David Weber, Talei Kunkel, Alexander Martinez and, Rebecca Shultis Solutions for Chapter: Algebraic Expressions and Equations Puzzles and Tricks, Exercise 11: Practice 4

Write a simplified algebraic expression using written description $:$

The product of triple a number and double a different number is added to eleven then halved.

Create a written description that would fit this algebraic expression $:$

$4x+10$.

Create a written description that would fit this algebraic expression$:$

$2\left(x-6\right)$.

Create a written description that would fit this algebraic expression $:$

$\frac{7x-8y}{3}$.

Create a written description that would fit this algebraic expression $:$

$\frac{3x\left(y+6\right)}{2}$.

Try this trick with someone whose birthday you don't know.

Ask him/her to write down the number of the month in which he/she was born. For effect, turn your back to the person and have them complete the following instructions as you say them.

Take the birthday month, double it and then add $5$. Multiply the result by $50$. To this number, have the person add his/her current age. From this most recent number, ask him/her to subtract $365$.

At this point, turn around and ask the person to tell you the final number he/she got. Now, in your head, add $115$ to the result you just head. The first digit of your result is the person's birth month and the remaining digits represents the person's current age$!$

Justify why this using algebra.

There are people who consider sum shortcuts in mathematics to be 'tricks'. For example, here are divisibility rules that make it very easy to figure out if a number is divisible by $2, 5$ or $9$. Why do this work$?$

Show that the number represented by $ABC$ is equal to $99A+9B+A+B+C$. Hence, describe why the divisibility rule for $3$ and $9$ works.

Have someone pick two numbers and write them one on top of the other $($in a column$)$. Have them find the next number in the list by finding the sum of the two numbers above it. Have him/her write it down and repeat the process until there are ten numbers it the list.

Tell the person you can ad those  $10$ numbers faster than everyone, including anyone with a calculator. Have them try to find the sum before you do, using mental math or a calculator.

$($ All you have to do is just multiply the $7\mathrm{th}$ item by $11!)$

For an easy way to multiply any number by $11$, visit the site themathword.com and search for 'math trick'.