Chapter 2: Solving Equations and Inequalities
Numbers in the Real World

Number Magic

Computing with numbers often uncovers interesting relationships between numbers.

To square any two-digit numeral that ends in 5, such as 15, 25, 35, etc., you can multiply the tens digit by the next highest integer and place that result in front of 25. For example, 45 squared = (4*5)25 =2025.

What is the square of 65?


The square of any number is equal to one more than the product of the consecutive integers above and below the number. For example, 8 squared = 7(9) + 1.

Compute the square of 65 using this method.

You can prove that this method works using very basic algebra. Hint: Choose the number that you are squaring as x, then represent the other numbers in terms of x. Why does this method work?


To find multiples of 9 up through 90, hold both hands in front of you. Lower the finger that represents the number you want to multiply by 9. The number of fingers to the left of the down finger is the tens digit, and the number of fingers to the right represent the units digit. This is a great way to learn to multiply by 9!

Compute the product of 6 x 9 using your fingers.

Why does this method work? Discuss this with your classmates and instructor to discover this answer.

Check Your Answers