Step-by-step explanation:
"times" is always the indication for multiplication. we do things over and over again so and so many times.
like when adding the same number several times.
e.g.
3+3+3+3+3
then I added the number 3 five times.
now, I could do all the basic additions, or I could simply say 3×5.
a multiplication is simply the short form of doing the same addition multiple times.
of course, in such a simple example we could easily do both, but it really gets annoying to do e.g. 3256 × 635 as single additions ...
so, the original question was : how many times as many dimes does he have than quarters?
he has 10 dimes and 2 quarters.
so, the numbers in play are 10 and 2.
therefore, the question really is, how many times is 10 of 2 ? or nicer : how many times of 2 is 10 ?
how often, how many times do I need to add 2 to get 10 ?
so, what do I need to multiply with 2 to get 10 ?
I am sure, you see the answer already.
formally in math we try to express such "riddles" as equations with the unknown and to be determined element as a generic variable named most of the time by a single letter like "x".
so, or problem here looks like
2*x = 10
"x" is what I have to multiply 2 with to get 10.
what value is that "x" ?
well, the beauty of such an equation is - we simplify it by performing the same operation on both sides of the "=" sign without changing its meaning.
so, we can divide both sides by 2 and get
x = 10/2 = 5
and that is our solution and answer.
he has 5 times as many dimes as he has dollars.
