Video: Finding a Number given the Result of Dividing It by Another Number

I take a number and divide it by 3, and then divide by 6. The result is 2. What is the number?

02:57

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 𝑛 be the number. Our first step is to divide this number by three. We usually write this when dealing with algebra as 𝑛 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 𝑛 over 18 or 𝑛 divided by 18. Dividing a number by three and then by six is the same as dividing the number by 18.

We’re told in the question that the result or answer is two. Therefore, 𝑛 divided by 18 equals two. We can solve this equation for 𝑛 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 𝑛. 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 𝑛, 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 𝑛 was equal to 36.

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