The Math Kids: A Sequence of Events
Page 8
MENTAL MATH
Mental math is math you can do in your head. It can amaze your friends and can even make doing your homework easier. Catherine taught her friends to multiply two-digit numbers in their heads.
Here are the rules that make it work:
Both numbers must be two digits.
The first digit (the tens digit) must be the same for both numbers.
The last digit (the ones digit) of each number must add up to 10.
Let’s try this for 45 × 45. We can do this because the tens digit is 4 for both numbers and the ones digits add up to 10.
To get the first two digits of the answer, multiply the tens digit by one more than the tens digit. The tens digit is 4, so we want to multiply 4 × 5 (because 5 is one more than 4):
4 × 5 = 20
To get the last two digits of the answer, just multiply the ones digits together:
5 × 5 = 25
Put all four digits together and we get the answer of 2,025.
There is one more thing you need to know. If the two ones digits are 1 and 9, we only get 9 when we multiply them together. Since these are the last two digits of the answer, we’ll show this as 09 in our answer. For example, 31 × 39 = 1,209.
CONTEST ANSWERS
1) In a 500-page book, the page number is printed at the bottom of each page. How many times does the number 1 appear?
Hints that will help you solve this problem:
In the first 100 pages, how many pages have the number 1?
Is it the same for the next 100 pages?
Is there anything different about the pages 100–199?
Answer: 200
2) The product of two numbers is 10,000. If neither of the numbers contains a 0, what are the two numbers?
Hints that will help you solve this problem:
If we multiply two numbers and get a 0 in the ones digit, one of the two numbers must end in 5 and the other must end in 2, 4, 6, or 8 (since 2 × 5 = 10, 4 × 5 = 20, 6 × 5 = 30, and 8 × 5 = 40).
Try dividing 10,000 by different numbers ending in 5 to narrow down the choices.
Answer: 16 and 625
3) When the order of the digits of 2,552 is reversed, the number is the same. How many counting numbers between 100 and 1000 are the same when the order of their digits is reversed?
Hints that will help you solve this problem:
How many reversible numbers are there between 100 and 200?
How many reversible numbers are there between 200 and 300?
Do you see a pattern?
Answer: 90
4) In the addition problem below, each letter represents a digit. What four-digit number does DEER represent?
Hints that will help you solve this problem:
D must be equal to 1 since it is carried.
R must be equal to 9 since we know it carries over.
N must be equal to 8 since N + 1 = 9.
Answer: DEER = 1,009
The whole equation is
5) To write the numbers from 12 to 14, we will write a total of six digits (1 2 1 3 1 4). How many digits will it take to write the numbers from 1 to 150?
Hints that will help you solve this problem:
How many one-digit numbers are there?
How many two-digit numbers are there?
How many three-digit numbers are there?
Answer: 342 digits
ACKNOWLEDGMENTS
The whole team at Common Deer Press continues to amaze me with their dedication and professionalism, all while being the most supportive team on the planet. Thanks, team!
There aren’t enough accolades I can give to Kirsten Marion. The characters in these books seem to come alive under your brilliant and insightful guidance. I think you know Stephanie and the rest of the kids even better than I do.
Thanks to Heather Kohlmann, for making sure all my t’s were crossed and my i’s dotted. Your attention to detail is amazing!
Once again, Shannon O’Toole’s beautiful artwork blew me away, bringing words to life in a way only she can.
In a conversation over lunch one day, I mentioned my writing aspirations to Jeremy Rodriguez, a work colleague. He encouraged me to try to publish these books, even providing me with a primer on book publishing. The seed he planted grew into The Math Kids series. These books would be just ones and zeros on a dusty hard drive somewhere without his inspiration.
To my son Jordan, who always has a hug for me every morning—you’ll never know how much those hugs mean.
As a parent, you want your kids to be happy and successful, but also for them to treat other people well and to make the world a better place. If I’m graded for my kids someday, I feel pretty good about the A+ I am going to receive.
Finally, for my wife—who is ecstatic that I’ve found a hobby that doesn’t cost her any money—thanks for always listening, even when I’m just venting (especially when I’m just venting).
ABOUT THE AUTHOR
David Cole has been interested in math since was very young. He pursued degrees in math and computer science. He has shared this love of math at many levels, including teaching at the college level and coaching elementary math teams. He also ran a summer math camp for a number of years. He has always loved to write and penned a number of plays which have found their way on stage. David had always wanted to combine his love of math and writing, and now with The Math Kids, he has done just that! He feels that writing about math is a great way to exercise both sides of the brain at the same time.
In case you haven’t already, catch the beginning of this adventure by reading Math Kids: The Prime-Time Burglars.