Amp up Your Mental Multiplication Skills
mental math series, part 4
How often have you caught yourself in public, perhaps even at work, needing to make a multiplication calculation that is just out of reach?
You scramble for your phone or computer to help you. What if you could with confidence and ease perform that calculation mentally? How useful and impressive would that be!
Well that’s what this mental math series is all about! Gaining confidence and understanding through numeracy.
To begin there are very few memorizations I find necessary. Multiplication facts are one of those few. If you don’t already have them in your active memory, read the next section and get memorizing!
If you have them memorized, congrats!
You’re one step ahead of the game. Feel free to skip the basics section and move on to the mental multiplication tricks below it.
Necessary Basics
Multiplication is short-hand for repeated addition. Suppose I add together seven sets of two.
What I’m really saying is that I want to know what the total of seven times 2 is, or seven copies of two.
With a small change in perspective, we could look at the above picture as a different repeated addition: 7 + 7.
Here we’re asking what is the total of 2 copies of 7 , or two times seven. Therefore, these two multiplications are equivalent.
This is the commutative property of multiplication.
Note: the commutative property does not hold for subtraction or division. The following are not equal.
Notice that any number multiplied by zero results in zero, this is an important rule called the zero-product property.
Classic Times Table
Yeah, I know that looks overwhelming. But on the bright side because of the commutative property, half of the table are repeats.
There are a few patterns in the table that will make memorization easier. The first row of the table is trivial because whenever we multiply by 1 the result is the number itself. Furthermore anything times 10 is the number itself with a zero appended to it.
Additionally, the values from 11 x 1 up to 11 x 9 follow a simple pattern.
The 5's have a nice pattern as well.
And most likely the 2's multiplication facts will come naturally to you.
Therefore, we can remove the 1's, 2's, 5's, 10's, and most of the 11's from our table, allowing us to focus on the more difficult multiplication facts.
That leaves 31 facts to learn. These ones are the trickier ones, so focus on memorizing them and you’ll be golden!
Mental Multiplication by One-Digit Numbers
Let’s begin with a technique for 2-by-1 multiplication problems.
Step one: Begin by splitting up 17 into 10 + 7.
Note: We need to use parenthesis to keep the 17 bonded together.
Step two: Multiply the 8 through the parenthesis and find the products.
The process of multiplying a number through an addition inside parenthesis is called the distributive property.
Step three: Finish the sum.
Note: This is what will happen if we forget to write 10 + 7 in parenthesis!!
Which is results in the wrong answer. Don’t let this happen to you!
Example 2
Step 1: Break apart 33.
Step 2: Distribute the 7 through.
Step 3: Perform the multiplications and finish the addition.
Example 3
Step one: Write out the expanded form of 562.
Step two: Distribute the 8.
Step three: Perform the smaller multiplications.
In order to multiply 500 x 8 take advantage of the following rule.
Rule: When multiplying multiples of 10, simply multiply the non-zero digits together and append an equal number of zeros as in the problem to it.
Therefore,
Now multiply 60 x 8.
And lastly, 2 x 8.
Finally add them up!
That’s all for today! In the next lesson we’ll continue learning more mental multiplication tricks!
Next Lesson: Solve It In 5.18 Seconds
Thanks for reading!
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