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Archive for the ‘Multiplication Tricks’ Category

Multiplication Trick — Multiplying by 5


Time for a math trick …

Q:  How do you multiply an even number by 5 in lightning speed?

A:  Divide the number by 2, then tack on a “0.”

Example:   5 x 24

Divide 24 by 2 to get 12.

Tack a “0” onto 12 to get 120. Presto, nothing up your sleeve. It’s that easy.

Why does it work? Hint: Think about how we multiply by 10. Then think about how multiplying by 5 compares to multiplying by 10.

Rotated version of File:Symbol support2 vote.svg.

Image via Wikipedia


Try these for fun (answers at bottom of post):

a)  5  x  16

b)  5  x  8

c)  5  x  28

d)  5  x  64

e)  5  x  142

f)  5  x  2,468

g)  5  x  6,042

h)  5  x  86,432

j)  5  x  888,888


Answers:

a)  5  x  16 = 80

b)  5  x  8 = 40

c)  5  x  28 = 140

d)  5  x  64 = 320

e)  5  x  142 = 710

f)  5  x  2,468 = 12,340

g)  5  x  6,042 = 30,210

h)  5  x  86,432 = 432,160

j)  5 x 888,888 = 4,444,440

k)  5  x  2,486,248 = 12,431,240

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Times Tables, Learning the Threes


What’s more important for early math than knowing the times tables?

Not much, right?

Since the times table facts are so fundamental, and because many students struggle with them, I’d like to share a strategy I came up with today for
learning the 3s. This technique works particularly well with students
who struggle with memorizing apparently random facts. (We know these
facts are not random, but if learned with nothing more than flash cards,
they can appear random.)

The strategy involves three stages, each stage bringing the child closer
to being able to QUICKLY access the desired multiplication facts. Here are the stages, in order they should be taught.

STAGE ONE:  “Patty-Cake Threes”

What I do here amounts to a “patty-cake” approach to learning the threes, which works like this.

The student and I sit facing each other with our hands up. We hit our right hands together and say “one,” then hit our left hands together and say “two.” Then we
hit BOTH HANDS TOGETHER and say, “THREE.” When saying the “one” and “two,” we utter the numbers quietly. But when we say “THREE” and all successive multiples of three, we say these numbers loudly, almost (but
not quite) shouting.

After three, we continue:  “four, five, SIX … seven, eight, NINE, ten,
eleven, TWELVE … ” and so on. So this gives children a fun way to
hear — and get a feel in their body for — the multiples of three, in the proper
order.

Patty Cake

Image by davie_the_amazing via Flickr

STAGE TWO:  “Finger-Drumming”.

After the child has the rhythm of the number three, from the “patty-cake” approach, we do “finger-drumming.” To “finger-drum” the multiples of 3, the child makes a fist with one hand, and shakes it, saying with each shake, “one, two, THREE!” And when saying “THREE,” the child extends one finger from the fist. The child continues: “four, five, SIX,” and at “SIX,” he extends another finger, so he has two fingers out.

Then you ask the child, for example, “What is three times two?” Answer: the number he just said, “six.”

In this way, the child can “finger-drum” out all of the multiples of three. To
reinforce the times tables as you go, ask questions like:  “What is 3 x 4? What is
3 x 5? etc.” Each time you ask, the child must “finger-drum” till s/he gets the
correct answer. This flows very nicely from the “patty-cake” approach as it
builds on the rhythmic feel for counting in threes.

STAGE THREE:   “Finger-Skip-Counting”   The third stage follows “finger-
drumming.” To begin finger-skip-counting, the child must have done enough “finger-drumming” so s/he is quite familiar with the multiples in the correct order.

To “finger-skip-count,” 3 x 4, for example, the child holds out a fist and
runs through the multiples of 3, like this:  “Three (extending one finger), Six (extending two fingers), Nine (extending three), Twelve (extending four fingers).”  You ask, “So what is 3 x 4?” And the child answers:  “3 x 4 equals 12.”

I found it helpful to first just challenge the child with the multiples from 3 x 1 through 3 x 5. Once s/he develops competence there, proceed to “finger-skip-counting” the multiples from 3 x 6 through 3 x 10. Finally do 3 x 11 and 3 x 12.

Put all together, these three stages offer a fun and rhythmic way for children
to learn their multiples of three. I’m curious to find out if I can use a similar
approach for the 4s, and I’ll find out soon.

I can’t be sure, but it seems like children could probably learn their 4s
by jumping rope, or doing other activities with a rhythmic nature.

If any of you have used an approach like this one for learning the times
tables, feel free to share it.

Multiplication Trick: x 25


This is a simple trick that anyone can easily learn. It is just a trick for
multiplying a number by 25.

If someone asked you what 25 times 36 equals, you’d probably be tempted
to reach for a calculator and start punching buttons. But remarkably, you’d
probably be able to work it out even faster in your head.

Since 25 is one-fourth of 100, multiplying by 25 is the same thing as
multiplying by 100 and dividing by 4. Or, even more simply:
first divide by 4,
then add two zeros.

Here’s the example:

Problem: 36 x 25
First divide 36 by 4 to get 9.
Then add two zeros to get: 900.
That, amazingly enough, is the answer.

Another example: 88 x 25
First divide 88 by 4 to get 22.
Then add two zeros to get: 2,200.

Now try these problems in your head:

a) 25 x 12
b) 25 x 28
c) 25 x 48
d) 25 x 60
e) 25 x 84
f) 25 x 96

Here are the answers:
a) 300
b) 700
c) 1,200
d) 1,500
e) 2,100
f) 2,400

But, you say, what if the number you start with is not divisible by 4.
No problem. Just use this fact:
if the remainder is 1, that is the same as 1/4 or .25
if the remainder is 2, that is the same as 2/4 or .50
if the remainder is 3, that is the same as 3/4 or .75

So take a problem like this: 25 x 17
dividing 17 by 4, you get 4 remainder 1.
But that is the same as 4.25
Now just move the decimal right two places (same as multiplying by 100)
Answer is: 425

Another example: 25 x 18
dividing 18 by 4, you get 4 remainder 2.
But that is the same as 4.50
Now move the decimal right two places.
Answer: 450

Another example: 25 x 19
dividing 19 by 4, you get 4 remainder 3.
But that is the same as 4.75
Now move the decimal two places to the right.
Answer is: 475

Now try these in your head:
A) 25 x 21
B) 25 x 26
C) 25 x 35
D) 25 x 42
E) 25 x 63
F) 25 x 81

And here are the answers:

A) 525
B) 650
C) 875
D) 1,050
E) 1,575
F) 2,025

Multiplication Trick #5 — How to Multiply Two-Digit Numbers by 11


This is the fifth in my series on multiplication tricks. I suggest that you make mental math “tricks” a steady part of your math instruction. Benefits students will reap include:

—  delight with the tricks themselves

—  enhanced confidence in working with numbers

—  students who otherwise don’t like math — or don’t like it much — often find the tricks irresistibly fun and interesting

TRICK #5:

WHAT THE TRICK LETS YOU DO: Multiply two-digit numbers by 11.

HOW YOU DO IT:  To multiply a two-digit number by 11, first realize that the answer will have three digits. The first (left-most) digit of the answer is the first digit of the number; the last (right-most) digit of the answer is the last digit of the number; and the middle digit is the sum of the first and last digits.

But those are just words … here’s a living, breathing example …

Example:  11 x 25

 

Look at 25. The first digit is 2; the last digit is 5.

First digit of answer is 2, so thus far we know the answer looks like:  2 _ _

Last digit of answer is 5, so now we know the answer looks like:  2 _ 5

Middle digit is 7, since 2 + 5 = 7.

The answer is the three-digit number:  2 7 5, more casually known as 275.

It’s that easy!

ANOTHER EXAMPLE:  11 x  63

First digit of answer is 6, so thus far we know the answer looks like:  6 _ _

Last digit of answer is 3, so now we know the answer looks like:  6 _ 3

Middle digit is 9, since 6 + 3 = 9.

The answer is the three-digit number: 6 9 3, or just 693.

Try these for practice:

11 x 24

11 x 31

11 x 52

11 x 27

11 x 34

11 x 26

11 x 62

 Answers:

11 x 24 = 264

11 x 31 = 341

11 x 52 = 572

11 x 27 = 297

11 x 34 = 374

11 x 26 = 286

11 x 62 = 682

NOTE:  If you’re clever (and we’re sure that you are), you have probably realized that this trick, as described, works only when the digits add up to 9 or less. So what do you do when the digits add up to 10 or more? Some of you may figure this out on your own. For those who need a little help, the answer to this will be included in an upcoming blog post.

Josh Rappaport is the author of five books on math, including the Parents Choice-award winning Algebra Survival Guide. If you like how Josh explains these problems, you’ll certainly  like the Algebra Survival Guide and companion Workbook, both of which are available on Amazon.com  Just click the links in the sidebar for more information! 

Multiplication Trick #2 — How to Multiply by 15 FAST!


Here’s the second in my set of multiplication tricks. (The first was a trick or multiplying by 5.)

TRICK #2:

WHAT THE TRICK LETS YOU DO: Multiply numbers by 15 — FAST!

HOW YOU DO IT: When multiplying a number by 15, simply multiply the number by 10, then add half.

EXAMPLE:15 x 6

6 x 10 = 60

Half of 60 is 30.

60 + 30 = 90

That’s the answer:15 x 6 = 90.

ANOTHER EXAMPLE:15 x 24

24 x 10 = 240

Half of 240 is 120.

240 + 120 = 360

That’s the answer:15 x 24 = 360.

EXAMPLE WITH AN ODD NUMBER:15 x 9

9 x 10 = 90

Half of 90 is 45.

90 + 45 = 135

That’s the answer:15 x 9 = 135.

EXAMPLE WITH A LARGER ODD NUMBER:23 x 15

23 x 10 = 230

Half of 230 is 115.

230 + 115= 345

That’s the answer:15 x 23 = 345.

PRACTICE Set:(Answers below)

15 x 4

15 x 5

15 x 8

15 x 12

15 x 17

15 x 20

15 x 28

ANSWERS Set:

15 x 4=60

15 x 5=75

15 x 8=120

15 x 12=180

15 x 17=255

15 x 20=300

15 x 28=420

 

Josh Rappaport is the author of five books on math, including the Parents Choice-award winning Algebra Survival Guide. If you like how Josh explains these problems, you’ll certainly  like the Algebra Survival Guide and companion Workbook, both of which are available on Amazon.com  Just click the links in the sidebar for more information! 
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Multiplication Trick #4: Multiplying Teen Numbers


Ever wondered if there’s a quick way to multiply two number in the teens, problems like: 14 x 17, or 18 x 16?

Well, there is. And if you just stick around for two minutes, you’ll learn the trick. Let’s start wih 18 x 16.

First, add up the two digits in the one’s place. Here that’s the 8 and the 6. 8 + 6 = 14.

Next take that sum (14) and add 10 to it. 14 + 10 = 24.

Then tack a zero on at the end. 24 becomes 240.

Finally multiply the two numbers in the one’s place, and add the sum to the 240.

8 x 6 = 48, and 240 + 48 = 288.

That’s your answer. This may seem tricky at first, but it gets pretty easy if you try it a few times. Trust me …

O.K., don’t trust me. But just try it one more time, with 14 x 17, and see for yourself.

4 + 7 = 11. 11 + 10 = 21.

21 becomes 210.

4 x 7 = 28, and 210 + 28 = 238.

That’s all there is to it.

Now try these:

a) 13 x 16
b) 12 x 17
c) 14 x 19
d) 12 x 19
e) 13 x 14
f) 17 x 18
g) 19 x 17
h) 15 x 19
j) 16 x 17
k) 18 x 19

Answers:

a) 13 x 16 = 208
b) 12 x 17 = 204
c) 14 x 19 = 266
d) 12 x 19 = 228
e) 13 x 14 = 182
f) 17 x 18 = 306
g) 19 x 17 = 323
h) 15 x 19 = 285
j) 16 x 17 = 272
k) 18 x 19 = 342