1. ## Can someone explain this to a 6th Grader?

Someone in grade 6 came to me with this math question. Its very simple to find the answer, but I am having a hard time explaining it using 6th Grade math material.

Question: Two numbers have a product of 676. The same two numbers have a quotient of 4. What are the two numbers.

Using Algebra I know xy = 676 and x / y = 4 -> x = 4y -> 4y*y = 676 -> y = 13. Therefor x = 52.

The Grade 6'er in question tells me they do not use letters in math, thus I am finding it difficult to explain how to find the answer without using "letters".

djino
"Your help would be appreciated! Thanks!"

2. maybe you could list the possible factor pairs?

Ah ... or, you could say that since the quotient is 4, it means that one of the numbers is 4 times the other ... so what you actually have is 4 times a number times the same number ... so, you divide 676 by 4 to get 169, and so 13 would be that same number multiplied to itself (so the other number would be 13 times 4) ... essentially, reduce it to one variable and "explain" it that way ... but if you're asking how to solve it, on paper, without using letters ... that's kinda tough ... use stars? haha (Or a question mark, maybe that will make more sense to him/her)

I'm not sure what grade 6 covers, I looked it up, this might be an introductory problem to using variables .... so maybe you just need to explain what the letter represent

3. Hello, djino!

Two numbers have a product of 676.
The same two numbers have a quotient of 4.
What are the two numbers.

I think Bingk's first suggestion is appropriate.

Find the pairs of numbers with a product of 676.

Divide 676 successively by 1, 2, 3, 4, . . .
. . Keep the ones that divide evenly,
. . then examine their quotients.

. . . . $\begin{array}{cc}\text{Factors} & \text{Quotient} \\ \hline

1 \times 676 & 676 \\ 2 \times 338 & 169\\ 4\times 169 & \frac{1690}{4}\\ {\color{red}13 \times 52} & {\color{red}4} \\ 26 \times 26 & 1 \end{array}$

4. THANK YOU SO MUCH GUYS, I'll use your examples!!

djino