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Math Tricks &Helpful Hints
By: Mrs. Azar's 2014-2015 PEG 5th Grade Class
Ayush N., Olivia H., Renee M., Jenica L., Anbar S.
Welcome to our Helpful Hints and Tricks book!
The 2014-2015 Gifted and Talented PEG fifth graders decided to create a kid
friendly math book to help students with multiplying, adding, subtracting, squaring
numbers and more!
After the helpful hints, you will see 5 fun and exciting math tricks for all ages! Try
them out yourself and then stump your friends.
Table of Contents
Page Level Title Created By
2 1 Multiplying a 2 Digit Number
by a 1 Digit Number Jenica L.
3 1 Subtracting Three Digit Numbers Renée M. 4 1 Multiplying By 11 (part 1) Olivia H.
5 2 Multiplying By 11 (part 2) Olivia H.
6 2 Square Any Number Ayush N.
7 2 Squaring Double Digit
Numbers that End in 5 Anbar S.
8 3
Multiplying Double Digit Numbers
Where the Tens Digit
and the Ones Digit Add Up to 10
Anbar S.
9 3 The Sum Checker Jenica L.
10 3 The Criss –Cross Method Ayush N.
11 Trick #1 Psychic Math Anbar S.
12 Trick #2 It’s Always 18! Olivia H.
13 Trick #3 Back to the Beginning Jenica L.
14 Trick #4 Find Their Age Renée M.
15 Trick #5 15 Again Renée M.
1
Have you ever wondered how to easily multiply a two
digit number by a one digit number? Wonder no more!
The solution is here!
1.Take the one digit of both of your numbers.
Multiply them. This shouldn’t be hard because both of
those number are only one digit.
1 x =24
2. Take the tens digit number from the two digit
number and multiply it by the one digit number. Add a
zero after your answer.
3. Add your two answers together, and that’s the
answer to the problem!
Ex: If you wanted to
solve 16x4,you would
do 16x4, or using
only ones digits,
6x4, which equals 24.
6 4
Ex: In 16x4, the ten digit is
1, and the one digit number
is 4. Therefore, we do 1x4
and add a 0.
Ex: The first answer was 24, and the
second answer was 40. 24+40=64. This
means that the answer to 16x4=64!
?(10x6)+(4x6)?
17
x9
__
153
Helpful Hint Level 1 By: Jenica L.
2
I have a math trick to help you subtract pairs of 3-
digit numbers!
Step 1- Put the smaller number into extended
notation. Example: 314 = 300 + 10 + 4
Step 2- Take your larger number and subtract the
hundred(s) you found in step 1.
Step 3- Take the answer from step 2 and subtract the
ten(s) you found in step 1.
Step 4- Take the answer from step 3 and subtract the
one(s) you found in step 1.
Example 1:
The numbers that I'll be subtracting are 734 and 314.
314=300+10+4
734-300=434 434-10=424 424-4=420!
Example 2: The numbers that I'll be subtracting are
645 and 368. 368=300+60+8, 645-300=345, 345-60=285,
285-8=277!
3
7_2 → 792 72 × 11 = 792
4
5
Square Any Number
Squaring a number is to multiply a number by itself. It may be easy for one
digit numbers, or numbers ending with zero, but it may take a piece of
paper and a pencil to square 19. I am here to teach you to do it mentally!
Let’s start with something simple. Say 192
. Now, estimate 19
to the nearest ten; 20. How did we get to 20? Well, we added
1 to 19. So 19 + 1 = 20. Now let’s subtract 1 from 19. 19 – 1 =
18. Now we multiply 20 with 18. 20 X 18 = 360. Now since we
added and subtracted 1, we will add 12
to 360. 12
+ 360 = 1 +
360 = 361. Therefore 192
= 361.
Now let’s try 23….
Rounding to the nearest ten would
give us 20. Since we subtracted 3,
we must add 3 to 23, which gives us
26. Now we multiply 20 x 26…
20 X 26 = 520.
Since we added and subtracted 3,
we will add 32
to 520. 520 + 32
= 520
+ 9 = 529. Therefore 232
= 529.
6
Today I will be explaining how to square any double-
digit number that ends with the number 5. There are
two easy steps that you have to follow to achieve this
mathematic feat of excellence! Get ready TO AMAZE
YOUR FAMILY, FRIENDS, AND TEACHERS WITH THIS
HELPFUL HINT. If you practice these types of hints
and tricks often, your teacher might even ask you to
teach the class these tricks!
Here’s Step One: Here is Step Two:
Put 25 as the last two digits Multiply the tens digit
of your answer. number by the next
consecutive number and
put THAT before the “25” as
the first two digits of the
answer.
Example: 35
3 X 4 X 35 25
12 25
NOW WASN’T THAT EASY!!!!!
7
The title says it all. You will be learning how to multiply
double-digit numbers where the tens digit are the same
and the ones digits add up to 10. Some pairs of single-
digit numbers that add up to 10 are 1 and 9, 2 and 8, 3
and 7, 4 and 6, and 5 and 5. Get ready to learn a trick
that will baffle the minds of the people you know when
they see this helpful hint in action. This Helpful little
hint only has two steps you have to learn in order to do it.
Example: 37
3 X 4 X 33 7 X 3
12 21
SEE!!! IT IS THAT EASY!!!
8
17777777777
Ex: Lets say the answer you originally
wanted to check is 3,989. You would do
3+9+8+9=29,2+9=11,1+1=2.
Ex: If you did 3,435+554 and got
3,989, you would do 3+9+8+9= 29,
2+9=11, then 1+1=2.
Have you ever finished an addition problem and wanted to
see if it was right without asking your teacher?
Your savior has come!
1. Take the first addend (number that you are
adding) and add the digits in that number together. Keep
adding the sum of the digits together again and again
until you get just one digit.
2. Do the same thing with the other addend; just
keep adding until you get to one digit for each number.
3. Do the same for the original answer that you got
and would like to check.
4. Take all the one digit numbers that you got from
the addends, and add them up until you get another one
digit number.
If that number is the same number as the one that
you got from the sum, then your answer is correct!
Ex: If you had the number 3,435,
you would do 3+4+3+5, which equals
15. To get one digit, you would
need to do 1+5, which equals 6.
Ex: From 3,435, you got 6, and from 554, you got 5.
Because of this, you do 5+6=11, then 1+1=2. The number
that you got from your original answer was also 2. This
means that you answer of 3,989 is correct!
Ex: If you were doing 3,435 + 554,
you would do next 5+5+4=14. 1+4=5.
?
?
?
?
?
?
Helpful Hint Level 3 By: Jenica Liang
9
The Criss-Cross Method
Sometimes multiplying two digit by two digit numbers can be a hassle,
especially without a calculator. Even though this trick is complicated to master
mentally, it is quite easy on paper.
To solve 23 X 46, write out the numbers as shown below.
Step 1: You will multiply the two right hand side numbers (3 X 6 = 18).
The last digit of the product (or the only digit) will be the ones
digit of your answer (8). The tens digit of the product (1) will be
used in the next step.
Step 2: The top left number times the bottom right number plus the
top right number times the bottom left number plus the tens
digit number from the previous step (2 x 6) + (3 x 4) + 1 = 25.
The last digit of the product will be the tens digit of your
answer (5).
Step 3: Now multiply the top left number with the bottom left number
(2 x 4 = 8) and add the tens digit from the previous step (2).
8 + 2 = 10. The answer to this question is the first two digits of
your answer.
23 x 46 = 1058
23
X 46 ----------
2 3
4 6
10
Say to a volunteer in the audience, “think of
a number, any number.” and you Should alSo
Say, “but to make it eaSier, think of a one or
two-digit number.” after you’ve reminded
your volunteer that there is no way you
could know his/her number, ask him/her to:
1. Double the number 2. Add 12
3. Divide the total
by 2
4. And subtract the
original number
No matter what number you picked at the start,
you will always end up with 6. It’s like MAGIC!!!
11
It’s always 18, it’s always 18… I just can’t get over how
this math trick always gives me a final answer of 18!
Let me share it with you!
This trick is a bit “tricky” but I think you guys will get
it. First, choose 3 numbers between 1 and 9. Put them
in order from largest to smallest. Then, put them in
order from smallest to largest. For example, if I chose
the numbers 3, 5, and 7, I would order them like this:
Next, subtract the smaller number from the larger
number.
If you add the digits of your answer, you should get 18!
3, 5, and 7 → 753
3, 5, and 7 → 357
753
-357
396
3 + 9 + 6 = 18!
12
Ever wanted a cool to know a cool Math Trick to
impress your friends? Well, you’ll sure impress them with this
magic!
1. Pick a number between 1 and 10, then write it down.
Write down the next four numbers following that first
number.
2. Add these five numbers together and divide the
sum by 5.
3.
4. Wow! You now have your original number back!
It’s just like magic!
Ex: You picked the number 5. The next
four numbers are 6, 7, 8, and 9. You
write all of these numbers down.
Ex: Remember the numbers you wrote
down? 5, 6, 7, 8, and 9. Adding
these all together, you get a total
of 35. Divide 35 by 5, and what do
you get? 7!
Ex:7-2= 5. Does
the number 5 seem
familiar to you?
Magic!
Math Trick #3 By: Jenica L.
13
Have you ever wanted to find someone's age without directly asking them?
If you answered yes, then I have a math trick for you!
Step 1- have the person multiply the first digit of his/her age by 5
Step 2- increase (add) the product by 3
Step 3- multiply the sum by 2
Step 4- have the person increase the product by the second number of
his/her age
Step 5- subtract 6
(If you were finding the age of someone under the age of 10, their age will
be the first number of the result.)
Example 1: The age of the person is 24. 2x5=10 10+3=13 13x2=26 26+4=30
30-6=24!
Example 2: The age of the person is 7. 7x5=35 35+3=38 38x2=76 76+7=83
83-6=77!
14
I have a simple 5-step trick to make any number less than 10 turn into 15!
Step 1- multiply your number by 3
Step 2- increase the product by 45
Step 3- multiply your answer by 2
Step 4- divide the product by 6
Step 5- subtract your number from the final answer
Your answer is 15, isn't it?
Example 1: The number is 9. 9x3=27 27+45=72 72x2=144
144/6=24 24-9=15!
Example 2: The number is 5. 5x3=15 15+45=60 60x2=120
120/6=20 20-5=15!
Example 3: The number is 2. 2x3=6 6+45=51 51x2=102 102/6=17
17-2=15!
15
Do you know any tricks or tips?Add them below!
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Do you know any tricks or tips?Add them below!
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Do you know any tricks or tips?Add them below!
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Do you know any tricks or tips?Add them below!
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