Video Transcript
I take a number and divide it by
three and then divide by six. The result is two. What is the number?
We can solve this problem in lots
of ways. We will look at setting up a linear
equation and also using function machines. We will begin by letting π be the
number. Our first step is to divide this
number by three. We usually write this when dealing
with algebra as π over three. We then need to divide this answer
by six. This is the same as multiplying by
one-sixth as dividing by number is the same as multiplying by the reciprocal of that
number. Multiplying the numerators and the
denominators gives us π over 18 or π divided by 18. Dividing a number by three and then
by six is the same as dividing the number by 18.
Weβre told in the question that the
result or answer is two. Therefore, π divided by 18 equals
two. We can solve this equation for π
by multiplying both sides of the equation by 18. This is because the reciprocal of
dividing by 18 is multiplying by 18. And we must perform the same
operation to both sides. On the left-hand side, the
eighteens cancel, leaving us with π. Two multiplied by 18 is equal to
36. The number that we started with is
therefore 36. We can check this answer by firstly
dividing 36 by three. This gives us 12. Dividing 12 by six gives us
two. This means that our answer of 36
was correct.
As mentioned at the start, an
alternative method here would be to use function machines. We are beginning with an input of
π, dividing by three, and then dividing by six and getting an output of two. The reciprocal or inverse of
dividing by six is multiplying by six. Dividing by three has an inverse of
multiplying by three. If we know that the output is two,
we can calculate the input by firstly multiplying by six and then multiplying by
three. Two multiplied by six is equal to
12. 12 multiplied by three is equal to
36. This confirms that our input number
π was equal to 36.
