number of gallons and so we can multiply
it out or we can simplify it ahead of
time we could say this is 7 times 16
over 8 times 1 but both the numerator
and the denominator is divisible by 8 so
let's divide this by 8 so let's divide
by 8 and let's divide by 8 this 8 and
this 8 will cancel out 16 divided by 8
is 2 so we get 7 times 2 is 14 over 1
which is the same thing as 14 gallons
left so we're done how many gallons were
left in the tank
14 is essentially just 7 eighths the
fraction that's full times the total
number of gallons that the tank can hold