How would you go about writing a multiplication sentence for two numbers when their product is close to 10 with 3 decimal places and one number is less than 1 and the other greater than 1?

Answer 1

The first step is to give each of the numbers a letter. A simple choice is x and y.

Their product can also be given a letter, say p.

Then the multiplication sentence might be written as:

p = x × y

However, the multiplication symbol (×) looks very much like the letter x; so to avoid any confusion in algebra multiplication is not written explicitly (using the multiplication symbol above), but implicitly by writing letters together - whenever any two (or more) items in algebra are next to each other it means multiply them together, eg "xy" means "x times y", "5y" means "5 times y", "5xy" means "5 times x times y". Thus the multiplication sentence is written as:

p = xy

Now, there are further restrictions given, namely:

1. The product is about 10 with 3 decimal places
2. one number is less than 1
3. the other number is greater than 1

The first of these is not easy to state. The best I can offer is:

p ≈ 10 with 3 dp

The second and third are easy and straightforward:

Chose one of the letters (say x) for the condition that one number is less than 1, and the other letter (in this case y) for the condition that the other is greater than one; these are then written in mathematical terms:

x >1, y < 1

Which makes the whole multiplication sentence:

p = xy given x>1, y<1 and p≈10 with 3 dp