Question

Assume x and y are 2 numbers, where xy=24
a- what values could x and y equal if they are whole numbers? Try to list as many as possible.
b- What values could x and y equal if they can be decimals, fractions or whole numbers?

Answer 1

Dugald substitutes different whole numbers into the expression 5 * (a+a). He notices that the result always ends in the digit 0. Try a few values and explain why thus pattern occurs.

Answer 2

a- Possible values for x and y as whole numbers:
1, 24
2, 12
3, 8
4, 6
6, 4
8, 3
12, 2
24, 1

b- Possible values for x and y as decimals, fractions, or whole numbers:
1, 24
2, 12
3, 8
4, 6
6, 4
8, 3
12, 2
24, 1
-1, -24
-2, -12
-3, -8
-4, -6
-6, -4
-8, -3
-12, -2
-24, -1

These are the possible values assuming the numbers can be any real numbers, including decimals, fractions, or whole numbers.

Answer 3

Let's substitute some whole numbers into the expression 5 * (a + a) and observe the results:

For a = 1:
5 * (1 + 1) = 5 * 2 = 10

For a = 2:
5 * (2 + 2) = 5 * 4 = 20

For a = 3:
5 * (3 + 3) = 5 * 6 = 30

For a = 4:
5 * (4 + 4) = 5 * 8 = 40

From these examples, we can see that regardless of the value of a, the result always ends in the digit 0. This pattern occurs because multiplying any number by 5 will always result in a multiple of 5. And when we multiply a multiple of 5 by 2 (which is what we get when we add a + a), the result will always be a multiple of 10, which ends in the digit 0.

In other words, the expression 5 * (a + a) can be simplified as 10 * a. Since a is a whole number, multiplying it by 10 will always yield a result that ends in 0.